Average Error: 0.6 → 0.6
Time: 49.0s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(\sqrt{5} \cdot v\right) \cdot \left(\sqrt{5} \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\right)}}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(\sqrt{5} \cdot v\right) \cdot \left(\sqrt{5} \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\right)}}
double f(double v) {
        double r1712331 = 1.0;
        double r1712332 = 5.0;
        double r1712333 = v;
        double r1712334 = r1712333 * r1712333;
        double r1712335 = r1712332 * r1712334;
        double r1712336 = r1712331 - r1712335;
        double r1712337 = r1712334 - r1712331;
        double r1712338 = r1712336 / r1712337;
        double r1712339 = acos(r1712338);
        return r1712339;
}
↓
double f(double v) {
        double r1712340 = 1.0;
        double r1712341 = 5.0;
        double r1712342 = sqrt(r1712341);
        double r1712343 = v;
        double r1712344 = r1712342 * r1712343;
        double r1712345 = r1712344 * r1712344;
        double r1712346 = r1712340 - r1712345;
        double r1712347 = r1712343 * r1712343;
        double r1712348 = r1712347 - r1712340;
        double r1712349 = r1712346 / r1712348;
        double r1712350 = acos(r1712349);
        double r1712351 = log(r1712350);
        double r1712352 = sqrt(r1712351);
        double r1712353 = r1712347 * r1712341;
        double r1712354 = r1712340 - r1712353;
        double r1712355 = r1712354 / r1712348;
        double r1712356 = acos(r1712355);
        double r1712357 = log(r1712356);
        double r1712358 = sqrt(r1712357);
        double r1712359 = r1712352 * r1712358;
        double r1712360 = exp(r1712359);
        return r1712360;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied add-exp-log0.6

    \[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.6

    \[\leadsto e^{\color{blue}{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.6

    \[\leadsto e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \color{blue}{\left(\sqrt{5} \cdot \sqrt{5}\right)} \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}}\]

  8. Applied unswap-sqr0.6

    \[\leadsto e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \color{blue}{\left(\sqrt{5} \cdot v\right) \cdot \left(\sqrt{5} \cdot v\right)}}{v \cdot v - 1}\right)\right)}}\]

  9. Final simplification0.6

    \[\leadsto e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(\sqrt{5} \cdot v\right) \cdot \left(\sqrt{5} \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\right)}}\]

Reproduce

herbie shell --seed 2019151 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))