Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B

Average Error: 0.0 → 0.0

Time: 1.7s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x y) x) y))

↓

(FPCore (x y) :precision binary64 (+ y (+ x (* x y))))

C

double code(double x, double y) {
	return ((x * y) + x) + y;
}

↓

double code(double x, double y) {
	return y + (x + (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * y) + x) + y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x + (x * y))
end function

Java

public static double code(double x, double y) {
	return ((x * y) + x) + y;
}

↓

public static double code(double x, double y) {
	return y + (x + (x * y));
}

Python

def code(x, y):
	return ((x * y) + x) + y

↓

def code(x, y):
	return y + (x + (x * y))

Julia

function code(x, y)
	return Float64(Float64(Float64(x * y) + x) + y)
end

↓

function code(x, y)
	return Float64(y + Float64(x + Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * y) + x) + y;
end

↓

function tmp = code(x, y)
	tmp = y + (x + (x * y));
end

Wolfram

code[x_, y_] := N[(N[(N[(x * y), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision]

↓

code[x_, y_] := N[(y + N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	19.3
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-68} \lor \neg \left(y \leq 3.7 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	18.9
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-67} \lor \neg \left(y \leq 2.1 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	18.8
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-116}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-70} \lor \neg \left(y \leq 5 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	23.7
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-67}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	28.2
Cost	460

\[\begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6
Error	36.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022354 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))