Average Error: 12.8 → 0.6
Time: 35.7s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\frac{0.125}{\frac{1 - v}{3 - v \cdot 2}}}{\frac{\frac{1}{r \cdot w}}{\sqrt[3]{r}}} \cdot \left(\frac{1}{\frac{1}{w}} \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) - 4.5\]
\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{2}{r \cdot r}\right) - \frac{\frac{0.125}{\frac{1 - v}{3 - v \cdot 2}}}{\frac{\frac{1}{r \cdot w}}{\sqrt[3]{r}}} \cdot \left(\frac{1}{\frac{1}{w}} \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) - 4.5
double f(double v, double w, double r) {
        double r70946 = 3.0;
        double r70947 = 2.0;
        double r70948 = r;
        double r70949 = r70948 * r70948;
        double r70950 = r70947 / r70949;
        double r70951 = r70946 + r70950;
        double r70952 = 0.125;
        double r70953 = v;
        double r70954 = r70947 * r70953;
        double r70955 = r70946 - r70954;
        double r70956 = r70952 * r70955;
        double r70957 = w;
        double r70958 = r70957 * r70957;
        double r70959 = r70958 * r70948;
        double r70960 = r70959 * r70948;
        double r70961 = r70956 * r70960;
        double r70962 = 1.0;
        double r70963 = r70962 - r70953;
        double r70964 = r70961 / r70963;
        double r70965 = r70951 - r70964;
        double r70966 = 4.5;
        double r70967 = r70965 - r70966;
        return r70967;
}
↓
double f(double v, double w, double r) {
        double r70968 = 3.0;
        double r70969 = 2.0;
        double r70970 = r;
        double r70971 = r70970 * r70970;
        double r70972 = r70969 / r70971;
        double r70973 = r70968 + r70972;
        double r70974 = 0.125;
        double r70975 = 1.0;
        double r70976 = v;
        double r70977 = r70975 - r70976;
        double r70978 = r70976 * r70969;
        double r70979 = r70968 - r70978;
        double r70980 = r70977 / r70979;
        double r70981 = r70974 / r70980;
        double r70982 = 1.0;
        double r70983 = w;
        double r70984 = r70970 * r70983;
        double r70985 = r70982 / r70984;
        double r70986 = cbrt(r70970);
        double r70987 = r70985 / r70986;
        double r70988 = r70981 / r70987;
        double r70989 = r70982 / r70983;
        double r70990 = r70982 / r70989;
        double r70991 = r70986 * r70986;
        double r70992 = r70990 * r70991;
        double r70993 = r70988 * r70992;
        double r70994 = r70973 - r70993;
        double r70995 = 4.5;
        double r70996 = r70994 - r70995;
        return r70996;
}

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 12.8

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

  3. Applied associate-/l*8.4

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

  4. Simplified3.8

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

  6. Applied *-un-lft-identity3.8

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

  7. Applied div-inv3.8

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

  8. Applied times-frac2.3

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

  9. Applied associate-/r*2.3

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

  10. Simplified2.3

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

  12. Applied add-cube-cbrt2.5

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

  13. Applied add-cube-cbrt2.5

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

  14. Applied times-frac2.3

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

  15. Applied times-frac0.6

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

  16. Applied *-un-lft-identity0.6

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

  17. Applied *-un-lft-identity0.6

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

  18. Applied times-frac0.6

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

  19. Applied *-un-lft-identity0.6

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

  20. Applied times-frac0.6

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

  21. Applied times-frac0.6

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

  22. Simplified0.6

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

  23. Final simplification0.6

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

Reproduce

herbie shell --seed 2019196 
(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))