Average Error: 9.0 → 0.1
Time: 12.6s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}
double f(double x, double y) {
        double r40411062 = x;
        double r40411063 = y;
        double r40411064 = r40411062 / r40411063;
        double r40411065 = 1.0;
        double r40411066 = r40411064 + r40411065;
        double r40411067 = r40411062 * r40411066;
        double r40411068 = r40411062 + r40411065;
        double r40411069 = r40411067 / r40411068;
        return r40411069;
}
↓
double f(double x, double y) {
        double r40411070 = x;
        double r40411071 = 1.0;
        double r40411072 = r40411071 + r40411070;
        double r40411073 = y;
        double r40411074 = r40411070 / r40411073;
        double r40411075 = r40411071 + r40411074;
        double r40411076 = r40411072 / r40411075;
        double r40411077 = r40411070 / r40411076;
        return r40411077;
}

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

    \[\leadsto \frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019172 
(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)))