Average Error: 8.0 → 0.0
Time: 3.0s
Precision: binary64
Cost: 448
\[\frac{x \cdot y}{y + 1}\]
↓
\[x \cdot \frac{y}{y + 1}\]
\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 (x * y) / (y + 1.0);
}
↓
double code(double x, double y) {
	return x * (y / (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

Original8.0
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Alternatives

Alternative 1
Error0.1
Cost1090
\[\begin{array}{l} \mathbf{if}\;y \leq -1.5694996696535266 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 377651835409134.2:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 2
Error0.7
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0003074357708648 \lor \neg \left(y \leq 0.9940051049383496\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(1 - y\right)\\ \end{array}\]
Alternative 3
Error1.1
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0003074357708648 \lor \neg \left(y \leq 1.3326255057572964\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]
Alternative 4
Error1.4
Cost834
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0003074357708648:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.9940051049383496:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 5
Error24.3
Cost706
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0003074357708648:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6086501547041264 \cdot 10^{-17}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 6
Error54.1
Cost64
\[0\]
Alternative 7
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 8.0

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

  3. Applied *-un-lft-identity_binary64_191748.0

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

  4. Applied times-frac_binary64_191800.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(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)))