Average Error: 14.1 → 3.3
Time: 29.1s
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 r4862188 = x;
        double r4862189 = y;
        double r4862190 = z;
        double r4862191 = r4862189 / r4862190;
        double r4862192 = t;
        double r4862193 = r4862191 * r4862192;
        double r4862194 = r4862193 / r4862192;
        double r4862195 = r4862188 * r4862194;
        return r4862195;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4862196 = y;
        double r4862197 = z;
        double r4862198 = cbrt(r4862197);
        double r4862199 = r4862196 / r4862198;
        double r4862200 = cbrt(r4862199);
        double r4862201 = r4862200 * r4862200;
        double r4862202 = cbrt(r4862198);
        double r4862203 = r4862202 * r4862202;
        double r4862204 = r4862201 / r4862203;
        double r4862205 = cbrt(r4862204);
        double r4862206 = r4862205 * r4862205;
        double r4862207 = r4862198 * r4862198;
        double r4862208 = cbrt(r4862207);
        double r4862209 = cbrt(r4862208);
        double r4862210 = r4862206 / r4862209;
        double r4862211 = r4862205 / r4862209;
        double r4862212 = r4862200 / r4862202;
        double r4862213 = r4862212 / r4862209;
        double r4862214 = x;
        double r4862215 = r4862214 / r4862202;
        double r4862216 = r4862213 * r4862215;
        double r4862217 = r4862211 * r4862216;
        double r4862218 = r4862210 * r4862217;
        return r4862218;
}

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)))