Average Error: 9.0 → 0.1
Time: 14.0s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)
double f(double x, double y) {
        double r35013194 = x;
        double r35013195 = y;
        double r35013196 = r35013194 / r35013195;
        double r35013197 = 1.0;
        double r35013198 = r35013196 + r35013197;
        double r35013199 = r35013194 * r35013198;
        double r35013200 = r35013194 + r35013197;
        double r35013201 = r35013199 / r35013200;
        return r35013201;
}
↓
double f(double x, double y) {
        double r35013202 = x;
        double r35013203 = 1.0;
        double r35013204 = r35013203 + r35013202;
        double r35013205 = r35013202 / r35013204;
        double r35013206 = y;
        double r35013207 = r35013202 / r35013206;
        double r35013208 = r35013203 + r35013207;
        double r35013209 = r35013205 * r35013208;
        return r35013209;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +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)))