Average Error: 0.4 → 0.2
Time: 7.5s
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 r553602 = x;
        double r553603 = 100.0;
        double r553604 = r553602 * r553603;
        double r553605 = y;
        double r553606 = r553602 + r553605;
        double r553607 = r553604 / r553606;
        return r553607;
}
↓
double f(double x, double y) {
        double r553608 = 100.0;
        double r553609 = x;
        double r553610 = y;
        double r553611 = r553609 + r553610;
        double r553612 = r553608 / r553611;
        double r553613 = r553612 * r553609;
        return r553613;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(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)))