Average Error: 0.6 → 0.6
Time: 1.5m
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)
double f(double v) {
        double r60858734 = 1.0;
        double r60858735 = 5.0;
        double r60858736 = v;
        double r60858737 = r60858736 * r60858736;
        double r60858738 = r60858735 * r60858737;
        double r60858739 = r60858734 - r60858738;
        double r60858740 = r60858737 - r60858734;
        double r60858741 = r60858739 / r60858740;
        double r60858742 = acos(r60858741);
        return r60858742;
}
↓
double f(double v) {
        double r60858743 = 1.0;
        double r60858744 = v;
        double r60858745 = r60858744 * r60858744;
        double r60858746 = 5.0;
        double r60858747 = r60858745 * r60858746;
        double r60858748 = r60858743 - r60858747;
        double r60858749 = r60858745 - r60858743;
        double r60858750 = r60858748 / r60858749;
        double r60858751 = acos(r60858750);
        return r60858751;
}

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

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

Reproduce

herbie shell --seed 2019125 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))