Average Error: 0.5 → 0.5
Time: 47.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \sqrt[3]{\left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 125}}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - \sqrt[3]{\left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 125}}{v \cdot v - 1}\right)
double f(double v) {
        double r49855487 = 1.0;
        double r49855488 = 5.0;
        double r49855489 = v;
        double r49855490 = r49855489 * r49855489;
        double r49855491 = r49855488 * r49855490;
        double r49855492 = r49855487 - r49855491;
        double r49855493 = r49855490 - r49855487;
        double r49855494 = r49855492 / r49855493;
        double r49855495 = acos(r49855494);
        return r49855495;
}
↓
double f(double v) {
        double r49855496 = 1.0;
        double r49855497 = v;
        double r49855498 = r49855497 * r49855497;
        double r49855499 = r49855497 * r49855498;
        double r49855500 = r49855499 * r49855499;
        double r49855501 = 125.0;
        double r49855502 = r49855500 * r49855501;
        double r49855503 = cbrt(r49855502);
        double r49855504 = r49855496 - r49855503;
        double r49855505 = r49855498 - r49855496;
        double r49855506 = r49855504 / r49855505;
        double r49855507 = acos(r49855506);
        return r49855507;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

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

  3. Applied add-cbrt-cube0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot \color{blue}{\sqrt[3]{\left(v \cdot v\right) \cdot v}}\right)}{v \cdot v - 1}\right)\]

  4. Applied add-cbrt-cube0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \left(\color{blue}{\sqrt[3]{\left(v \cdot v\right) \cdot v}} \cdot \sqrt[3]{\left(v \cdot v\right) \cdot v}\right)}{v \cdot v - 1}\right)\]

  5. Applied cbrt-unprod0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - 5 \cdot \color{blue}{\sqrt[3]{\left(\left(v \cdot v\right) \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot v\right)}}}{v \cdot v - 1}\right)\]

  6. Applied add-cbrt-cube0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - \color{blue}{\sqrt[3]{\left(5 \cdot 5\right) \cdot 5}} \cdot \sqrt[3]{\left(\left(v \cdot v\right) \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot v\right)}}{v \cdot v - 1}\right)\]

  7. Applied cbrt-unprod0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - \color{blue}{\sqrt[3]{\left(\left(5 \cdot 5\right) \cdot 5\right) \cdot \left(\left(\left(v \cdot v\right) \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot v\right)\right)}}}{v \cdot v - 1}\right)\]

  8. Simplified0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - \sqrt[3]{\color{blue}{125 \cdot \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right)}}}{v \cdot v - 1}\right)\]

  9. Final simplification0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - \sqrt[3]{\left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 125}}{v \cdot v - 1}\right)\]

Reproduce

herbie shell --seed 2019107 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))