Average Error: 9.0 → 0.1
Time: 8.5s
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 r770252 = x;
        double r770253 = y;
        double r770254 = r770252 / r770253;
        double r770255 = 1.0;
        double r770256 = r770254 + r770255;
        double r770257 = r770252 * r770256;
        double r770258 = r770252 + r770255;
        double r770259 = r770257 / r770258;
        return r770259;
}
↓
double f(double x, double y) {
        double r770260 = x;
        double r770261 = 1.0;
        double r770262 = r770260 + r770261;
        double r770263 = y;
        double r770264 = r770260 / r770263;
        double r770265 = r770264 + r770261;
        double r770266 = r770262 / r770265;
        double r770267 = r770260 / r770266;
        return r770267;
}

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

Original9.0
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.0

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2020024 
(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)))