Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{\frac{x}{y + x} \cdot \left(\frac{x}{y + x} \cdot \frac{x}{y + x}\right) - \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}{\frac{x}{y + x} \cdot \frac{x}{y + x} + \left(\frac{x}{y + x} + \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}\]
\frac{x - y}{x + y}
↓
\frac{\frac{x}{y + x} \cdot \left(\frac{x}{y + x} \cdot \frac{x}{y + x}\right) - \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}{\frac{x}{y + x} \cdot \frac{x}{y + x} + \left(\frac{x}{y + x} + \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}
double f(double x, double y) {
        double r39783986 = x;
        double r39783987 = y;
        double r39783988 = r39783986 - r39783987;
        double r39783989 = r39783986 + r39783987;
        double r39783990 = r39783988 / r39783989;
        return r39783990;
}
↓
double f(double x, double y) {
        double r39783991 = x;
        double r39783992 = y;
        double r39783993 = r39783992 + r39783991;
        double r39783994 = r39783991 / r39783993;
        double r39783995 = r39783994 * r39783994;
        double r39783996 = r39783994 * r39783995;
        double r39783997 = r39783992 / r39783993;
        double r39783998 = r39783997 * r39783997;
        double r39783999 = r39783998 * r39783997;
        double r39784000 = r39783996 - r39783999;
        double r39784001 = r39783994 + r39783997;
        double r39784002 = r39784001 * r39783997;
        double r39784003 = r39783995 + r39784002;
        double r39784004 = r39784000 / r39784003;
        return r39784004;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

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

  3. Applied div-sub0.0

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

  5. Applied flip3--0.0

    \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{3} - {\left(\frac{y}{x + y}\right)}^{3}}{\frac{x}{x + y} \cdot \frac{x}{x + y} + \left(\frac{y}{x + y} \cdot \frac{y}{x + y} + \frac{x}{x + y} \cdot \frac{y}{x + y}\right)}}\]

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

    \[\leadsto \frac{\frac{x}{y + x} \cdot \left(\frac{x}{y + x} \cdot \frac{x}{y + x}\right) - \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}{\frac{x}{y + x} \cdot \frac{x}{y + x} + \left(\frac{x}{y + x} + \frac{y}{y + x}\right) \cdot \frac{y}{y + x}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))