Average Error: 0.6 → 0.6
Time: 42.4s
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 r10432907 = 1.0;
        double r10432908 = 5.0;
        double r10432909 = v;
        double r10432910 = r10432909 * r10432909;
        double r10432911 = r10432908 * r10432910;
        double r10432912 = r10432907 - r10432911;
        double r10432913 = r10432910 - r10432907;
        double r10432914 = r10432912 / r10432913;
        double r10432915 = acos(r10432914);
        return r10432915;
}
↓
double f(double v) {
        double r10432916 = 1.0;
        double r10432917 = v;
        double r10432918 = r10432917 * r10432917;
        double r10432919 = 5.0;
        double r10432920 = r10432918 * r10432919;
        double r10432921 = r10432916 - r10432920;
        double r10432922 = r10432918 - r10432916;
        double r10432923 = r10432921 / r10432922;
        double r10432924 = acos(r10432923);
        return r10432924;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))