Average Error: 1.0 → 0.0
Time: 12.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r4771085 = 4.0;
        double r4771086 = 3.0;
        double r4771087 = atan2(1.0, 0.0);
        double r4771088 = r4771086 * r4771087;
        double r4771089 = 1.0;
        double r4771090 = v;
        double r4771091 = r4771090 * r4771090;
        double r4771092 = r4771089 - r4771091;
        double r4771093 = r4771088 * r4771092;
        double r4771094 = 2.0;
        double r4771095 = 6.0;
        double r4771096 = r4771095 * r4771091;
        double r4771097 = r4771094 - r4771096;
        double r4771098 = sqrt(r4771097);
        double r4771099 = r4771093 * r4771098;
        double r4771100 = r4771085 / r4771099;
        return r4771100;
}
↓
double f(double v) {
        double r4771101 = 4.0;
        double r4771102 = atan2(1.0, 0.0);
        double r4771103 = 3.0;
        double r4771104 = r4771102 * r4771103;
        double r4771105 = 1.0;
        double r4771106 = v;
        double r4771107 = r4771106 * r4771106;
        double r4771108 = r4771105 - r4771107;
        double r4771109 = r4771104 * r4771108;
        double r4771110 = r4771101 / r4771109;
        double r4771111 = 2.0;
        double r4771112 = 6.0;
        double r4771113 = r4771112 * r4771107;
        double r4771114 = r4771111 - r4771113;
        double r4771115 = sqrt(r4771114);
        double r4771116 = r4771110 / r4771115;
        return r4771116;
}

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. Using strategy rm

  3. Applied associate-/r*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))