Average Error: 14.4 → 2.6
Time: 48.0s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot y}{\sqrt[3]{z}}\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot y}{\sqrt[3]{z}}\right)
double f(double x, double y, double z, double t) {
        double r5341486 = x;
        double r5341487 = y;
        double r5341488 = z;
        double r5341489 = r5341487 / r5341488;
        double r5341490 = t;
        double r5341491 = r5341489 * r5341490;
        double r5341492 = r5341491 / r5341490;
        double r5341493 = r5341486 * r5341492;
        return r5341493;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r5341494 = x;
        double r5341495 = cbrt(r5341494);
        double r5341496 = cbrt(r5341495);
        double r5341497 = z;
        double r5341498 = cbrt(r5341497);
        double r5341499 = r5341496 / r5341498;
        double r5341500 = r5341495 * r5341495;
        double r5341501 = r5341500 / r5341498;
        double r5341502 = cbrt(r5341500);
        double r5341503 = y;
        double r5341504 = r5341502 * r5341503;
        double r5341505 = r5341504 / r5341498;
        double r5341506 = r5341501 * r5341505;
        double r5341507 = r5341499 * r5341506;
        return r5341507;
}

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 14.4

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

  2. Simplified6.2

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

  4. Applied *-un-lft-identity6.2

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

  5. Applied add-cube-cbrt7.0

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

  6. Applied times-frac7.0

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

  7. Applied associate-*r*5.6

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

  8. Simplified5.6

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

  10. Applied add-cube-cbrt5.8

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

  11. Applied add-cube-cbrt5.8

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

  12. Applied cbrt-prod5.9

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

  13. Applied times-frac5.9

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

  14. Applied associate-*r*4.7

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

  15. Simplified2.6

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

  16. Final simplification2.6

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

Reproduce

herbie shell --seed 2019165 +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)))