Average Error: 7.5 → 0.0
Time: 762.0ms
Precision: binary64
\[\frac{x \cdot y}{y + 1} \]
↓
\[x \cdot \frac{y}{1 + y} \]
\frac{x \cdot y}{y + 1}
↓
x \cdot \frac{y}{1 + y}

(FPCore (x y) :precision binary64 (/ (* x y) (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (* x (/ y (+ 1.0 y))))
double code(double x, double y) {
	return (x * y) / (y + 1.0);
}
↓
double code(double x, double y) {
	return x * (y / (1.0 + y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.5
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array} \]

Derivation

  1. Initial program 7.5

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

  2. Applied *-un-lft-identity_binary647.5

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot \left(y + 1\right)}} \]

  3. Applied times-frac_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022039 
(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 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1.0)))