Average Error: 9.5 → 0.1
Time: 13.0s
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 r509780 = x;
        double r509781 = y;
        double r509782 = r509780 / r509781;
        double r509783 = 1.0;
        double r509784 = r509782 + r509783;
        double r509785 = r509780 * r509784;
        double r509786 = r509780 + r509783;
        double r509787 = r509785 / r509786;
        return r509787;
}
↓
double f(double x, double y) {
        double r509788 = x;
        double r509789 = 1.0;
        double r509790 = r509788 + r509789;
        double r509791 = y;
        double r509792 = r509788 / r509791;
        double r509793 = r509792 + r509789;
        double r509794 = r509790 / r509793;
        double r509795 = r509788 / r509794;
        return r509795;
}

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

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

Reproduce

herbie shell --seed 2019306 +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)))