Average Error: 9.0 → 0.1
Time: 2.8s
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 r855103 = x;
        double r855104 = y;
        double r855105 = r855103 / r855104;
        double r855106 = 1.0;
        double r855107 = r855105 + r855106;
        double r855108 = r855103 * r855107;
        double r855109 = r855103 + r855106;
        double r855110 = r855108 / r855109;
        return r855110;
}
↓
double f(double x, double y) {
        double r855111 = x;
        double r855112 = 1.0;
        double r855113 = r855111 + r855112;
        double r855114 = y;
        double r855115 = r855111 / r855114;
        double r855116 = r855115 + r855112;
        double r855117 = r855113 / r855116;
        double r855118 = r855111 / r855117;
        return r855118;
}

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 2020060 
(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)))