Average Error: 1.0 → 0.0
Time: 27.4s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\sqrt{\left(\left(\left(v \cdot v\right) \cdot 6\right) \cdot 2 + \left(\left(v \cdot v\right) \cdot 6\right) \cdot \left(\left(v \cdot v\right) \cdot 6\right)\right) + 4} \cdot \frac{\frac{\frac{4}{3}}{\sqrt{8 - \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 216}}}{\pi - \log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}\]
\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)}}
↓
\sqrt{\left(\left(\left(v \cdot v\right) \cdot 6\right) \cdot 2 + \left(\left(v \cdot v\right) \cdot 6\right) \cdot \left(\left(v \cdot v\right) \cdot 6\right)\right) + 4} \cdot \frac{\frac{\frac{4}{3}}{\sqrt{8 - \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 216}}}{\pi - \log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}
double f(double v) {
        double r5531187 = 4.0;
        double r5531188 = 3.0;
        double r5531189 = atan2(1.0, 0.0);
        double r5531190 = r5531188 * r5531189;
        double r5531191 = 1.0;
        double r5531192 = v;
        double r5531193 = r5531192 * r5531192;
        double r5531194 = r5531191 - r5531193;
        double r5531195 = r5531190 * r5531194;
        double r5531196 = 2.0;
        double r5531197 = 6.0;
        double r5531198 = r5531197 * r5531193;
        double r5531199 = r5531196 - r5531198;
        double r5531200 = sqrt(r5531199);
        double r5531201 = r5531195 * r5531200;
        double r5531202 = r5531187 / r5531201;
        return r5531202;
}
↓
double f(double v) {
        double r5531203 = v;
        double r5531204 = r5531203 * r5531203;
        double r5531205 = 6.0;
        double r5531206 = r5531204 * r5531205;
        double r5531207 = 2.0;
        double r5531208 = r5531206 * r5531207;
        double r5531209 = r5531206 * r5531206;
        double r5531210 = r5531208 + r5531209;
        double r5531211 = 4.0;
        double r5531212 = r5531210 + r5531211;
        double r5531213 = sqrt(r5531212);
        double r5531214 = 1.3333333333333333;
        double r5531215 = 8.0;
        double r5531216 = r5531203 * r5531204;
        double r5531217 = r5531216 * r5531216;
        double r5531218 = 216.0;
        double r5531219 = r5531217 * r5531218;
        double r5531220 = r5531215 - r5531219;
        double r5531221 = sqrt(r5531220);
        double r5531222 = r5531214 / r5531221;
        double r5531223 = atan2(1.0, 0.0);
        double r5531224 = r5531204 * r5531223;
        double r5531225 = exp(r5531224);
        double r5531226 = log(r5531225);
        double r5531227 = r5531223 - r5531226;
        double r5531228 = r5531222 / r5531227;
        double r5531229 = r5531213 * r5531228;
        return r5531229;
}

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

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

  4. Applied flip3--0.0

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

  5. Applied sqrt-div0.0

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

  6. Applied associate-/r/0.0

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

  7. Simplified0.0

    \[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\sqrt{8 - \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 216}}}{\pi - \left(v \cdot v\right) \cdot \pi}} \cdot \sqrt{2 \cdot 2 + \left(\left(6 \cdot \left(v \cdot v\right)\right) \cdot \left(6 \cdot \left(v \cdot v\right)\right) + 2 \cdot \left(6 \cdot \left(v \cdot v\right)\right)\right)}\]
  8. Using strategy rm

  9. Applied add-log-exp0.0

    \[\leadsto \frac{\frac{\frac{4}{3}}{\sqrt{8 - \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 216}}}{\pi - \color{blue}{\log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}} \cdot \sqrt{2 \cdot 2 + \left(\left(6 \cdot \left(v \cdot v\right)\right) \cdot \left(6 \cdot \left(v \cdot v\right)\right) + 2 \cdot \left(6 \cdot \left(v \cdot v\right)\right)\right)}\]

  10. Final simplification0.0

    \[\leadsto \sqrt{\left(\left(\left(v \cdot v\right) \cdot 6\right) \cdot 2 + \left(\left(v \cdot v\right) \cdot 6\right) \cdot \left(\left(v \cdot v\right) \cdot 6\right)\right) + 4} \cdot \frac{\frac{\frac{4}{3}}{\sqrt{8 - \left(\left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)\right) \cdot 216}}}{\pi - \log \left(e^{\left(v \cdot v\right) \cdot \pi}\right)}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))