Average Error: 0.4 → 0.2
Time: 11.6s
Precision: 64
\[\frac{x \cdot 100.0}{x + y}\]
↓
\[\frac{\frac{x}{y + x}}{\frac{1}{100.0}}\]
\frac{x \cdot 100.0}{x + y}
↓
\frac{\frac{x}{y + x}}{\frac{1}{100.0}}
double f(double x, double y) {
        double r33033467 = x;
        double r33033468 = 100.0;
        double r33033469 = r33033467 * r33033468;
        double r33033470 = y;
        double r33033471 = r33033467 + r33033470;
        double r33033472 = r33033469 / r33033471;
        return r33033472;
}
↓
double f(double x, double y) {
        double r33033473 = x;
        double r33033474 = y;
        double r33033475 = r33033474 + r33033473;
        double r33033476 = r33033473 / r33033475;
        double r33033477 = 1.0;
        double r33033478 = 100.0;
        double r33033479 = r33033477 / r33033478;
        double r33033480 = r33033476 / r33033479;
        return r33033480;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100.0}{x + y}\]

Derivation

  1. Initial program 0.4

    \[\frac{x \cdot 100.0}{x + y}\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100.0}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100.0}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{\frac{1}{100.0}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y + x}}{\frac{1}{100.0}}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1) (/ 100.0 (+ x y)))

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