Average Error: 9.0 → 0.1
Time: 2.9s
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 r1145005 = x;
        double r1145006 = y;
        double r1145007 = r1145005 / r1145006;
        double r1145008 = 1.0;
        double r1145009 = r1145007 + r1145008;
        double r1145010 = r1145005 * r1145009;
        double r1145011 = r1145005 + r1145008;
        double r1145012 = r1145010 / r1145011;
        return r1145012;
}
↓
double f(double x, double y) {
        double r1145013 = x;
        double r1145014 = 1.0;
        double r1145015 = r1145013 + r1145014;
        double r1145016 = y;
        double r1145017 = r1145013 / r1145016;
        double r1145018 = r1145017 + r1145014;
        double r1145019 = r1145015 / r1145018;
        double r1145020 = r1145013 / r1145019;
        return r1145020;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(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)))