Average Error: 9.5 → 0.1
Time: 25.2s
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 r45777224 = x;
        double r45777225 = y;
        double r45777226 = r45777224 / r45777225;
        double r45777227 = 1.0;
        double r45777228 = r45777226 + r45777227;
        double r45777229 = r45777224 * r45777228;
        double r45777230 = r45777224 + r45777227;
        double r45777231 = r45777229 / r45777230;
        return r45777231;
}
↓
double f(double x, double y) {
        double r45777232 = x;
        double r45777233 = 1.0;
        double r45777234 = r45777232 + r45777233;
        double r45777235 = y;
        double r45777236 = r45777232 / r45777235;
        double r45777237 = r45777236 + r45777233;
        double r45777238 = r45777234 / r45777237;
        double r45777239 = r45777232 / r45777238;
        return r45777239;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019200 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

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

  (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))