Average Error: 9.5 → 0.1
Time: 21.4s
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 r42853592 = x;
        double r42853593 = y;
        double r42853594 = r42853592 / r42853593;
        double r42853595 = 1.0;
        double r42853596 = r42853594 + r42853595;
        double r42853597 = r42853592 * r42853596;
        double r42853598 = r42853592 + r42853595;
        double r42853599 = r42853597 / r42853598;
        return r42853599;
}
↓
double f(double x, double y) {
        double r42853600 = x;
        double r42853601 = 1.0;
        double r42853602 = r42853601 + r42853600;
        double r42853603 = y;
        double r42853604 = r42853600 / r42853603;
        double r42853605 = r42853601 + r42853604;
        double r42853606 = r42853602 / r42853605;
        double r42853607 = r42853600 / r42853606;
        return r42853607;
}

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

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

Reproduce

herbie shell --seed 2019171 
(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)))