Average Error: 0.4 → 0.2
Time: 33.1s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{100}{y + x} \cdot x\]
\frac{x \cdot 100}{x + y}
↓
\frac{100}{y + x} \cdot x
double f(double x, double y) {
        double r34568517 = x;
        double r34568518 = 100.0;
        double r34568519 = r34568517 * r34568518;
        double r34568520 = y;
        double r34568521 = r34568517 + r34568520;
        double r34568522 = r34568519 / r34568521;
        return r34568522;
}
↓
double f(double x, double y) {
        double r34568523 = 100.0;
        double r34568524 = y;
        double r34568525 = x;
        double r34568526 = r34568524 + r34568525;
        double r34568527 = r34568523 / r34568526;
        double r34568528 = r34568527 * r34568525;
        return r34568528;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

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

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

Reproduce

herbie shell --seed 2019200 +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)))