Average Error: 0.0 → 0.0
Time: 54.0s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\frac{x}{y + x} - \frac{1}{\frac{y + x}{y}}}\]
\frac{x + y}{x - y}
↓
\frac{1}{\frac{x}{y + x} - \frac{1}{\frac{y + x}{y}}}
double f(double x, double y) {
        double r17324228 = x;
        double r17324229 = y;
        double r17324230 = r17324228 + r17324229;
        double r17324231 = r17324228 - r17324229;
        double r17324232 = r17324230 / r17324231;
        return r17324232;
}
↓
double f(double x, double y) {
        double r17324233 = 1.0;
        double r17324234 = x;
        double r17324235 = y;
        double r17324236 = r17324235 + r17324234;
        double r17324237 = r17324234 / r17324236;
        double r17324238 = r17324236 / r17324235;
        double r17324239 = r17324233 / r17324238;
        double r17324240 = r17324237 - r17324239;
        double r17324241 = r17324233 / r17324240;
        return r17324241;
}

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x + y}}}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}}\]
  6. Using strategy rm

  7. Applied clear-num0.0

    \[\leadsto \frac{1}{\frac{x}{x + y} - \color{blue}{\frac{1}{\frac{x + y}{y}}}}\]

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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