Average Error: 0.5 → 0.5
Time: 46.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)
double f(double v) {
        double r33756538 = 1.0;
        double r33756539 = 5.0;
        double r33756540 = v;
        double r33756541 = r33756540 * r33756540;
        double r33756542 = r33756539 * r33756541;
        double r33756543 = r33756538 - r33756542;
        double r33756544 = r33756541 - r33756538;
        double r33756545 = r33756543 / r33756544;
        double r33756546 = acos(r33756545);
        return r33756546;
}
↓
double f(double v) {
        double r33756547 = 1.0;
        double r33756548 = v;
        double r33756549 = r33756548 * r33756548;
        double r33756550 = 5.0;
        double r33756551 = r33756549 * r33756550;
        double r33756552 = r33756547 - r33756551;
        double r33756553 = r33756549 - r33756547;
        double r33756554 = r33756552 / r33756553;
        double r33756555 = acos(r33756554);
        return r33756555;
}

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

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

Reproduce

herbie shell --seed 2019112 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))