Average Error: 9.5 → 0.1
Time: 21.7s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}
double f(double x, double y) {
        double r34030409 = x;
        double r34030410 = y;
        double r34030411 = r34030409 / r34030410;
        double r34030412 = 1.0;
        double r34030413 = r34030411 + r34030412;
        double r34030414 = r34030409 * r34030413;
        double r34030415 = r34030409 + r34030412;
        double r34030416 = r34030414 / r34030415;
        return r34030416;
}
↓
double f(double x, double y) {
        double r34030417 = x;
        double r34030418 = 1.0;
        double r34030419 = r34030418 + r34030417;
        double r34030420 = y;
        double r34030421 = r34030417 / r34030420;
        double r34030422 = r34030418 + r34030421;
        double r34030423 = r34030419 / r34030422;
        double r34030424 = r34030417 / r34030423;
        return r34030424;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

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

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

Reproduce

herbie shell --seed 2019171 +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)))