Average Error: 0.5 → 0.5
Time: 5.8s
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 r289419 = 1.0;
        double r289420 = 5.0;
        double r289421 = v;
        double r289422 = r289421 * r289421;
        double r289423 = r289420 * r289422;
        double r289424 = r289419 - r289423;
        double r289425 = r289422 - r289419;
        double r289426 = r289424 / r289425;
        double r289427 = acos(r289426);
        return r289427;
}
↓
double f(double v) {
        double r289428 = 1.0;
        double r289429 = 5.0;
        double r289430 = v;
        double r289431 = r289430 * r289430;
        double r289432 = r289429 * r289431;
        double r289433 = r289428 - r289432;
        double r289434 = r289431 - r289428;
        double r289435 = r289433 / r289434;
        double r289436 = acos(r289435);
        return r289436;
}

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 2020059 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))