Average Error: 15.0 → 2.0
Time: 4.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r124269 = x;
        double r124270 = y;
        double r124271 = z;
        double r124272 = r124270 / r124271;
        double r124273 = t;
        double r124274 = r124272 * r124273;
        double r124275 = r124274 / r124273;
        double r124276 = r124269 * r124275;
        return r124276;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r124277 = x;
        double r124278 = y;
        double r124279 = cbrt(r124278);
        double r124280 = r124279 * r124279;
        double r124281 = z;
        double r124282 = cbrt(r124281);
        double r124283 = r124282 * r124282;
        double r124284 = cbrt(r124283);
        double r124285 = cbrt(r124282);
        double r124286 = r124284 * r124285;
        double r124287 = r124286 * r124282;
        double r124288 = r124280 / r124287;
        double r124289 = r124277 * r124288;
        double r124290 = r124279 / r124282;
        double r124291 = r124289 * r124290;
        return r124291;
}

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 15.0

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

  2. Simplified6.4

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

  4. Applied add-cube-cbrt7.2

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

  5. Applied add-cube-cbrt7.4

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

  6. Applied times-frac7.4

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

  7. Applied associate-*r*2.0

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

  9. Applied add-cube-cbrt2.0

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

  10. Applied cbrt-prod2.0

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

  11. Final simplification2.0

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

Reproduce

herbie shell --seed 2020062 
(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)))