Average Error: 9.0 → 0.1
Time: 3.4s
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 r1382107 = x;
        double r1382108 = y;
        double r1382109 = r1382107 / r1382108;
        double r1382110 = 1.0;
        double r1382111 = r1382109 + r1382110;
        double r1382112 = r1382107 * r1382111;
        double r1382113 = r1382107 + r1382110;
        double r1382114 = r1382112 / r1382113;
        return r1382114;
}
↓
double f(double x, double y) {
        double r1382115 = x;
        double r1382116 = 1.0;
        double r1382117 = r1382115 + r1382116;
        double r1382118 = y;
        double r1382119 = r1382115 / r1382118;
        double r1382120 = r1382119 + r1382116;
        double r1382121 = r1382117 / r1382120;
        double r1382122 = r1382115 / r1382121;
        return r1382122;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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)))