Average Error: 0.5 → 0.5
Time: 5.0s
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 r302787 = 1.0;
        double r302788 = 5.0;
        double r302789 = v;
        double r302790 = r302789 * r302789;
        double r302791 = r302788 * r302790;
        double r302792 = r302787 - r302791;
        double r302793 = r302790 - r302787;
        double r302794 = r302792 / r302793;
        double r302795 = acos(r302794);
        return r302795;
}
↓
double f(double v) {
        double r302796 = 1.0;
        double r302797 = 5.0;
        double r302798 = v;
        double r302799 = r302798 * r302798;
        double r302800 = r302797 * r302799;
        double r302801 = r302796 - r302800;
        double r302802 = r302799 - r302796;
        double r302803 = r302801 / r302802;
        double r302804 = acos(r302803);
        return r302804;
}

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 2019353 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))