Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)
double f(double x, double y) {
        double r850639 = x;
        double r850640 = y;
        double r850641 = r850639 - r850640;
        double r850642 = r850639 + r850640;
        double r850643 = r850641 / r850642;
        return r850643;
}
↓
double f(double x, double y) {
        double r850644 = x;
        double r850645 = y;
        double r850646 = r850644 + r850645;
        double r850647 = r850644 / r850646;
        double r850648 = r850645 / r850646;
        double r850649 = exp(r850648);
        double r850650 = log(r850649);
        double r850651 = r850647 - r850650;
        return r850651;
}

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 add-log-exp0.0

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

  6. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\]

Reproduce

herbie shell --seed 2019350 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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