Average Error: 13.1 → 2.3
Time: 40.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \le -2.943062400229215877571579017740335303393 \cdot 10^{176}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(\left(3 - 2 \cdot v\right) \cdot 0.125\right) \cdot \left(\left(\left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right) \cdot \left(w \cdot \left(w \cdot r\right)\right)\right) \cdot \sqrt[3]{r}\right)}{1 - v}\right) - 4.5\\ \mathbf{elif}\;r \le 5.011565409680118343325145261599835434747 \cdot 10^{-14}:\\ \;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{1 - v}{w}}}{\frac{\frac{\frac{1}{w}}{r}}{r}}\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{-\frac{\frac{1 - v}{w \cdot \left(w \cdot r\right)}}{-r}}\right) - 4.5\\ \end{array}\]
\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5
↓
\begin{array}{l}
\mathbf{if}\;r \le -2.943062400229215877571579017740335303393 \cdot 10^{176}:\\
\;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(\left(3 - 2 \cdot v\right) \cdot 0.125\right) \cdot \left(\left(\left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right) \cdot \left(w \cdot \left(w \cdot r\right)\right)\right) \cdot \sqrt[3]{r}\right)}{1 - v}\right) - 4.5\\

\mathbf{elif}\;r \le 5.011565409680118343325145261599835434747 \cdot 10^{-14}:\\
\;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{1 - v}{w}}}{\frac{\frac{\frac{1}{w}}{r}}{r}}\right) - 4.5\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{-\frac{\frac{1 - v}{w \cdot \left(w \cdot r\right)}}{-r}}\right) - 4.5\\

\end{array}
double f(double v, double w, double r) {
        double r41856 = 3.0;
        double r41857 = 2.0;
        double r41858 = r;
        double r41859 = r41858 * r41858;
        double r41860 = r41857 / r41859;
        double r41861 = r41856 + r41860;
        double r41862 = 0.125;
        double r41863 = v;
        double r41864 = r41857 * r41863;
        double r41865 = r41856 - r41864;
        double r41866 = r41862 * r41865;
        double r41867 = w;
        double r41868 = r41867 * r41867;
        double r41869 = r41868 * r41858;
        double r41870 = r41869 * r41858;
        double r41871 = r41866 * r41870;
        double r41872 = 1.0;
        double r41873 = r41872 - r41863;
        double r41874 = r41871 / r41873;
        double r41875 = r41861 - r41874;
        double r41876 = 4.5;
        double r41877 = r41875 - r41876;
        return r41877;
}
↓
double f(double v, double w, double r) {
        double r41878 = r;
        double r41879 = -2.943062400229216e+176;
        bool r41880 = r41878 <= r41879;
        double r41881 = 3.0;
        double r41882 = 2.0;
        double r41883 = r41878 * r41878;
        double r41884 = r41882 / r41883;
        double r41885 = r41881 + r41884;
        double r41886 = v;
        double r41887 = r41882 * r41886;
        double r41888 = r41881 - r41887;
        double r41889 = 0.125;
        double r41890 = r41888 * r41889;
        double r41891 = cbrt(r41878);
        double r41892 = r41891 * r41891;
        double r41893 = w;
        double r41894 = r41893 * r41878;
        double r41895 = r41893 * r41894;
        double r41896 = r41892 * r41895;
        double r41897 = r41896 * r41891;
        double r41898 = r41890 * r41897;
        double r41899 = 1.0;
        double r41900 = r41899 - r41886;
        double r41901 = r41898 / r41900;
        double r41902 = r41885 - r41901;
        double r41903 = 4.5;
        double r41904 = r41902 - r41903;
        double r41905 = 5.0115654096801183e-14;
        bool r41906 = r41878 <= r41905;
        double r41907 = r41882 / r41878;
        double r41908 = r41907 / r41878;
        double r41909 = r41908 + r41881;
        double r41910 = r41900 / r41893;
        double r41911 = r41890 / r41910;
        double r41912 = 1.0;
        double r41913 = r41912 / r41893;
        double r41914 = r41913 / r41878;
        double r41915 = r41914 / r41878;
        double r41916 = r41911 / r41915;
        double r41917 = r41909 - r41916;
        double r41918 = r41917 - r41903;
        double r41919 = r41900 / r41895;
        double r41920 = -r41878;
        double r41921 = r41919 / r41920;
        double r41922 = -r41921;
        double r41923 = r41890 / r41922;
        double r41924 = r41909 - r41923;
        double r41925 = r41924 - r41903;
        double r41926 = r41906 ? r41918 : r41925;
        double r41927 = r41880 ? r41904 : r41926;
        return r41927;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if r < -2.943062400229216e+176

