Average Error: 0.6 → 0.6
Time: 44.0s
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 r10432583 = 1.0;
        double r10432584 = 5.0;
        double r10432585 = v;
        double r10432586 = r10432585 * r10432585;
        double r10432587 = r10432584 * r10432586;
        double r10432588 = r10432583 - r10432587;
        double r10432589 = r10432586 - r10432583;
        double r10432590 = r10432588 / r10432589;
        double r10432591 = acos(r10432590);
        return r10432591;
}
↓
double f(double v) {
        double r10432592 = 1.0;
        double r10432593 = v;
        double r10432594 = r10432593 * r10432593;
        double r10432595 = 5.0;
        double r10432596 = r10432594 * r10432595;
        double r10432597 = r10432592 - r10432596;
        double r10432598 = r10432594 - r10432592;
        double r10432599 = r10432597 / r10432598;
        double r10432600 = acos(r10432599);
        return r10432600;
}

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 2019200 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))