Average Error: 0.5 → 0.5
Time: 26.0s
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 r230981 = 1.0;
        double r230982 = 5.0;
        double r230983 = v;
        double r230984 = r230983 * r230983;
        double r230985 = r230982 * r230984;
        double r230986 = r230981 - r230985;
        double r230987 = r230984 - r230981;
        double r230988 = r230986 / r230987;
        double r230989 = acos(r230988);
        return r230989;
}
↓
double f(double v) {
        double r230990 = 1.0;
        double r230991 = 5.0;
        double r230992 = v;
        double r230993 = r230992 * r230992;
        double r230994 = r230991 * r230993;
        double r230995 = r230990 - r230994;
        double r230996 = r230993 - r230990;
        double r230997 = r230995 / r230996;
        double r230998 = acos(r230997);
        return r230998;
}

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))))