Average Error: 9.4 → 0.1
Time: 3.2s
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 r893246 = x;
        double r893247 = y;
        double r893248 = r893246 / r893247;
        double r893249 = 1.0;
        double r893250 = r893248 + r893249;
        double r893251 = r893246 * r893250;
        double r893252 = r893246 + r893249;
        double r893253 = r893251 / r893252;
        return r893253;
}
↓
double f(double x, double y) {
        double r893254 = x;
        double r893255 = 1.0;
        double r893256 = r893254 + r893255;
        double r893257 = y;
        double r893258 = r893254 / r893257;
        double r893259 = r893258 + r893255;
        double r893260 = r893256 / r893259;
        double r893261 = r893254 / r893260;
        return r893261;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.4
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.4

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2020003 
(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)))