Average Error: 8.9 → 0.1
Time: 4.6s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}
double f(double x, double y) {
        double r722367 = x;
        double r722368 = y;
        double r722369 = r722367 / r722368;
        double r722370 = 1.0;
        double r722371 = r722369 + r722370;
        double r722372 = r722367 * r722371;
        double r722373 = r722367 + r722370;
        double r722374 = r722372 / r722373;
        return r722374;
}
↓
double f(double x, double y) {
        double r722375 = x;
        double r722376 = 1.0;
        double r722377 = r722375 + r722376;
        double r722378 = y;
        double r722379 = r722375 / r722378;
        double r722380 = r722379 + r722376;
        double r722381 = r722377 / r722380;
        double r722382 = r722375 / r722381;
        return r722382;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.9
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 8.9

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

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

  (/ (* x (+ (/ x y) 1)) (+ x 1)))