Average Error: 13.9 → 1.5
Time: 11.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{x \cdot \sqrt[3]{1}} \cdot \sqrt[3]{x \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \left(\frac{\sqrt[3]{x \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{x \cdot \sqrt[3]{1}} \cdot \sqrt[3]{x \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}} \cdot \left(\frac{\sqrt[3]{x \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{z}}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) (((double) (((double) (y / z)) * t)) / t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (((double) cbrt(((double) (x * ((double) cbrt(1.0)))))) * ((double) cbrt(((double) (x * ((double) cbrt(1.0)))))))) / ((double) cbrt(((double) (((double) cbrt(z)) * ((double) cbrt(z)))))))) * ((double) (((double) (((double) cbrt(((double) (x * ((double) cbrt(1.0)))))) / ((double) cbrt(((double) cbrt(z)))))) * ((double) (((double) (((double) cbrt(y)) * ((double) cbrt(y)))) / ((double) cbrt(z)))))))) * ((double) (((double) cbrt(y)) / ((double) cbrt(z))))));
}

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 13.9

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

  2. Simplified6.1

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

  4. Applied add-cube-cbrt6.9

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

  5. Applied add-cube-cbrt7.1

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

  6. Applied times-frac7.1

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

  7. Applied associate-*r*2.0

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

  9. Applied *-un-lft-identity2.0

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

  10. Applied cbrt-prod2.0

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

  11. Applied associate-*r*2.0

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

  12. Applied *-un-lft-identity2.0

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

  13. Applied cbrt-prod2.0

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

  14. Applied *-un-lft-identity2.0

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

  15. Applied cbrt-prod2.0

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

  16. Applied swap-sqr2.0

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

  17. Applied times-frac2.0

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

  18. Applied associate-*r*2.5

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

  19. Simplified2.5

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

  21. Applied add-cube-cbrt2.5

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

  22. Applied cbrt-prod2.6

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

  23. Applied add-cube-cbrt2.7

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

  24. Applied times-frac2.7

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

  25. Applied associate-*l*1.5

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

  26. Final simplification1.5

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))