Average Error: 0.5 → 0.5
Time: 5.7s
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 r235360 = 1.0;
        double r235361 = 5.0;
        double r235362 = v;
        double r235363 = r235362 * r235362;
        double r235364 = r235361 * r235363;
        double r235365 = r235360 - r235364;
        double r235366 = r235363 - r235360;
        double r235367 = r235365 / r235366;
        double r235368 = acos(r235367);
        return r235368;
}
↓
double f(double v) {
        double r235369 = 1.0;
        double r235370 = 5.0;
        double r235371 = v;
        double r235372 = r235371 * r235371;
        double r235373 = r235370 * r235372;
        double r235374 = r235369 - r235373;
        double r235375 = r235372 - r235369;
        double r235376 = r235374 / r235375;
        double r235377 = acos(r235376);
        return r235377;
}

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))))