Average Error: 14.5 → 2.2
Time: 47.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}}}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}}}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r4038012 = x;
        double r4038013 = y;
        double r4038014 = z;
        double r4038015 = r4038013 / r4038014;
        double r4038016 = t;
        double r4038017 = r4038015 * r4038016;
        double r4038018 = r4038017 / r4038016;
        double r4038019 = r4038012 * r4038018;
        return r4038019;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4038020 = x;
        double r4038021 = z;
        double r4038022 = cbrt(r4038021);
        double r4038023 = y;
        double r4038024 = cbrt(r4038023);
        double r4038025 = r4038022 / r4038024;
        double r4038026 = r4038020 / r4038025;
        double r4038027 = r4038026 / r4038022;
        double r4038028 = r4038024 * r4038024;
        double r4038029 = r4038028 / r4038022;
        double r4038030 = r4038027 * r4038029;
        return r4038030;
}

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 14.5

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

  2. Simplified6.0

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

  4. Applied add-cube-cbrt6.8

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

  5. Applied *-un-lft-identity6.8

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

  6. Applied times-frac6.8

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

  7. Applied associate-*l*5.4

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

  9. Applied associate-*l/5.4

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

  10. Simplified5.5

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

  12. Applied add-cube-cbrt5.7

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

  13. Applied *-un-lft-identity5.7

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

  14. Applied times-frac5.7

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

  15. Applied *-un-lft-identity5.7

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

  16. Applied times-frac4.4

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

  17. Applied times-frac2.2

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

  18. Simplified2.2

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

  19. Final simplification2.2

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))