Average Error: 0.0 → 0.0
Time: 54.2s
Precision: binary64
Cost: 448
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \left(x + y \cdot x\right)\]
\left(x \cdot y + x\right) + y
↓
y + \left(x + y \cdot x\right)
(FPCore (x y) :precision binary64 (+ (+ (* x y) x) y))
↓
(FPCore (x y) :precision binary64 (+ y (+ x (* y x))))
double code(double x, double y) {
	return ((x * y) + x) + y;
}
↓
double code(double x, double y) {
	return y + (x + (y * x));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error9.7
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -1.706181835159425 \cdot 10^{-49} \lor \neg \left(y \leq 1.2847169968971026 \cdot 10^{-12}\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array}\]
Alternative 2
Error9.7
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -9.261641250575342 \cdot 10^{-50} \lor \neg \left(y \leq 7.689496445623949 \cdot 10^{-13}\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 3
Error19.0
Cost706
\[\begin{array}{l} \mathbf{if}\;y \leq -9.261641250575342 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.378475912546423 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]
Alternative 4
Error36.1
Cost64
\[y\]

Error

Time

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + x\right) + y\]
  2. Using strategy rm

  3. Applied pow1_binary64_32080.0

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

  4. Taylor expanded around 0 0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto y + \left(x + y \cdot x\right)\]

Reproduce

herbie shell --seed 2021045 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))