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

Error

Bits error versus alphax

Bits error versus u

Try it out

Your Program's Arguments

Results

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
  4. Applied add-exp-log0.0

    \[\leadsto \color{blue}{e^{\log \left(\frac{1}{\sqrt{1 - \left(\mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right) \cdot \mathsf{fmin}\left(\mathsf{fmax}\left(alphax, 0\right), 2\right)\right) \cdot \log \left(1 - \mathsf{fmin}\left(\mathsf{fmax}\left(u, 0\right), 0.9999999\right)\right)}}\right)}}\]
  5. Using strategy rm
  6. Applied add-sqr-sqrt0.0

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