Average Error: 14.7 → 2.8
Time: 19.7s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double t) {
        double r5072122 = x;
        double r5072123 = y;
        double r5072124 = z;
        double r5072125 = r5072123 / r5072124;
        double r5072126 = t;
        double r5072127 = r5072125 * r5072126;
        double r5072128 = r5072127 / r5072126;
        double r5072129 = r5072122 * r5072128;
        return r5072129;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r5072130 = y;
        double r5072131 = cbrt(r5072130);
        double r5072132 = z;
        double r5072133 = cbrt(r5072132);
        double r5072134 = r5072131 / r5072133;
        double r5072135 = x;
        double r5072136 = r5072135 / r5072133;
        double r5072137 = r5072134 * r5072136;
        double r5072138 = r5072131 * r5072131;
        double r5072139 = r5072138 / r5072133;
        double r5072140 = r5072137 * r5072139;
        return r5072140;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Simplified6.1

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

  4. Applied add-cube-cbrt6.9

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

  5. Applied *-un-lft-identity6.9

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

  6. Applied times-frac6.9

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

  7. Applied associate-*r*5.5

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

  8. Simplified5.5

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

  10. Applied add-cube-cbrt5.7

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

  11. Applied times-frac5.7

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

  12. Applied associate-*l*2.8

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

  13. Final simplification2.8

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))