Average Error: 1.0 → 0.0
Time: 17.9s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 + v \cdot \left(v \cdot -6\right)}}\]
double f(double v) {
        double r25418077 = 4.0;
        double r25418078 = 3.0;
        double r25418079 = atan2(1.0, 0.0);
        double r25418080 = r25418078 * r25418079;
        double r25418081 = 1.0;
        double r25418082 = v;
        double r25418083 = r25418082 * r25418082;
        double r25418084 = r25418081 - r25418083;
        double r25418085 = r25418080 * r25418084;
        double r25418086 = 2.0;
        double r25418087 = 6.0;
        double r25418088 = r25418087 * r25418083;
        double r25418089 = r25418086 - r25418088;
        double r25418090 = sqrt(r25418089);
        double r25418091 = r25418085 * r25418090;
        double r25418092 = r25418077 / r25418091;
        return r25418092;
}
↓
double f(double v) {
        double r25418093 = 1.3333333333333333;
        double r25418094 = atan2(1.0, 0.0);
        double r25418095 = v;
        double r25418096 = r25418095 * r25418095;
        double r25418097 = r25418096 * r25418094;
        double r25418098 = r25418094 - r25418097;
        double r25418099 = r25418093 / r25418098;
        double r25418100 = 2.0;
        double r25418101 = -6.0;
        double r25418102 = r25418095 * r25418101;
        double r25418103 = r25418095 * r25418102;
        double r25418104 = r25418100 + r25418103;
        double r25418105 = sqrt(r25418104);
        double r25418106 = r25418099 / r25418105;
        return r25418106;
}


\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{2 + v \cdot \left(v \cdot -6\right)}}

Error

Bits error versus v

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))