Average Error: 0.1 → 0.1
Time: 2.2s
Precision: binary64
Cost: 448
\[\frac{x + y}{y + y}\]
↓
\[\frac{x + y}{y + y}\]
\frac{x + y}{y + y}
↓
\frac{x + y}{y + y}
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))
↓
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))
double code(double x, double y) {
	return (x + y) / (y + y);
}
↓
double code(double x, double y) {
	return (x + y) / (y + 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

Original0.1
Target0.0
Herbie0.1
\[0.5 \cdot \frac{x}{y} + 0.5\]

Alternatives

Alternative 1
Error19.3
Cost1366
\[\begin{array}{l} \mathbf{if}\;y \leq -7.185736607712673 \cdot 10^{-44}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq -1.4695836432165667 \cdot 10^{-126} \lor \neg \left(y \leq -9.538543098076214 \cdot 10^{-177}\right) \land \left(y \leq 1.8923122223253836 \cdot 10^{-80} \lor \neg \left(y \leq 34.872192135791586\right) \land y \leq 2055727150675.5154\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array}\]
Alternative 2
Error19.4
Cost1366
\[\begin{array}{l} \mathbf{if}\;y \leq -1.3376001740133537 \cdot 10^{-43}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;y \leq -1.5232664493634675 \cdot 10^{-121} \lor \neg \left(y \leq -7.865311228066508 \cdot 10^{-177}\right) \land \left(y \leq 1.1157231824719229 \cdot 10^{-78} \lor \neg \left(y \leq 11.761591508070724\right) \land y \leq 34266237198.333717\right):\\ \;\;\;\;x \cdot \frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array}\]
Alternative 3
Error26.8
Cost64
\[0.5\]
Alternative 4
Error56.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))