Average Error: 0.1 → 0.0
Time: 19.2s
Precision: 64
Internal Precision: 320
$\frac{1}{\sqrt{1 + \left(\left(-\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}$
$e^{\log \left(\frac{\frac{1}{\sqrt{\sqrt{1 - \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right) \cdot \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right)}}}}{\sqrt{\sqrt{1 - \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right) \cdot \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right)}}}\right)}$

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Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 0.1

$\frac{1}{\sqrt{1 + \left(\left(-\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}$
2. Initial simplification0.1

$\leadsto \frac{1}{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}$
3. Using strategy rm

$\leadsto \color{blue}{e^{\log \left(\frac{1}{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}\right)}}$
5. Using strategy rm

$\leadsto e^{\log \left(\frac{1}{\color{blue}{\sqrt{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}} \cdot \sqrt{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}}}\right)}$
7. Applied associate-/r*0.0

$\leadsto e^{\log \color{blue}{\left(\frac{\frac{1}{\sqrt{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}}}{\sqrt{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}}\right)}}$
8. Final simplification0.0

$\leadsto e^{\log \left(\frac{\frac{1}{\sqrt{\sqrt{1 - \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right) \cdot \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right)}}}}{\sqrt{\sqrt{1 - \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right) \cdot \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right)}}}\right)}$

Runtime

Time bar (total: 19.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (alphax u)
:name "1 / sqrt(1 + -fmin(fmax(alphax, 0), 2) * fmin(fmax(alphax, 0), 2) * log(1 - fmin(fmax(u, 0), .9999999)))"
(/ 1 (sqrt (+ 1 (* (* (- (fmin (fmax alphax 0) 2)) (fmin (fmax alphax 0) 2)) (log (- 1 (fmin (fmax u 0) 0.9999999))))))))