Average Error: 8.7 → 0.1
Time: 3.4s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)
double f(double x, double y) {
        double r1017712 = x;
        double r1017713 = y;
        double r1017714 = r1017712 / r1017713;
        double r1017715 = 1.0;
        double r1017716 = r1017714 + r1017715;
        double r1017717 = r1017712 * r1017716;
        double r1017718 = r1017712 + r1017715;
        double r1017719 = r1017717 / r1017718;
        return r1017719;
}
↓
double f(double x, double y) {
        double r1017720 = x;
        double r1017721 = 1.0;
        double r1017722 = r1017720 + r1017721;
        double r1017723 = r1017720 / r1017722;
        double r1017724 = y;
        double r1017725 = r1017720 / r1017724;
        double r1017726 = r1017725 + r1017721;
        double r1017727 = r1017723 * r1017726;
        return r1017727;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.7
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 8.7

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

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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)))