Average Error: 0.4 → 0.2
Time: 1.7s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[x \cdot \frac{100}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
x \cdot \frac{100}{x + y}
double f(double x, double y) {
        double r1328427 = x;
        double r1328428 = 100.0;
        double r1328429 = r1328427 * r1328428;
        double r1328430 = y;
        double r1328431 = r1328427 + r1328430;
        double r1328432 = r1328429 / r1328431;
        return r1328432;
}
↓
double f(double x, double y) {
        double r1328433 = x;
        double r1328434 = 100.0;
        double r1328435 = y;
        double r1328436 = r1328433 + r1328435;
        double r1328437 = r1328434 / r1328436;
        double r1328438 = r1328433 * r1328437;
        return r1328438;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

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

  3. Applied *-un-lft-identity0.4

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

  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

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ 100 (+ x y)))

  (/ (* x 100) (+ x y)))