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 r39189445 = x;
        double r39189446 = 100.0;
        double r39189447 = r39189445 * r39189446;
        double r39189448 = y;
        double r39189449 = r39189445 + r39189448;
        double r39189450 = r39189447 / r39189449;
        return r39189450;
}
↓
double f(double x, double y) {
        double r39189451 = 100.0;
        double r39189452 = x;
        double r39189453 = y;
        double r39189454 = r39189452 + r39189453;
        double r39189455 = r39189451 / r39189454;
        double r39189456 = r39189455 * r39189452;
        return r39189456;
}

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)))