Average Error: 1.0 → 0.0
Time: 26.5s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}}{\sqrt{\left(v \cdot -6\right) \cdot v + 2}}\]
\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 - \log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}}{\sqrt{\left(v \cdot -6\right) \cdot v + 2}}
double f(double v) {
        double r31462804 = 4.0;
        double r31462805 = 3.0;
        double r31462806 = atan2(1.0, 0.0);
        double r31462807 = r31462805 * r31462806;
        double r31462808 = 1.0;
        double r31462809 = v;
        double r31462810 = r31462809 * r31462809;
        double r31462811 = r31462808 - r31462810;
        double r31462812 = r31462807 * r31462811;
        double r31462813 = 2.0;
        double r31462814 = 6.0;
        double r31462815 = r31462814 * r31462810;
        double r31462816 = r31462813 - r31462815;
        double r31462817 = sqrt(r31462816);
        double r31462818 = r31462812 * r31462817;
        double r31462819 = r31462804 / r31462818;
        return r31462819;
}
↓
double f(double v) {
        double r31462820 = 1.3333333333333333;
        double r31462821 = atan2(1.0, 0.0);
        double r31462822 = v;
        double r31462823 = r31462822 * r31462822;
        double r31462824 = r31462823 * r31462821;
        double r31462825 = exp(r31462824);
        double r31462826 = log(r31462825);
        double r31462827 = r31462821 - r31462826;
        double r31462828 = r31462820 / r31462827;
        double r31462829 = -6.0;
        double r31462830 = r31462822 * r31462829;
        double r31462831 = r31462830 * r31462822;
        double r31462832 = 2.0;
        double r31462833 = r31462831 + r31462832;
        double r31462834 = sqrt(r31462833);
        double r31462835 = r31462828 / r31462834;
        return r31462835;
}

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

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

  4. Applied add-log-exp0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019121 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))