Average Error: 14.9 → 2.0
Time: 24.6s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot x\right)
double f(double x, double y, double z, double t) {
        double r62247 = x;
        double r62248 = y;
        double r62249 = z;
        double r62250 = r62248 / r62249;
        double r62251 = t;
        double r62252 = r62250 * r62251;
        double r62253 = r62252 / r62251;
        double r62254 = r62247 * r62253;
        return r62254;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r62255 = y;
        double r62256 = cbrt(r62255);
        double r62257 = r62256 * r62256;
        double r62258 = z;
        double r62259 = cbrt(r62258);
        double r62260 = r62259 * r62259;
        double r62261 = r62257 / r62260;
        double r62262 = r62256 / r62259;
        double r62263 = x;
        double r62264 = r62262 * r62263;
        double r62265 = r62261 * r62264;
        return r62265;
}

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 14.9

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

  2. Simplified6.3

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

  4. Applied add-cube-cbrt7.1

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

  5. Applied add-cube-cbrt7.3

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

  6. Applied times-frac7.3

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

  7. Applied associate-*l*2.0

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

  8. Final simplification2.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))