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 r339320 = 1.0;
        double r339321 = 5.0;
        double r339322 = v;
        double r339323 = r339322 * r339322;
        double r339324 = r339321 * r339323;
        double r339325 = r339320 - r339324;
        double r339326 = r339323 - r339320;
        double r339327 = r339325 / r339326;
        double r339328 = acos(r339327);
        return r339328;
}
↓
double f(double v) {
        double r339329 = 1.0;
        double r339330 = 5.0;
        double r339331 = v;
        double r339332 = r339331 * r339331;
        double r339333 = r339330 * r339332;
        double r339334 = r339329 - r339333;
        double r339335 = r339332 - r339329;
        double r339336 = r339334 / r339335;
        double r339337 = acos(r339336);
        return r339337;
}

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