Average Error: 0.5 → 0.5
Time: 48.8s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)
double f(double v) {
        double r7286793 = 1.0;
        double r7286794 = 5.0;
        double r7286795 = v;
        double r7286796 = r7286795 * r7286795;
        double r7286797 = r7286794 * r7286796;
        double r7286798 = r7286793 - r7286797;
        double r7286799 = r7286796 - r7286793;
        double r7286800 = r7286798 / r7286799;
        double r7286801 = acos(r7286800);
        return r7286801;
}
↓
double f(double v) {
        double r7286802 = 1.0;
        double r7286803 = v;
        double r7286804 = r7286803 * r7286803;
        double r7286805 = 5.0;
        double r7286806 = r7286804 * r7286805;
        double r7286807 = r7286802 - r7286806;
        double r7286808 = r7286804 - r7286802;
        double r7286809 = r7286807 / r7286808;
        double r7286810 = acos(r7286809);
        return r7286810;
}

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

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

Reproduce

herbie shell --seed 2019143 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))