Average Error: 0.6 → 0.6
Time: 17.6s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\left(\sqrt{\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)}} \cdot \sqrt{\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\left(\sqrt{\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)}} \cdot \sqrt{\sqrt[3]{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}
double f(double v) {
        double r2316422 = 1.0;
        double r2316423 = 5.0;
        double r2316424 = v;
        double r2316425 = r2316424 * r2316424;
        double r2316426 = r2316423 * r2316425;
        double r2316427 = r2316422 - r2316426;
        double r2316428 = r2316425 - r2316422;
        double r2316429 = r2316427 / r2316428;
        double r2316430 = acos(r2316429);
        return r2316430;
}
↓
double f(double v) {
        double r2316431 = 1.0;
        double r2316432 = v;
        double r2316433 = r2316432 * r2316432;
        double r2316434 = 5.0;
        double r2316435 = r2316433 * r2316434;
        double r2316436 = r2316431 - r2316435;
        double r2316437 = r2316433 - r2316431;
        double r2316438 = r2316436 / r2316437;
        double r2316439 = acos(r2316438);
        double r2316440 = sqrt(r2316439);
        double r2316441 = r2316440 * r2316440;
        double r2316442 = r2316440 * r2316441;
        double r2316443 = cbrt(r2316442);
        double r2316444 = sqrt(r2316443);
        double r2316445 = r2316444 * r2316444;
        double r2316446 = r2316445 * r2316440;
        return r2316446;
}

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-sqr-sqrt1.5

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

  5. Applied add-cbrt-cube1.5

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

  7. Applied add-sqr-sqrt0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019154 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))