Average Error: 14.1 → 2.0
Time: 30.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot y\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r3056287 = x;
        double r3056288 = y;
        double r3056289 = z;
        double r3056290 = r3056288 / r3056289;
        double r3056291 = t;
        double r3056292 = r3056290 * r3056291;
        double r3056293 = r3056292 / r3056291;
        double r3056294 = r3056287 * r3056293;
        return r3056294;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3056295 = x;
        double r3056296 = cbrt(r3056295);
        double r3056297 = z;
        double r3056298 = cbrt(r3056297);
        double r3056299 = r3056296 / r3056298;
        double r3056300 = y;
        double r3056301 = r3056299 * r3056300;
        double r3056302 = r3056296 * r3056296;
        double r3056303 = r3056298 * r3056298;
        double r3056304 = r3056302 / r3056303;
        double r3056305 = r3056301 * r3056304;
        return r3056305;
}

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 14.1

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

  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 add-cube-cbrt7.0

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

  6. Applied times-frac7.0

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

  7. Applied associate-*l*2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2019151 +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)))