Average Error: 14.5 → 2.0
Time: 14.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\frac{y}{\frac{\sqrt[3]{z}}{\sqrt[3]{x}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{x}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{x}}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\frac{y}{\frac{\sqrt[3]{z}}{\sqrt[3]{x}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{x}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{x}}}
double f(double x, double y, double z, double t) {
        double r3396511 = x;
        double r3396512 = y;
        double r3396513 = z;
        double r3396514 = r3396512 / r3396513;
        double r3396515 = t;
        double r3396516 = r3396514 * r3396515;
        double r3396517 = r3396516 / r3396515;
        double r3396518 = r3396511 * r3396517;
        return r3396518;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3396519 = y;
        double r3396520 = z;
        double r3396521 = cbrt(r3396520);
        double r3396522 = x;
        double r3396523 = cbrt(r3396522);
        double r3396524 = r3396521 / r3396523;
        double r3396525 = r3396524 * r3396524;
        double r3396526 = r3396519 / r3396525;
        double r3396527 = r3396526 / r3396524;
        return r3396527;
}

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. Simplified5.8

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

  4. Applied associate-*r/5.9

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

  6. Applied associate-/l*5.8

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

  8. Applied add-cube-cbrt6.6

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

  9. Applied add-cube-cbrt6.7

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

  10. Applied times-frac6.7

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

  11. Applied associate-/r*1.9

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

  12. Simplified2.0

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

  13. Final simplification2.0

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

Reproduce

herbie shell --seed 2019164 +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)))