Average Error: 9.0 → 0.1
Time: 12.4s
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 r44479384 = x;
        double r44479385 = y;
        double r44479386 = r44479384 / r44479385;
        double r44479387 = 1.0;
        double r44479388 = r44479386 + r44479387;
        double r44479389 = r44479384 * r44479388;
        double r44479390 = r44479384 + r44479387;
        double r44479391 = r44479389 / r44479390;
        return r44479391;
}
↓
double f(double x, double y) {
        double r44479392 = x;
        double r44479393 = 1.0;
        double r44479394 = r44479393 + r44479392;
        double r44479395 = r44479392 / r44479394;
        double r44479396 = y;
        double r44479397 = r44479392 / r44479396;
        double r44479398 = r44479393 + r44479397;
        double r44479399 = r44479395 * r44479398;
        return r44479399;
}

Error

Bits error versus x

Bits error versus y

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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 2019172 
(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)))