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

Average Error: 0.0 → 0.0

Time: 2.5s

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	23.7
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-43}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Error	11.0
Cost	850

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-17} \lor \neg \left(y \leq 6.8 \cdot 10^{-168} \lor \neg \left(y \leq 8 \cdot 10^{-129}\right) \land y \leq 1.85 \cdot 10^{-89}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	20.0
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-130} \lor \neg \left(y \leq 1.16 \cdot 10^{-88}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	27.2
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	36.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023045 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))