Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)\]
\frac{x - y}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)
double f(double x, double y) {
        double r1105431 = x;
        double r1105432 = y;
        double r1105433 = r1105431 - r1105432;
        double r1105434 = r1105431 + r1105432;
        double r1105435 = r1105433 / r1105434;
        return r1105435;
}
↓
double f(double x, double y) {
        double r1105436 = x;
        double r1105437 = y;
        double r1105438 = r1105436 + r1105437;
        double r1105439 = r1105436 / r1105438;
        double r1105440 = r1105437 / r1105438;
        double r1105441 = exp(r1105440);
        double r1105442 = log(r1105441);
        double r1105443 = r1105439 - r1105442;
        double r1105444 = expm1(r1105443);
        double r1105445 = log1p(r1105444);
        return r1105445;
}

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. Using strategy rm

  7. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)}\]

  8. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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)))