Average Error: 0.4 → 0.2
Time: 8.9s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{y + x}}{\frac{1}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{y + x}}{\frac{1}{100}}
double f(double x, double y) {
        double r880032 = x;
        double r880033 = 100.0;
        double r880034 = r880032 * r880033;
        double r880035 = y;
        double r880036 = r880032 + r880035;
        double r880037 = r880034 / r880036;
        return r880037;
}
↓
double f(double x, double y) {
        double r880038 = x;
        double r880039 = y;
        double r880040 = r880039 + r880038;
        double r880041 = r880038 / r880040;
        double r880042 = 1.0;
        double r880043 = 100.0;
        double r880044 = r880042 / r880043;
        double r880045 = r880041 / r880044;
        return r880045;
}

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 associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

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

  6. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{\frac{1}{100}}}\]

  7. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{x}{y + x}}}{\frac{1}{100}}\]

  8. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y + x}}{\frac{1}{100}}\]

Reproduce

herbie shell --seed 2020047 
(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)))