Average Error: 9.5 → 0.2
Time: 22.0s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{\frac{x}{y} + 1}{\frac{x + 1}{x}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{\frac{x}{y} + 1}{\frac{x + 1}{x}}
double f(double x, double y) {
        double r552330 = x;
        double r552331 = y;
        double r552332 = r552330 / r552331;
        double r552333 = 1.0;
        double r552334 = r552332 + r552333;
        double r552335 = r552330 * r552334;
        double r552336 = r552330 + r552333;
        double r552337 = r552335 / r552336;
        return r552337;
}
↓
double f(double x, double y) {
        double r552338 = x;
        double r552339 = y;
        double r552340 = r552338 / r552339;
        double r552341 = 1.0;
        double r552342 = r552340 + r552341;
        double r552343 = r552338 + r552341;
        double r552344 = r552343 / r552338;
        double r552345 = r552342 / r552344;
        return r552345;
}

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

Derivation

  1. Initial program 9.5

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +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)))