Average Error: 15.1 → 2.6
Time: 20.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \left(\frac{y}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}}\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \left(\frac{y}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}}\right)
double f(double x, double y, double z, double t) {
        double r4817281 = x;
        double r4817282 = y;
        double r4817283 = z;
        double r4817284 = r4817282 / r4817283;
        double r4817285 = t;
        double r4817286 = r4817284 * r4817285;
        double r4817287 = r4817286 / r4817285;
        double r4817288 = r4817281 * r4817287;
        return r4817288;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4817289 = x;
        double r4817290 = cbrt(r4817289);
        double r4817291 = z;
        double r4817292 = cbrt(r4817291);
        double r4817293 = r4817290 / r4817292;
        double r4817294 = y;
        double r4817295 = r4817294 / r4817292;
        double r4817296 = r4817290 * r4817290;
        double r4817297 = r4817296 / r4817292;
        double r4817298 = r4817295 * r4817297;
        double r4817299 = r4817293 * r4817298;
        return r4817299;
}

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 15.1

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

  2. Simplified5.9

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

  4. Applied add-cube-cbrt6.7

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

  5. Applied *-un-lft-identity6.7

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

  6. Applied times-frac6.7

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

  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. Simplified5.5

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

  10. Applied *-un-lft-identity5.5

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

  11. Applied cbrt-prod5.5

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

  12. Applied add-cube-cbrt5.7

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

  13. Applied times-frac5.7

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

  14. Applied associate-*r*4.6

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

  15. Simplified2.6

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

  16. Final simplification2.6

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))