Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\frac{y}{2} \cdot x - \frac{z}{8}\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\frac{y}{2} \cdot x - \frac{z}{8}
double f(double x, double y, double z) {
        double r11775151 = x;
        double r11775152 = y;
        double r11775153 = r11775151 * r11775152;
        double r11775154 = 2.0;
        double r11775155 = r11775153 / r11775154;
        double r11775156 = z;
        double r11775157 = 8.0;
        double r11775158 = r11775156 / r11775157;
        double r11775159 = r11775155 - r11775158;
        return r11775159;
}
↓
double f(double x, double y, double z) {
        double r11775160 = y;
        double r11775161 = 2.0;
        double r11775162 = r11775160 / r11775161;
        double r11775163 = x;
        double r11775164 = r11775162 * r11775163;
        double r11775165 = z;
        double r11775166 = 8.0;
        double r11775167 = r11775165 / r11775166;
        double r11775168 = r11775164 - r11775167;
        return r11775168;
}

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

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} - \frac{z}{8}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} - \frac{z}{8}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{2} - \frac{z}{8}\]

  6. Final simplification0.0

    \[\leadsto \frac{y}{2} \cdot x - \frac{z}{8}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))