Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[x + \left(\left(\sqrt[3]{-1} \cdot x\right) \cdot y - \left(y \cdot z\right) \cdot \sqrt[3]{-1}\right)\]
x + y \cdot \left(z - x\right)
↓
x + \left(\left(\sqrt[3]{-1} \cdot x\right) \cdot y - \left(y \cdot z\right) \cdot \sqrt[3]{-1}\right)
double f(double x, double y, double z) {
        double r11896 = x;
        double r11897 = y;
        double r11898 = z;
        double r11899 = r11898 - r11896;
        double r11900 = r11897 * r11899;
        double r11901 = r11896 + r11900;
        return r11901;
}
↓
double f(double x, double y, double z) {
        double r11902 = x;
        double r11903 = -1.0;
        double r11904 = cbrt(r11903);
        double r11905 = r11904 * r11902;
        double r11906 = y;
        double r11907 = r11905 * r11906;
        double r11908 = z;
        double r11909 = r11906 * r11908;
        double r11910 = r11909 * r11904;
        double r11911 = r11907 - r11910;
        double r11912 = r11902 + r11911;
        return r11912;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]

  2. Simplified0.0

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

  4. Applied add-cbrt-cube18.1

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

  5. Applied add-cbrt-cube43.5

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

  6. Applied cbrt-unprod45.2

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

  7. Simplified26.8

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

  8. Taylor expanded around -inf 0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

    \[\leadsto x + \left(\left(\sqrt[3]{-1} \cdot x\right) \cdot y - \left(y \cdot z\right) \cdot \sqrt[3]{-1}\right)\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))