Average Error: 0.5 → 0.5
Time: 5.6s
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 r274129 = 1.0;
        double r274130 = 5.0;
        double r274131 = v;
        double r274132 = r274131 * r274131;
        double r274133 = r274130 * r274132;
        double r274134 = r274129 - r274133;
        double r274135 = r274132 - r274129;
        double r274136 = r274134 / r274135;
        double r274137 = acos(r274136);
        return r274137;
}
↓
double f(double v) {
        double r274138 = 1.0;
        double r274139 = 5.0;
        double r274140 = v;
        double r274141 = r274140 * r274140;
        double r274142 = r274139 * r274141;
        double r274143 = r274138 - r274142;
        double r274144 = r274141 - r274138;
        double r274145 = r274143 / r274144;
        double r274146 = acos(r274145);
        return r274146;
}

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