Average Error: 14.7 → 2.6
Time: 1.2m
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r22468386 = x;
        double r22468387 = y;
        double r22468388 = z;
        double r22468389 = r22468387 / r22468388;
        double r22468390 = t;
        double r22468391 = r22468389 * r22468390;
        double r22468392 = r22468391 / r22468390;
        double r22468393 = r22468386 * r22468392;
        return r22468393;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r22468394 = x;
        double r22468395 = cbrt(r22468394);
        double r22468396 = z;
        double r22468397 = cbrt(r22468396);
        double r22468398 = r22468395 / r22468397;
        double r22468399 = y;
        double r22468400 = r22468399 / r22468397;
        double r22468401 = r22468398 * r22468400;
        double r22468402 = r22468395 * r22468395;
        double r22468403 = r22468402 / r22468397;
        double r22468404 = r22468401 * r22468403;
        return r22468404;
}

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 14.7

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

  2. Simplified5.9

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

  4. Applied add-cube-cbrt6.7

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

  5. Applied times-frac5.5

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

  7. Applied add-cube-cbrt5.7

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

  8. Applied times-frac5.7

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

  9. Applied associate-*l*2.6

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

  10. Final simplification2.6

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

Reproduce

herbie shell --seed 2019125 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))