Average Error: 0.5 → 0.5
Time: 6.0s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
double f(double v) {
        double r275290 = 1.0;
        double r275291 = 5.0;
        double r275292 = v;
        double r275293 = r275292 * r275292;
        double r275294 = r275291 * r275293;
        double r275295 = r275290 - r275294;
        double r275296 = r275293 - r275290;
        double r275297 = r275295 / r275296;
        double r275298 = acos(r275297);
        return r275298;
}
↓
double f(double v) {
        double r275299 = 1.0;
        double r275300 = 5.0;
        double r275301 = v;
        double r275302 = r275301 * r275301;
        double r275303 = r275300 * r275302;
        double r275304 = r275299 - r275303;
        double r275305 = r275302 - r275299;
        double r275306 = r275304 / r275305;
        double r275307 = acos(r275306);
        return r275307;
}

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

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))