Average Error: 0.5 → 0.5
Time: 31.3s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
double f(double v) {
        double r113681 = 1.0;
        double r113682 = 5.0;
        double r113683 = v;
        double r113684 = r113683 * r113683;
        double r113685 = r113682 * r113684;
        double r113686 = r113681 - r113685;
        double r113687 = r113684 - r113681;
        double r113688 = r113686 / r113687;
        double r113689 = acos(r113688);
        return r113689;
}
↓
double f(double v) {
        double r113690 = 1.0;
        double r113691 = 5.0;
        double r113692 = v;
        double r113693 = r113692 * r113692;
        double r113694 = r113691 * r113693;
        double r113695 = r113690 - r113694;
        double r113696 = r113693 - r113690;
        double r113697 = r113695 / r113696;
        double r113698 = acos(r113697);
        return r113698;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019326 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))