Average Error: 0.5 → 0.2
Time: 15.0s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{100}{x + y} \cdot x\]
\frac{x \cdot 100}{x + y}
↓
\frac{100}{x + y} \cdot x
double f(double x, double y) {
        double r32515468 = x;
        double r32515469 = 100.0;
        double r32515470 = r32515468 * r32515469;
        double r32515471 = y;
        double r32515472 = r32515468 + r32515471;
        double r32515473 = r32515470 / r32515472;
        return r32515473;
}
↓
double f(double x, double y) {
        double r32515474 = 100.0;
        double r32515475 = x;
        double r32515476 = y;
        double r32515477 = r32515475 + r32515476;
        double r32515478 = r32515474 / r32515477;
        double r32515479 = r32515478 * r32515475;
        return r32515479;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.5
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.5

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.5

    \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{x + y}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{x} \cdot \frac{100}{x + y}\]

  6. Final simplification0.2

    \[\leadsto \frac{100}{x + y} \cdot x\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))