Average Error: 1.0 → 0.0
Time: 18.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{1}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}} \cdot \frac{4}{3}\]
\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{1}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}} \cdot \frac{4}{3}
double f(double v) {
        double r5174942 = 4.0;
        double r5174943 = 3.0;
        double r5174944 = atan2(1.0, 0.0);
        double r5174945 = r5174943 * r5174944;
        double r5174946 = 1.0;
        double r5174947 = v;
        double r5174948 = r5174947 * r5174947;
        double r5174949 = r5174946 - r5174948;
        double r5174950 = r5174945 * r5174949;
        double r5174951 = 2.0;
        double r5174952 = 6.0;
        double r5174953 = r5174952 * r5174948;
        double r5174954 = r5174951 - r5174953;
        double r5174955 = sqrt(r5174954);
        double r5174956 = r5174950 * r5174955;
        double r5174957 = r5174942 / r5174956;
        return r5174957;
}
↓
double f(double v) {
        double r5174958 = 1.0;
        double r5174959 = atan2(1.0, 0.0);
        double r5174960 = v;
        double r5174961 = r5174960 * r5174960;
        double r5174962 = r5174961 * r5174959;
        double r5174963 = r5174959 - r5174962;
        double r5174964 = r5174958 / r5174963;
        double r5174965 = -6.0;
        double r5174966 = r5174961 * r5174965;
        double r5174967 = 2.0;
        double r5174968 = r5174966 + r5174967;
        double r5174969 = sqrt(r5174968);
        double r5174970 = r5174964 / r5174969;
        double r5174971 = 1.3333333333333333;
        double r5174972 = r5174970 * r5174971;
        return r5174972;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-*l*0.0

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

  7. Applied div-inv0.0

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

  8. Simplified0.0

    \[\leadsto \frac{\frac{4}{3} \cdot \color{blue}{\frac{1}{\pi - \pi \cdot \left(v \cdot v\right)}}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}\]
  9. Using strategy rm

  10. Applied *-un-lft-identity0.0

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

  11. Applied sqrt-prod0.0

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

  12. Applied times-frac0.0

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

  13. Simplified0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))