Average Error: 0.6 → 0.6
Time: 6.1s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
\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 r269370 = 1.0;
        double r269371 = 5.0;
        double r269372 = v;
        double r269373 = r269372 * r269372;
        double r269374 = r269371 * r269373;
        double r269375 = r269370 - r269374;
        double r269376 = r269373 - r269370;
        double r269377 = r269375 / r269376;
        double r269378 = acos(r269377);
        return r269378;
}
↓
double f(double v) {
        double r269379 = 1.0;
        double r269380 = 5.0;
        double r269381 = v;
        double r269382 = r269381 * r269381;
        double r269383 = r269380 * r269382;
        double r269384 = r269379 - r269383;
        double r269385 = r269382 - r269379;
        double r269386 = r269384 / r269385;
        double r269387 = acos(r269386);
        return r269387;
}

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

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))