Average Error: 0.5 → 0.5
Time: 24.1s
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 r11479419 = 1.0;
        double r11479420 = 5.0;
        double r11479421 = v;
        double r11479422 = r11479421 * r11479421;
        double r11479423 = r11479420 * r11479422;
        double r11479424 = r11479419 - r11479423;
        double r11479425 = r11479422 - r11479419;
        double r11479426 = r11479424 / r11479425;
        double r11479427 = acos(r11479426);
        return r11479427;
}
↓
double f(double v) {
        double r11479428 = 1.0;
        double r11479429 = v;
        double r11479430 = r11479429 * r11479429;
        double r11479431 = 5.0;
        double r11479432 = r11479430 * r11479431;
        double r11479433 = r11479428 - r11479432;
        double r11479434 = r11479430 - r11479428;
        double r11479435 = r11479433 / r11479434;
        double r11479436 = acos(r11479435);
        return r11479436;
}

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 2019169 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))