    1. Initial program 30.6

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    2. Using strategy rm

    3. Applied add-cube-cbrt30.8

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot \color{blue}{\left(\left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right) \cdot \sqrt[3]{r}\right)}\right)}{1 - v}\right) - 4.5\]

    4. Applied associate-*r*30.8

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(\left(\left(\left(w \cdot w\right) \cdot r\right) \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right) \cdot \sqrt[3]{r}\right)}}{1 - v}\right) - 4.5\]

    5. Simplified11.2

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\color{blue}{\left(\left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right) \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)} \cdot \sqrt[3]{r}\right)}{1 - v}\right) - 4.5\]

    if -2.943062400229216e+176 < r < 5.0115654096801183e-14

    1. Initial program 10.3

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    2. Using strategy rm

    3. Applied associate-/l*7.2

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}}\right) - 4.5\]

    4. Simplified4.0

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\color{blue}{\frac{\frac{1 - v}{w \cdot \left(w \cdot r\right)}}{r}}}\right) - 4.5\]
    5. Using strategy rm

    6. Applied associate-/r*2.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\color{blue}{\frac{\frac{1 - v}{w}}{w \cdot r}}}{r}}\right) - 4.5\]
    7. Using strategy rm

    8. Applied associate-/r*2.4

      \[\leadsto \left(\left(3 + \color{blue}{\frac{\frac{2}{r}}{r}}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{\frac{1 - v}{w}}{w \cdot r}}{r}}\right) - 4.5\]
    9. Using strategy rm

    10. Applied *-un-lft-identity2.4

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{\frac{1 - v}{w}}{w \cdot r}}{\color{blue}{1 \cdot r}}}\right) - 4.5\]

    11. Applied div-inv2.4

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{\color{blue}{\left(1 - v\right) \cdot \frac{1}{w}}}{w \cdot r}}{1 \cdot r}}\right) - 4.5\]

    12. Applied times-frac2.4

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\color{blue}{\frac{1 - v}{w} \cdot \frac{\frac{1}{w}}{r}}}{1 \cdot r}}\right) - 4.5\]

    13. Applied times-frac0.8

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\color{blue}{\frac{\frac{1 - v}{w}}{1} \cdot \frac{\frac{\frac{1}{w}}{r}}{r}}}\right) - 4.5\]

    14. Applied associate-/r*0.8

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \color{blue}{\frac{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{1 - v}{w}}{1}}}{\frac{\frac{\frac{1}{w}}{r}}{r}}}\right) - 4.5\]

    15. Simplified0.8

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{\color{blue}{\frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{1 - v}{w}}}}{\frac{\frac{\frac{1}{w}}{r}}{r}}\right) - 4.5\]

    if 5.0115654096801183e-14 < r

    1. Initial program 14.3

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    2. Using strategy rm

    3. Applied associate-/l*7.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}}\right) - 4.5\]

    4. Simplified3.1

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\color{blue}{\frac{\frac{1 - v}{w \cdot \left(w \cdot r\right)}}{r}}}\right) - 4.5\]
    5. Using strategy rm

    6. Applied associate-/r*4.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\color{blue}{\frac{\frac{1 - v}{w}}{w \cdot r}}}{r}}\right) - 4.5\]
    7. Using strategy rm

    8. Applied associate-/r*4.4

      \[\leadsto \left(\left(3 + \color{blue}{\frac{\frac{2}{r}}{r}}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{\frac{1 - v}{w}}{w \cdot r}}{r}}\right) - 4.5\]
    9. Using strategy rm

    10. Applied frac-2neg4.4

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\color{blue}{\frac{-\frac{\frac{1 - v}{w}}{w \cdot r}}{-r}}}\right) - 4.5\]

    11. Simplified3.0

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\color{blue}{\frac{-\left(1 - v\right)}{w \cdot \left(r \cdot w\right)}}}{-r}}\right) - 4.5\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \le -2.943062400229215877571579017740335303393 \cdot 10^{176}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(\left(3 - 2 \cdot v\right) \cdot 0.125\right) \cdot \left(\left(\left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right) \cdot \left(w \cdot \left(w \cdot r\right)\right)\right) \cdot \sqrt[3]{r}\right)}{1 - v}\right) - 4.5\\ \mathbf{elif}\;r \le 5.011565409680118343325145261599835434747 \cdot 10^{-14}:\\ \;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{\frac{1 - v}{w}}}{\frac{\frac{\frac{1}{w}}{r}}{r}}\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{\frac{2}{r}}{r} + 3\right) - \frac{\left(3 - 2 \cdot v\right) \cdot 0.125}{-\frac{\frac{1 - v}{w \cdot \left(w \cdot r\right)}}{-r}}\right) - 4.5\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))