Average Error: 1.0 → 0.0
Time: 14.1s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r160153 = 4.0;
        double r160154 = 3.0;
        double r160155 = atan2(1.0, 0.0);
        double r160156 = r160154 * r160155;
        double r160157 = 1.0;
        double r160158 = v;
        double r160159 = r160158 * r160158;
        double r160160 = r160157 - r160159;
        double r160161 = r160156 * r160160;
        double r160162 = 2.0;
        double r160163 = 6.0;
        double r160164 = r160163 * r160159;
        double r160165 = r160162 - r160164;
        double r160166 = sqrt(r160165);
        double r160167 = r160161 * r160166;
        double r160168 = r160153 / r160167;
        return r160168;
}
↓
double f(double v) {
        double r160169 = 4.0;
        double r160170 = 3.0;
        double r160171 = atan2(1.0, 0.0);
        double r160172 = r160170 * r160171;
        double r160173 = r160169 / r160172;
        double r160174 = 1.0;
        double r160175 = v;
        double r160176 = r160175 * r160175;
        double r160177 = r160174 - r160176;
        double r160178 = r160173 / r160177;
        double r160179 = 2.0;
        double r160180 = 6.0;
        double r160181 = r160180 * r160176;
        double r160182 = r160179 - r160181;
        double r160183 = sqrt(r160182);
        double r160184 = r160178 / r160183;
        return r160184;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))