Average Error: 8.8 → 0.1
Time: 10.8s
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 r45029473 = x;
        double r45029474 = y;
        double r45029475 = r45029473 / r45029474;
        double r45029476 = 1.0;
        double r45029477 = r45029475 + r45029476;
        double r45029478 = r45029473 * r45029477;
        double r45029479 = r45029473 + r45029476;
        double r45029480 = r45029478 / r45029479;
        return r45029480;
}
↓
double f(double x, double y) {
        double r45029481 = x;
        double r45029482 = 1.0;
        double r45029483 = r45029482 + r45029481;
        double r45029484 = y;
        double r45029485 = r45029481 / r45029484;
        double r45029486 = r45029482 + r45029485;
        double r45029487 = r45029483 / r45029486;
        double r45029488 = r45029481 / r45029487;
        return r45029488;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.8
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.8

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  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 2019162 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1.0) (+ x 1.0)))

  (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))