Average Error: 0.5 → 0.5
Time: 5.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
\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 r155755 = 1.0;
        double r155756 = 5.0;
        double r155757 = v;
        double r155758 = r155757 * r155757;
        double r155759 = r155756 * r155758;
        double r155760 = r155755 - r155759;
        double r155761 = r155758 - r155755;
        double r155762 = r155760 / r155761;
        double r155763 = acos(r155762);
        return r155763;
}
↓
double f(double v) {
        double r155764 = 1.0;
        double r155765 = 5.0;
        double r155766 = v;
        double r155767 = r155766 * r155766;
        double r155768 = r155765 * r155767;
        double r155769 = r155764 - r155768;
        double r155770 = r155767 - r155764;
        double r155771 = r155769 / r155770;
        double r155772 = acos(r155771);
        return r155772;
}

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 2020001 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))