Average Error: 13.0 → 7.0
Time: 20.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{2}{r \cdot r} + \left(\frac{\left(-0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{{\left(\sqrt[3]{1 - v}\right)}^{3}} + \left(3 - 4.5\right)\right)\]
\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
↓
\frac{2}{r \cdot r} + \left(\frac{\left(-0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{{\left(\sqrt[3]{1 - v}\right)}^{3}} + \left(3 - 4.5\right)\right)
double f(double v, double w, double r) {
        double r25837 = 3.0;
        double r25838 = 2.0;
        double r25839 = r;
        double r25840 = r25839 * r25839;
        double r25841 = r25838 / r25840;
        double r25842 = r25837 + r25841;
        double r25843 = 0.125;
        double r25844 = v;
        double r25845 = r25838 * r25844;
        double r25846 = r25837 - r25845;
        double r25847 = r25843 * r25846;
        double r25848 = w;
        double r25849 = r25848 * r25848;
        double r25850 = r25849 * r25839;
        double r25851 = r25850 * r25839;
        double r25852 = r25847 * r25851;
        double r25853 = 1.0;
        double r25854 = r25853 - r25844;
        double r25855 = r25852 / r25854;
        double r25856 = r25842 - r25855;
        double r25857 = 4.5;
        double r25858 = r25856 - r25857;
        return r25858;
}
↓
double f(double v, double w, double r) {
        double r25859 = 2.0;
        double r25860 = r;
        double r25861 = r25860 * r25860;
        double r25862 = r25859 / r25861;
        double r25863 = 0.125;
        double r25864 = 3.0;
        double r25865 = v;
        double r25866 = r25859 * r25865;
        double r25867 = r25864 - r25866;
        double r25868 = r25863 * r25867;
        double r25869 = -r25868;
        double r25870 = w;
        double r25871 = r25870 * r25860;
        double r25872 = fabs(r25871);
        double r25873 = sqrt(r25872);
        double r25874 = 4.0;
        double r25875 = pow(r25873, r25874);
        double r25876 = r25869 * r25875;
        double r25877 = 1.0;
        double r25878 = r25877 - r25865;
        double r25879 = cbrt(r25878);
        double r25880 = 3.0;
        double r25881 = pow(r25879, r25880);
        double r25882 = r25876 / r25881;
        double r25883 = 4.5;
        double r25884 = r25864 - r25883;
        double r25885 = r25882 + r25884;
        double r25886 = r25862 + r25885;
        return r25886;
}

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 13.0

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

  3. Applied add-sqr-sqrt13.1

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

  4. Simplified13.0

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

  5. Simplified6.8

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

  7. Applied *-un-lft-identity6.8

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied add-cube-cbrt0.5

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

  13. Applied add-sqr-sqrt0.6

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

  14. Applied unpow-prod-down0.6

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

  15. Applied times-frac0.6

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

  16. Applied associate-*r*0.6

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

  17. Simplified0.5

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

  18. Final simplification7.0

    \[\leadsto \frac{2}{r \cdot r} + \left(\frac{\left(-0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(\sqrt{\left|w \cdot r\right|}\right)}^{4}}{{\left(\sqrt[3]{1 - v}\right)}^{3}} + \left(3 - 4.5\right)\right)\]

Reproduce

herbie shell --seed 2019297 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))