Average Error: 15.1 → 2.1
Time: 11.4s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{x}}{z} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)\right)\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{x}}{z} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r82099 = x;
        double r82100 = y;
        double r82101 = z;
        double r82102 = r82100 / r82101;
        double r82103 = t;
        double r82104 = r82102 * r82103;
        double r82105 = r82104 / r82103;
        double r82106 = r82099 * r82105;
        return r82106;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r82107 = y;
        double r82108 = cbrt(r82107);
        double r82109 = x;
        double r82110 = cbrt(r82109);
        double r82111 = r82108 * r82110;
        double r82112 = z;
        double r82113 = r82111 / r82112;
        double r82114 = r82108 * r82108;
        double r82115 = r82110 * r82114;
        double r82116 = r82110 * r82115;
        double r82117 = r82113 * r82116;
        return r82117;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Derivation

  1. Initial program 15.1

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

  2. Simplified6.2

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

  4. Applied associate-/l*6.1

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

  6. Applied add-cube-cbrt6.9

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

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

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

  8. Applied times-frac6.9

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

  9. Applied add-cube-cbrt7.2

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

  10. Applied times-frac3.3

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

  11. Simplified3.3

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

  12. Simplified2.1

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

  13. Final simplification2.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))