Average Error: 0.5 → 0.5
Time: 4.9s
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 r162930 = 1.0;
        double r162931 = 5.0;
        double r162932 = v;
        double r162933 = r162932 * r162932;
        double r162934 = r162931 * r162933;
        double r162935 = r162930 - r162934;
        double r162936 = r162933 - r162930;
        double r162937 = r162935 / r162936;
        double r162938 = acos(r162937);
        return r162938;
}
↓
double f(double v) {
        double r162939 = 1.0;
        double r162940 = 5.0;
        double r162941 = v;
        double r162942 = r162941 * r162941;
        double r162943 = r162940 * r162942;
        double r162944 = r162939 - r162943;
        double r162945 = r162942 - r162939;
        double r162946 = r162944 / r162945;
        double r162947 = acos(r162946);
        return r162947;
}

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))))