Average Error: 0.6 → 0.6
Time: 19.0s
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 r8298349 = 1.0;
        double r8298350 = 5.0;
        double r8298351 = v;
        double r8298352 = r8298351 * r8298351;
        double r8298353 = r8298350 * r8298352;
        double r8298354 = r8298349 - r8298353;
        double r8298355 = r8298352 - r8298349;
        double r8298356 = r8298354 / r8298355;
        double r8298357 = acos(r8298356);
        return r8298357;
}
↓
double f(double v) {
        double r8298358 = 1.0;
        double r8298359 = v;
        double r8298360 = r8298359 * r8298359;
        double r8298361 = 5.0;
        double r8298362 = r8298360 * r8298361;
        double r8298363 = r8298358 - r8298362;
        double r8298364 = r8298360 - r8298358;
        double r8298365 = r8298363 / r8298364;
        double r8298366 = acos(r8298365);
        return r8298366;
}

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 2019162 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))