Average Error: 9.5 → 0.1
Time: 13.6s
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 r40777934 = x;
        double r40777935 = y;
        double r40777936 = r40777934 / r40777935;
        double r40777937 = 1.0;
        double r40777938 = r40777936 + r40777937;
        double r40777939 = r40777934 * r40777938;
        double r40777940 = r40777934 + r40777937;
        double r40777941 = r40777939 / r40777940;
        return r40777941;
}
↓
double f(double x, double y) {
        double r40777942 = x;
        double r40777943 = 1.0;
        double r40777944 = r40777943 + r40777942;
        double r40777945 = y;
        double r40777946 = r40777942 / r40777945;
        double r40777947 = r40777943 + r40777946;
        double r40777948 = r40777944 / r40777947;
        double r40777949 = r40777942 / r40777948;
        return r40777949;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019170 +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)))