Average Error: 9.0 → 0.1
Time: 16.5s
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 r23851917 = x;
        double r23851918 = y;
        double r23851919 = r23851917 / r23851918;
        double r23851920 = 1.0;
        double r23851921 = r23851919 + r23851920;
        double r23851922 = r23851917 * r23851921;
        double r23851923 = r23851917 + r23851920;
        double r23851924 = r23851922 / r23851923;
        return r23851924;
}
↓
double f(double x, double y) {
        double r23851925 = x;
        double r23851926 = 1.0;
        double r23851927 = r23851926 + r23851925;
        double r23851928 = y;
        double r23851929 = r23851925 / r23851928;
        double r23851930 = r23851926 + r23851929;
        double r23851931 = r23851927 / r23851930;
        double r23851932 = r23851925 / r23851931;
        return r23851932;
}

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 +o rules:numerics
(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)))