Average Error: 9.0 → 0.1
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{x + 1} \cdot \frac{x}{y} + \frac{x}{x + 1} \cdot 1\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{x + 1} \cdot \frac{x}{y} + \frac{x}{x + 1} \cdot 1
double f(double x, double y) {
        double r1003562 = x;
        double r1003563 = y;
        double r1003564 = r1003562 / r1003563;
        double r1003565 = 1.0;
        double r1003566 = r1003564 + r1003565;
        double r1003567 = r1003562 * r1003566;
        double r1003568 = r1003562 + r1003565;
        double r1003569 = r1003567 / r1003568;
        return r1003569;
}
↓
double f(double x, double y) {
        double r1003570 = x;
        double r1003571 = 1.0;
        double r1003572 = r1003570 + r1003571;
        double r1003573 = r1003570 / r1003572;
        double r1003574 = y;
        double r1003575 = r1003570 / r1003574;
        double r1003576 = r1003573 * r1003575;
        double r1003577 = r1003573 * r1003571;
        double r1003578 = r1003576 + r1003577;
        return r1003578;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.0
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. Using strategy rm

  7. Applied distribute-lft-in0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

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

  (/ (* x (+ (/ x y) 1)) (+ x 1)))