Average Error: 14.4 → 1.9
Time: 28.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(y \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(y \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right) \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)
double f(double x, double y, double z, double t) {
        double r20519991 = x;
        double r20519992 = y;
        double r20519993 = z;
        double r20519994 = r20519992 / r20519993;
        double r20519995 = t;
        double r20519996 = r20519994 * r20519995;
        double r20519997 = r20519996 / r20519995;
        double r20519998 = r20519991 * r20519997;
        return r20519998;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r20519999 = y;
        double r20520000 = x;
        double r20520001 = cbrt(r20520000);
        double r20520002 = z;
        double r20520003 = cbrt(r20520002);
        double r20520004 = r20520001 / r20520003;
        double r20520005 = r20519999 * r20520004;
        double r20520006 = r20520004 * r20520004;
        double r20520007 = r20520005 * r20520006;
        return r20520007;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  2. Simplified6.3

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

  4. Applied associate-/l*6.0

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

  6. Applied *-un-lft-identity6.0

    \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 \cdot y}}}\]

  7. Applied add-cube-cbrt6.8

    \[\leadsto \frac{x}{\frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{1 \cdot y}}\]

  8. Applied times-frac6.8

    \[\leadsto \frac{x}{\color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{y}}}\]

  9. Applied add-cube-cbrt7.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{y}}\]

  10. Applied times-frac3.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{z}}{y}}}\]

  11. Simplified3.1

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

  12. Simplified1.9

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

  13. Final simplification1.9

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

Reproduce

herbie shell --seed 2019128 +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)))