Average Error: 8.2 → 0.0
Time: 2.0s
Precision: binary64
\[\frac{x \cdot y}{y + 1}\]
↓
\[x \cdot \frac{y}{y + 1}\]
\frac{x \cdot y}{y + 1}
↓
x \cdot \frac{y}{y + 1}
(FPCore (x y) :precision binary64 (/ (* x y) (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (* x (/ y (+ y 1.0))))
double code(double x, double y) {
	return (((double) (x * y)) / ((double) (y + 1.0)));
}
↓
double code(double x, double y) {
	return ((double) (x * (y / ((double) (y + 1.0)))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.2
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 Error: 8.2 bits

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

  3. Applied *-un-lft-identityError: 8.2 bits

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

  4. Applied times-fracError: 0.0 bits

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

  5. SimplifiedError: 0.0 bits

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

  6. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020205 
(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)))