Efficient tanh approximation
Efficient tanh algorithm using an approximation of the Hyperbolic function:
Speed Improvement of the Back-Propagation on Current Generation
Workstations" D. Anguita, G. Parodi and R. Zunino. Proceedings of the World
Congress on Neural Networking, 1993.
Error of the approximation
The approximation of tanh is not precise, but much faster:
| x | math.tanh | anguita.tanh | delta |
|---|---|---|---|
| -0.9 | -0.716297870199 | -0.689095742562 | -0.0272021276373 |
| -0.8 | -0.664036770268 | -0.633359378142 | -0.0306773921261 |
| -0.7 | -0.604367777117 | -0.572415613722 | -0.0319521633955 |
| -0.6 | -0.537049566998 | -0.506264449302 | -0.0307851176963 |
| -0.5 | -0.46211715726 | -0.434905884882 | -0.0272112723783 |
| -0.4 | -0.379948962255 | -0.358339920462 | -0.0216090417935 |
| -0.3 | -0.291312612452 | -0.276566556042 | -0.0147460564099 |
| -0.2 | -0.197375320225 | -0.189585791622 | -0.0077895286032 |
| -0.1 | -0.099667994625 | -0.0973976272017 | -0.00227036742325 |
| 0.1 | 0.099667994625 | 0.0973976272017 | 0.00227036742325 |
| 0.2 | 0.197375320225 | 0.189585791622 | 0.0077895286032 |
| 0.3 | 0.291312612452 | 0.276566556042 | 0.0147460564099 |
| 0.4 | 0.379948962255 | 0.358339920462 | 0.0216090417935 |
| 0.5 | 0.46211715726 | 0.434905884882 | 0.0272112723783 |
| 0.6 | 0.537049566998 | 0.506264449302 | 0.0307851176963 |
| 0.7 | 0.604367777117 | 0.572415613722 | 0.0319521633955 |
| 0.8 | 0.664036770268 | 0.633359378142 | 0.0306773921261 |
| 0.9 | 0.716297870199 | 0.689095742562 | 0.0272021276373 |