Average Error: 9.2 → 0.1
Time: 27.8s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
↓
\[\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}
↓
\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}
double f(double x, double y) {
        double r40993334 = x;
        double r40993335 = y;
        double r40993336 = r40993334 / r40993335;
        double r40993337 = 1.0;
        double r40993338 = r40993336 + r40993337;
        double r40993339 = r40993334 * r40993338;
        double r40993340 = r40993334 + r40993337;
        double r40993341 = r40993339 / r40993340;
        return r40993341;
}
↓
double f(double x, double y) {
        double r40993342 = x;
        double r40993343 = 1.0;
        double r40993344 = r40993343 + r40993342;
        double r40993345 = y;
        double r40993346 = r40993342 / r40993345;
        double r40993347 = r40993343 + r40993346;
        double r40993348 = r40993344 / r40993347;
        double r40993349 = r40993342 / r40993348;
        return r40993349;
}

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

Original9.2
Target0.1
Herbie0.1
\[\frac{x}{1.0} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 9.2

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1.0}{\frac{x}{y} + 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019165 
(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)))