Average Error: 0.6 → 0.6
Time: 17.8s
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 r8296981 = 1.0;
        double r8296982 = 5.0;
        double r8296983 = v;
        double r8296984 = r8296983 * r8296983;
        double r8296985 = r8296982 * r8296984;
        double r8296986 = r8296981 - r8296985;
        double r8296987 = r8296984 - r8296981;
        double r8296988 = r8296986 / r8296987;
        double r8296989 = acos(r8296988);
        return r8296989;
}
↓
double f(double v) {
        double r8296990 = 1.0;
        double r8296991 = v;
        double r8296992 = r8296991 * r8296991;
        double r8296993 = 5.0;
        double r8296994 = r8296992 * r8296993;
        double r8296995 = r8296990 - r8296994;
        double r8296996 = r8296992 - r8296990;
        double r8296997 = r8296995 / r8296996;
        double r8296998 = acos(r8296997);
        return r8296998;
}

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 2019162 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))