Average Error: 0.0 → 0.0
Time: 9.2s
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 r13238531 = x;
        double r13238532 = y;
        double r13238533 = r13238531 * r13238532;
        double r13238534 = 2.0;
        double r13238535 = r13238533 / r13238534;
        double r13238536 = z;
        double r13238537 = 8.0;
        double r13238538 = r13238536 / r13238537;
        double r13238539 = r13238535 - r13238538;
        return r13238539;
}
↓
double f(double x, double y, double z) {
        double r13238540 = y;
        double r13238541 = 2.0;
        double r13238542 = r13238540 / r13238541;
        double r13238543 = x;
        double r13238544 = r13238542 * r13238543;
        double r13238545 = z;
        double r13238546 = 8.0;
        double r13238547 = r13238545 / r13238546;
        double r13238548 = r13238544 - r13238547;
        return r13238548;
}

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)))