Average Error: 9.5 → 0.1
Time: 10.7s
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 r595563 = x;
        double r595564 = y;
        double r595565 = r595563 / r595564;
        double r595566 = 1.0;
        double r595567 = r595565 + r595566;
        double r595568 = r595563 * r595567;
        double r595569 = r595563 + r595566;
        double r595570 = r595568 / r595569;
        return r595570;
}
↓
double f(double x, double y) {
        double r595571 = x;
        double r595572 = 1.0;
        double r595573 = r595571 + r595572;
        double r595574 = y;
        double r595575 = r595571 / r595574;
        double r595576 = r595575 + r595572;
        double r595577 = r595573 / r595576;
        double r595578 = r595571 / r595577;
        return r595578;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019291 
(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)))