Average Error: 8.6 → 0.1
Time: 11.6s
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 r37567261 = x;
        double r37567262 = y;
        double r37567263 = r37567261 / r37567262;
        double r37567264 = 1.0;
        double r37567265 = r37567263 + r37567264;
        double r37567266 = r37567261 * r37567265;
        double r37567267 = r37567261 + r37567264;
        double r37567268 = r37567266 / r37567267;
        return r37567268;
}
↓
double f(double x, double y) {
        double r37567269 = x;
        double r37567270 = 1.0;
        double r37567271 = r37567270 + r37567269;
        double r37567272 = y;
        double r37567273 = r37567269 / r37567272;
        double r37567274 = r37567270 + r37567273;
        double r37567275 = r37567271 / r37567274;
        double r37567276 = r37567269 / r37567275;
        return r37567276;
}

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

Original8.6
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.6

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  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 2019165 
(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)))