Average Error: 0.5 → 0.5
Time: 20.0s
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 r3481254 = 1.0;
        double r3481255 = 5.0;
        double r3481256 = v;
        double r3481257 = r3481256 * r3481256;
        double r3481258 = r3481255 * r3481257;
        double r3481259 = r3481254 - r3481258;
        double r3481260 = r3481257 - r3481254;
        double r3481261 = r3481259 / r3481260;
        double r3481262 = acos(r3481261);
        return r3481262;
}
↓
double f(double v) {
        double r3481263 = 1.0;
        double r3481264 = v;
        double r3481265 = r3481264 * r3481264;
        double r3481266 = 5.0;
        double r3481267 = r3481265 * r3481266;
        double r3481268 = r3481263 - r3481267;
        double r3481269 = r3481265 - r3481263;
        double r3481270 = r3481268 / r3481269;
        double r3481271 = acos(r3481270);
        return r3481271;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019152 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))