Average Error: 14.1 → 3.3
Time: 28.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\right)
double f(double x, double y, double z, double t) {
        double r5420050 = x;
        double r5420051 = y;
        double r5420052 = z;
        double r5420053 = r5420051 / r5420052;
        double r5420054 = t;
        double r5420055 = r5420053 * r5420054;
        double r5420056 = r5420055 / r5420054;
        double r5420057 = r5420050 * r5420056;
        return r5420057;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r5420058 = y;
        double r5420059 = z;
        double r5420060 = cbrt(r5420059);
        double r5420061 = r5420058 / r5420060;
        double r5420062 = cbrt(r5420061);
        double r5420063 = r5420062 * r5420062;
        double r5420064 = cbrt(r5420060);
        double r5420065 = r5420064 * r5420064;
        double r5420066 = r5420063 / r5420065;
        double r5420067 = cbrt(r5420066);
        double r5420068 = r5420067 * r5420067;
        double r5420069 = r5420060 * r5420060;
        double r5420070 = cbrt(r5420069);
        double r5420071 = cbrt(r5420070);
        double r5420072 = r5420068 / r5420071;
        double r5420073 = r5420067 / r5420071;
        double r5420074 = r5420062 / r5420064;
        double r5420075 = r5420074 / r5420071;
        double r5420076 = x;
        double r5420077 = r5420076 / r5420064;
        double r5420078 = r5420075 * r5420077;
        double r5420079 = r5420073 * r5420078;
        double r5420080 = r5420072 * r5420079;
        return r5420080;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

    \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

  2. Simplified6.2

    \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt7.0

    \[\leadsto y \cdot \frac{x}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

  5. Applied *-un-lft-identity7.0

    \[\leadsto y \cdot \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]

  6. Applied times-frac7.0

    \[\leadsto y \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right)}\]

  7. Applied associate-*r*5.5

    \[\leadsto \color{blue}{\left(y \cdot \frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{x}{\sqrt[3]{z}}}\]

  8. Simplified5.4

    \[\leadsto \color{blue}{\frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}}} \cdot \frac{x}{\sqrt[3]{z}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt5.5

    \[\leadsto \frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}}\]

  11. Applied cbrt-prod5.6

    \[\leadsto \frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}} \cdot \frac{x}{\color{blue}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}\]

  12. Applied *-un-lft-identity5.6

    \[\leadsto \frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}} \cdot \frac{\color{blue}{1 \cdot x}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}\]

  13. Applied times-frac5.6

    \[\leadsto \frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)}\]

  14. Applied associate-*r*6.2

    \[\leadsto \color{blue}{\left(\frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}} \cdot \frac{1}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}}\]

  15. Simplified6.2

    \[\leadsto \color{blue}{\frac{\frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]
  16. Using strategy rm

  17. Applied add-cube-cbrt6.4

    \[\leadsto \frac{\frac{\frac{y}{\sqrt[3]{z}}}{\sqrt[3]{z}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]

  18. Applied add-cube-cbrt6.7

    \[\leadsto \frac{\frac{\frac{y}{\sqrt[3]{z}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]

  19. Applied add-cube-cbrt6.7

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}\right) \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}}{\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}}}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]

  20. Applied times-frac6.7

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}} \cdot \frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]

  21. Applied times-frac6.7

    \[\leadsto \color{blue}{\left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}\right)} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\]

  22. Applied associate-*l*3.3

    \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)}\]
  23. Using strategy rm

  24. Applied add-cube-cbrt3.3

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\]

  25. Applied times-frac3.3

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}\right)} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\]

  26. Applied associate-*l*3.3

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\right)}\]

  27. Final simplification3.3

    \[\leadsto \frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\sqrt[3]{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}} \cdot \sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \left(\frac{\frac{\sqrt[3]{\frac{y}{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}} \cdot \frac{x}{\sqrt[3]{\sqrt[3]{z}}}\right)\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))