Average Error: 0.6 → 0.6
Time: 16.7s
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 r232825 = 1.0;
        double r232826 = 5.0;
        double r232827 = v;
        double r232828 = r232827 * r232827;
        double r232829 = r232826 * r232828;
        double r232830 = r232825 - r232829;
        double r232831 = r232828 - r232825;
        double r232832 = r232830 / r232831;
        double r232833 = acos(r232832);
        return r232833;
}
↓
double f(double v) {
        double r232834 = 1.0;
        double r232835 = 5.0;
        double r232836 = v;
        double r232837 = r232836 * r232836;
        double r232838 = r232835 * r232837;
        double r232839 = r232834 - r232838;
        double r232840 = r232837 - r232834;
        double r232841 = r232839 / r232840;
        double r232842 = acos(r232841);
        return r232842;
}

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

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

Reproduce

herbie shell --seed 2019209 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))