Average Error: 8.9 → 0.1
Time: 10.8s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}
double f(double x, double y) {
        double r1516408 = x;
        double r1516409 = y;
        double r1516410 = r1516408 / r1516409;
        double r1516411 = 1.0;
        double r1516412 = r1516410 + r1516411;
        double r1516413 = r1516408 * r1516412;
        double r1516414 = r1516408 + r1516411;
        double r1516415 = r1516413 / r1516414;
        return r1516415;
}
↓
double f(double x, double y) {
        double r1516416 = x;
        double r1516417 = 1.0;
        double r1516418 = r1516416 + r1516417;
        double r1516419 = y;
        double r1516420 = r1516416 / r1516419;
        double r1516421 = r1516420 + r1516417;
        double r1516422 = r1516418 / r1516421;
        double r1516423 = r1516416 / r1516422;
        return r1516423;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original8.9
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 8.9

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(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)))