Average Error: 13.1 → 0.9
Time: 43.8s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(3 - v \cdot 2\right) \cdot \left(\sqrt[3]{\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\left(\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}\right) \cdot \sqrt[3]{0.125}}}{\sqrt[3]{1 - v}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}}\right) \cdot \left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)\right)\right)\]
\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
↓
\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(3 - v \cdot 2\right) \cdot \left(\sqrt[3]{\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\left(\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}\right) \cdot \sqrt[3]{0.125}}}{\sqrt[3]{1 - v}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}}\right) \cdot \left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)\right)\right)
double f(double v, double w, double r) {
        double r2190858 = 3.0;
        double r2190859 = 2.0;
        double r2190860 = r;
        double r2190861 = r2190860 * r2190860;
        double r2190862 = r2190859 / r2190861;
        double r2190863 = r2190858 + r2190862;
        double r2190864 = 0.125;
        double r2190865 = v;
        double r2190866 = r2190859 * r2190865;
        double r2190867 = r2190858 - r2190866;
        double r2190868 = r2190864 * r2190867;
        double r2190869 = w;
        double r2190870 = r2190869 * r2190869;
        double r2190871 = r2190870 * r2190860;
        double r2190872 = r2190871 * r2190860;
        double r2190873 = r2190868 * r2190872;
        double r2190874 = 1.0;
        double r2190875 = r2190874 - r2190865;
        double r2190876 = r2190873 / r2190875;
        double r2190877 = r2190863 - r2190876;
        double r2190878 = 4.5;
        double r2190879 = r2190877 - r2190878;
        return r2190879;
}
↓
double f(double v, double w, double r) {
        double r2190880 = 2.0;
        double r2190881 = r;
        double r2190882 = r2190881 * r2190881;
        double r2190883 = r2190880 / r2190882;
        double r2190884 = 3.0;
        double r2190885 = 4.5;
        double r2190886 = r2190884 - r2190885;
        double r2190887 = r2190883 + r2190886;
        double r2190888 = v;
        double r2190889 = r2190888 * r2190880;
        double r2190890 = r2190884 - r2190889;
        double r2190891 = 0.125;
        double r2190892 = cbrt(r2190891);
        double r2190893 = 1.0;
        double r2190894 = r2190893 - r2190888;
        double r2190895 = cbrt(r2190894);
        double r2190896 = r2190892 / r2190895;
        double r2190897 = cbrt(r2190896);
        double r2190898 = r2190892 * r2190892;
        double r2190899 = r2190898 * r2190892;
        double r2190900 = cbrt(r2190899);
        double r2190901 = r2190900 / r2190895;
        double r2190902 = cbrt(r2190901);
        double r2190903 = r2190897 * r2190902;
        double r2190904 = r2190890 * r2190903;
        double r2190905 = r2190904 * r2190897;
        double r2190906 = w;
        double r2190907 = r2190906 * r2190881;
        double r2190908 = r2190896 * r2190907;
        double r2190909 = r2190908 * r2190908;
        double r2190910 = r2190905 * r2190909;
        double r2190911 = r2190887 - r2190910;
        return r2190911;
}

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. Initial program 13.1

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

  2. Simplified7.0

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

  4. Applied add-cube-cbrt7.0

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

  5. Applied add-cube-cbrt7.2

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

  6. Applied times-frac7.2

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

  7. Applied associate-*r*7.3

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

  8. Simplified3.0

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

  10. Applied add-cube-cbrt3.1

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

  11. Applied associate-*r*3.1

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

  12. Simplified1.7

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

  14. Applied associate-*l*0.9

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

  16. Applied add-cbrt-cube0.9

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

  17. Final simplification0.9

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

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))