Average Error: 8.1 → 0.1
Time: 2.0s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\frac{x}{\frac{y + 1}{y}}\]
\frac{x \cdot y}{y + 1}
↓
\frac{x}{\frac{y + 1}{y}}
double f(double x, double y) {
        double r605953 = x;
        double r605954 = y;
        double r605955 = r605953 * r605954;
        double r605956 = 1.0;
        double r605957 = r605954 + r605956;
        double r605958 = r605955 / r605957;
        return r605958;
}
↓
double f(double x, double y) {
        double r605959 = x;
        double r605960 = y;
        double r605961 = 1.0;
        double r605962 = r605960 + r605961;
        double r605963 = r605962 / r605960;
        double r605964 = r605959 / r605963;
        return r605964;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.1
Target0.0
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 8.1

    \[\frac{x \cdot y}{y + 1}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1)))