Average Error: 9.5 → 0.1
Time: 4.6s
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 r681949 = x;
        double r681950 = y;
        double r681951 = r681949 / r681950;
        double r681952 = 1.0;
        double r681953 = r681951 + r681952;
        double r681954 = r681949 * r681953;
        double r681955 = r681949 + r681952;
        double r681956 = r681954 / r681955;
        return r681956;
}
↓
double f(double x, double y) {
        double r681957 = x;
        double r681958 = 1.0;
        double r681959 = r681957 + r681958;
        double r681960 = y;
        double r681961 = r681957 / r681960;
        double r681962 = r681961 + r681958;
        double r681963 = r681959 / r681962;
        double r681964 = r681957 / r681963;
        return r681964;
}

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 1978988140 
(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)))