Average Error: 0.5 → 0.5
Time: 26.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\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 r12790592 = 1.0;
        double r12790593 = 5.0;
        double r12790594 = v;
        double r12790595 = r12790594 * r12790594;
        double r12790596 = r12790593 * r12790595;
        double r12790597 = r12790592 - r12790596;
        double r12790598 = r12790595 - r12790592;
        double r12790599 = r12790597 / r12790598;
        double r12790600 = acos(r12790599);
        return r12790600;
}
↓
double f(double v) {
        double r12790601 = 1.0;
        double r12790602 = v;
        double r12790603 = r12790602 * r12790602;
        double r12790604 = 5.0;
        double r12790605 = r12790603 * r12790604;
        double r12790606 = r12790601 - r12790605;
        double r12790607 = r12790603 - r12790601;
        double r12790608 = r12790606 / r12790607;
        double r12790609 = acos(r12790608);
        return r12790609;
}

Error

Bits error versus v

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Your Program's Arguments

Results

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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

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

Reproduce

herbie shell --seed 2019171 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))