Average Error: 12.2 → 0.3
Time: 24.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{3 - v \cdot 2}{\frac{1 - v}{r \cdot w} \cdot \frac{\frac{\frac{1}{r}}{w}}{0.125}}\right) - 4.5\]
\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(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{3 - v \cdot 2}{\frac{1 - v}{r \cdot w} \cdot \frac{\frac{\frac{1}{r}}{w}}{0.125}}\right) - 4.5
double f(double v, double w, double r) {
        double r1620826 = 3.0;
        double r1620827 = 2.0;
        double r1620828 = r;
        double r1620829 = r1620828 * r1620828;
        double r1620830 = r1620827 / r1620829;
        double r1620831 = r1620826 + r1620830;
        double r1620832 = 0.125;
        double r1620833 = v;
        double r1620834 = r1620827 * r1620833;
        double r1620835 = r1620826 - r1620834;
        double r1620836 = r1620832 * r1620835;
        double r1620837 = w;
        double r1620838 = r1620837 * r1620837;
        double r1620839 = r1620838 * r1620828;
        double r1620840 = r1620839 * r1620828;
        double r1620841 = r1620836 * r1620840;
        double r1620842 = 1.0;
        double r1620843 = r1620842 - r1620833;
        double r1620844 = r1620841 / r1620843;
        double r1620845 = r1620831 - r1620844;
        double r1620846 = 4.5;
        double r1620847 = r1620845 - r1620846;
        return r1620847;
}
↓
double f(double v, double w, double r) {
        double r1620848 = 3.0;
        double r1620849 = 2.0;
        double r1620850 = r;
        double r1620851 = r1620849 / r1620850;
        double r1620852 = r1620851 / r1620850;
        double r1620853 = r1620848 + r1620852;
        double r1620854 = v;
        double r1620855 = r1620854 * r1620849;
        double r1620856 = r1620848 - r1620855;
        double r1620857 = 1.0;
        double r1620858 = r1620857 - r1620854;
        double r1620859 = w;
        double r1620860 = r1620850 * r1620859;
        double r1620861 = r1620858 / r1620860;
        double r1620862 = r1620857 / r1620850;
        double r1620863 = r1620862 / r1620859;
        double r1620864 = 0.125;
        double r1620865 = r1620863 / r1620864;
        double r1620866 = r1620861 * r1620865;
        double r1620867 = r1620856 / r1620866;
        double r1620868 = r1620853 - r1620867;
        double r1620869 = 4.5;
        double r1620870 = r1620868 - r1620869;
        return r1620870;
}

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 12.2

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

  2. Simplified0.3

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

  4. Applied associate-/r*0.3

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

  6. Applied div-inv0.4

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

  7. Applied associate-/r*0.4

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

  9. Applied add-cube-cbrt0.4

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

  10. Applied times-frac0.3

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

  11. Simplified0.3

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

  12. Simplified0.3

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

  14. Applied *-un-lft-identity0.3

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

  15. Applied times-frac0.3

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

  16. Applied associate-/l*0.3

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

  17. Simplified0.3

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

  18. Final simplification0.3

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

Reproduce

herbie shell --seed 2019162 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))