Average Error: 0.0 → 0.1
Time: 18.1s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}
double f(double x, double y) {
        double r535955 = x;
        double r535956 = y;
        double r535957 = r535955 - r535956;
        double r535958 = 2.0;
        double r535959 = r535955 + r535956;
        double r535960 = r535958 - r535959;
        double r535961 = r535957 / r535960;
        return r535961;
}
↓
double f(double x, double y) {
        double r535962 = 1.0;
        double r535963 = 2.0;
        double r535964 = x;
        double r535965 = r535963 / r535964;
        double r535966 = y;
        double r535967 = r535966 / r535964;
        double r535968 = r535962 + r535967;
        double r535969 = r535965 - r535968;
        double r535970 = r535962 / r535969;
        double r535971 = r535964 + r535966;
        double r535972 = r535963 - r535971;
        double r535973 = r535966 / r535972;
        double r535974 = r535970 - r535973;
        return r535974;
}

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
Herbie0.1
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
  4. Using strategy rm

  5. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x}}} - \frac{y}{2 - \left(x + y\right)}\]

  6. Taylor expanded around 0 0.1

    \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{1}{x} - \left(1 + \frac{y}{x}\right)}} - \frac{y}{2 - \left(x + y\right)}\]

  7. Simplified0.1

    \[\leadsto \frac{1}{\color{blue}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)}} - \frac{y}{2 - \left(x + y\right)}\]

  8. Final simplification0.1

    \[\leadsto \frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))