Average Error: 0.5 → 0.5
Time: 6.5s
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 r452486 = 1.0;
        double r452487 = 5.0;
        double r452488 = v;
        double r452489 = r452488 * r452488;
        double r452490 = r452487 * r452489;
        double r452491 = r452486 - r452490;
        double r452492 = r452489 - r452486;
        double r452493 = r452491 / r452492;
        double r452494 = acos(r452493);
        return r452494;
}
↓
double f(double v) {
        double r452495 = 1.0;
        double r452496 = 5.0;
        double r452497 = v;
        double r452498 = r452497 * r452497;
        double r452499 = r452496 * r452498;
        double r452500 = r452495 - r452499;
        double r452501 = r452498 - r452495;
        double r452502 = r452500 / r452501;
        double r452503 = acos(r452502);
        return r452503;
}

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