Average Error: 9.0 → 0.1
Time: 11.6s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)
double f(double x, double y) {
        double r28284914 = x;
        double r28284915 = y;
        double r28284916 = r28284914 / r28284915;
        double r28284917 = 1.0;
        double r28284918 = r28284916 + r28284917;
        double r28284919 = r28284914 * r28284918;
        double r28284920 = r28284914 + r28284917;
        double r28284921 = r28284919 / r28284920;
        return r28284921;
}
↓
double f(double x, double y) {
        double r28284922 = x;
        double r28284923 = 1.0;
        double r28284924 = r28284923 + r28284922;
        double r28284925 = r28284922 / r28284924;
        double r28284926 = y;
        double r28284927 = r28284922 / r28284926;
        double r28284928 = r28284923 + r28284927;
        double r28284929 = r28284925 * r28284928;
        return r28284929;
}

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. Using strategy rm

  5. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))