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

Average Error: 0.0 → 0.0

Time: 6.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	19.7
Cost	1112

\[\begin{array}{l} t_0 := \left(1 + x\right) \cdot y\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	19.4
Cost	980

\[\begin{array}{l} t_0 := \left(1 + x\right) \cdot y\\ t_1 := \left(1 + y\right) \cdot x\\ \mathbf{if}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	24.2
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4
Error	28.5
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	36.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))