Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left(e^{\frac{x + y}{x - y}}\right)\]
\frac{x + y}{x - y}
↓
\log \left(e^{\frac{x + y}{x - y}}\right)
double f(double x, double y) {
        double r502651 = x;
        double r502652 = y;
        double r502653 = r502651 + r502652;
        double r502654 = r502651 - r502652;
        double r502655 = r502653 / r502654;
        return r502655;
}
↓
double f(double x, double y) {
        double r502656 = x;
        double r502657 = y;
        double r502658 = r502656 + r502657;
        double r502659 = r502656 - r502657;
        double r502660 = r502658 / r502659;
        double r502661 = exp(r502660);
        double r502662 = log(r502661);
        return r502662;
}

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

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

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

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