Average Error: 14.2 → 1.5
Time: 19.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right) \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right)\right) \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right) \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right)\right) \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \sqrt[3]{x}\right)
double f(double x, double y, double z, double t) {
        double r3080951 = x;
        double r3080952 = y;
        double r3080953 = z;
        double r3080954 = r3080952 / r3080953;
        double r3080955 = t;
        double r3080956 = r3080954 * r3080955;
        double r3080957 = r3080956 / r3080955;
        double r3080958 = r3080951 * r3080957;
        return r3080958;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3080959 = y;
        double r3080960 = cbrt(r3080959);
        double r3080961 = z;
        double r3080962 = cbrt(r3080961);
        double r3080963 = r3080960 / r3080962;
        double r3080964 = x;
        double r3080965 = cbrt(r3080964);
        double r3080966 = r3080963 * r3080965;
        double r3080967 = r3080966 * r3080966;
        double r3080968 = r3080967 * r3080966;
        return r3080968;
}

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 14.2

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

  2. Simplified5.8

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

  4. Applied *-un-lft-identity5.8

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

  5. Applied add-cube-cbrt6.6

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

  6. Applied times-frac6.6

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

  7. Applied associate-*l*5.4

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

  9. Applied *-un-lft-identity5.4

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

  10. Applied associate-*l*5.4

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

  11. Simplified5.8

    \[\leadsto 1 \cdot \color{blue}{\frac{y}{\frac{z}{x}}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt6.6

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

  14. Applied add-cube-cbrt6.8

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

  15. Applied times-frac6.8

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

  16. Applied add-cube-cbrt6.9

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

  17. Applied times-frac2.1

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

  18. Simplified1.5

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

  19. Simplified1.5

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

  20. Final simplification1.5

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

Reproduce

herbie shell --seed 2019132 +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)))