Average Error: 8.5 → 0.1
Time: 13.0s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
↓
\[\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}
↓
\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}
double f(double x, double y) {
        double r43776141 = x;
        double r43776142 = y;
        double r43776143 = r43776141 / r43776142;
        double r43776144 = 1.0;
        double r43776145 = r43776143 + r43776144;
        double r43776146 = r43776141 * r43776145;
        double r43776147 = r43776141 + r43776144;
        double r43776148 = r43776146 / r43776147;
        return r43776148;
}
↓
double f(double x, double y) {
        double r43776149 = x;
        double r43776150 = 1.0;
        double r43776151 = r43776150 + r43776149;
        double r43776152 = y;
        double r43776153 = r43776149 / r43776152;
        double r43776154 = r43776150 + r43776153;
        double r43776155 = r43776151 / r43776154;
        double r43776156 = r43776149 / r43776155;
        return r43776156;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1.0}{\frac{x}{y} + 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1.0) (+ x 1.0)))

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