Average Error: 0.5 → 0.5
Time: 35.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\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 r7720911 = 1.0;
        double r7720912 = 5.0;
        double r7720913 = v;
        double r7720914 = r7720913 * r7720913;
        double r7720915 = r7720912 * r7720914;
        double r7720916 = r7720911 - r7720915;
        double r7720917 = r7720914 - r7720911;
        double r7720918 = r7720916 / r7720917;
        double r7720919 = acos(r7720918);
        return r7720919;
}
↓
double f(double v) {
        double r7720920 = 1.0;
        double r7720921 = v;
        double r7720922 = r7720921 * r7720921;
        double r7720923 = 5.0;
        double r7720924 = r7720922 * r7720923;
        double r7720925 = r7720920 - r7720924;
        double r7720926 = r7720922 - r7720920;
        double r7720927 = r7720925 / r7720926;
        double r7720928 = acos(r7720927);
        return r7720928;
}

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 2019152 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))