Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left(e^{\frac{y + x}{x - y}}\right)\]
\frac{x + y}{x - y}
↓
\log \left(e^{\frac{y + x}{x - y}}\right)
double f(double x, double y) {
        double r23584656 = x;
        double r23584657 = y;
        double r23584658 = r23584656 + r23584657;
        double r23584659 = r23584656 - r23584657;
        double r23584660 = r23584658 / r23584659;
        return r23584660;
}
↓
double f(double x, double y) {
        double r23584661 = y;
        double r23584662 = x;
        double r23584663 = r23584661 + r23584662;
        double r23584664 = r23584662 - r23584661;
        double r23584665 = r23584663 / r23584664;
        double r23584666 = exp(r23584665);
        double r23584667 = log(r23584666);
        return r23584667;
}

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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

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

  3. Applied add-log-exp0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

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