Average Error: 1.0 → 0.0
Time: 20.1s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{1}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}} \cdot \frac{4}{3}\]
\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 r5174939 = 4.0;
        double r5174940 = 3.0;
        double r5174941 = atan2(1.0, 0.0);
        double r5174942 = r5174940 * r5174941;
        double r5174943 = 1.0;
        double r5174944 = v;
        double r5174945 = r5174944 * r5174944;
        double r5174946 = r5174943 - r5174945;
        double r5174947 = r5174942 * r5174946;
        double r5174948 = 2.0;
        double r5174949 = 6.0;
        double r5174950 = r5174949 * r5174945;
        double r5174951 = r5174948 - r5174950;
        double r5174952 = sqrt(r5174951);
        double r5174953 = r5174947 * r5174952;
        double r5174954 = r5174939 / r5174953;
        return r5174954;
}
↓
double f(double v) {
        double r5174955 = 1.0;
        double r5174956 = atan2(1.0, 0.0);
        double r5174957 = v;
        double r5174958 = r5174957 * r5174957;
        double r5174959 = r5174958 * r5174956;
        double r5174960 = r5174956 - r5174959;
        double r5174961 = r5174955 / r5174960;
        double r5174962 = -6.0;
        double r5174963 = r5174958 * r5174962;
        double r5174964 = 2.0;
        double r5174965 = r5174963 + r5174964;
        double r5174966 = sqrt(r5174965);
        double r5174967 = r5174961 / r5174966;
        double r5174968 = 1.3333333333333333;
        double r5174969 = r5174967 * r5174968;
        return r5174969;
}

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)))))))