Average Error: 1.0 → 0.0
Time: 10.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]
\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}
double f(double v) {
        double r3173672 = 4.0;
        double r3173673 = 3.0;
        double r3173674 = atan2(1.0, 0.0);
        double r3173675 = r3173673 * r3173674;
        double r3173676 = 1.0;
        double r3173677 = v;
        double r3173678 = r3173677 * r3173677;
        double r3173679 = r3173676 - r3173678;
        double r3173680 = r3173675 * r3173679;
        double r3173681 = 2.0;
        double r3173682 = 6.0;
        double r3173683 = r3173682 * r3173678;
        double r3173684 = r3173681 - r3173683;
        double r3173685 = sqrt(r3173684);
        double r3173686 = r3173680 * r3173685;
        double r3173687 = r3173672 / r3173686;
        return r3173687;
}
↓
double f(double v) {
        double r3173688 = 1.3333333333333333;
        double r3173689 = atan2(1.0, 0.0);
        double r3173690 = v;
        double r3173691 = r3173690 * r3173690;
        double r3173692 = r3173691 * r3173689;
        double r3173693 = r3173689 - r3173692;
        double r3173694 = r3173688 / r3173693;
        double r3173695 = -6.0;
        double r3173696 = r3173695 * r3173691;
        double r3173697 = 2.0;
        double r3173698 = r3173696 + r3173697;
        double r3173699 = sqrt(r3173698);
        double r3173700 = r3173694 / r3173699;
        return r3173700;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 + -6 \cdot \left(v \cdot v\right)}}}\]

  3. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

Reproduce

herbie shell --seed 2019128 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))