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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 6

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot y + x\right) + y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y + x\right) + y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x + y \cdot \left(x + 1\right) \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ x (* y (+ x 1.0))))

C

assert(x < y);
double code(double x, double y) {
	return x + (y * (x + 1.0));
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * (x + 1.0d0))
end function

Java

assert x < y;
public static double code(double x, double y) {
	return x + (y * (x + 1.0));
}

Python

[x, y] = sort([x, y])
def code(x, y):
	return x + (y * (x + 1.0))

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(x + Float64(y * Float64(x + 1.0)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x + (y * (x + 1.0));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x + N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+290}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+249}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e+290)
   x
   (if (<= x -2.8e+249)
     (* y x)
     (if (<= x -1.85e-45) x (if (<= x 1.0) y (* y x))))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+290) {
		tmp = x;
	} else if (x <= -2.8e+249) {
		tmp = y * x;
	} else if (x <= -1.85e-45) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.15d+290)) then
        tmp = x
    else if (x <= (-2.8d+249)) then
        tmp = y * x
    else if (x <= (-1.85d-45)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+290) {
		tmp = x;
	} else if (x <= -2.8e+249) {
		tmp = y * x;
	} else if (x <= -1.85e-45) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.15e+290:
		tmp = x
	elif x <= -2.8e+249:
		tmp = y * x
	elif x <= -1.85e-45:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.15e+290)
		tmp = x;
	elseif (x <= -2.8e+249)
		tmp = Float64(y * x);
	elseif (x <= -1.85e-45)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.15e+290)
		tmp = x;
	elseif (x <= -2.8e+249)
		tmp = y * x;
	elseif (x <= -1.85e-45)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[x, -1.15e+290], x, If[LessEqual[x, -2.8e+249], N[(y * x), $MachinePrecision], If[LessEqual[x, -1.85e-45], x, If[LessEqual[x, 1.0], y, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000003e290 or -2.80000000000000018e249 < x < -1.85e-45

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.15000000000000003e290 < x < -2.80000000000000018e249 or 1 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.85e-45 < x < 1

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+290}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{+223}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1800000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e+290)
   x
   (if (<= x -1.16e+223) (* y x) (if (<= x 1800000.0) (+ x y) (* y x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+290) {
		tmp = x;
	} else if (x <= -1.16e+223) {
		tmp = y * x;
	} else if (x <= 1800000.0) {
		tmp = x + y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.15d+290)) then
        tmp = x
    else if (x <= (-1.16d+223)) then
        tmp = y * x
    else if (x <= 1800000.0d0) then
        tmp = x + y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+290) {
		tmp = x;
	} else if (x <= -1.16e+223) {
		tmp = y * x;
	} else if (x <= 1800000.0) {
		tmp = x + y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.15e+290:
		tmp = x
	elif x <= -1.16e+223:
		tmp = y * x
	elif x <= 1800000.0:
		tmp = x + y
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.15e+290)
		tmp = x;
	elseif (x <= -1.16e+223)
		tmp = Float64(y * x);
	elseif (x <= 1800000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.15e+290)
		tmp = x;
	elseif (x <= -1.16e+223)
		tmp = y * x;
	elseif (x <= 1800000.0)
		tmp = x + y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[x, -1.15e+290], x, If[LessEqual[x, -1.16e+223], N[(y * x), $MachinePrecision], If[LessEqual[x, 1800000.0], N[(x + y), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000003e290

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.15000000000000003e290 < x < -1.15999999999999993e223 or 1.8e6 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.15999999999999993e223 < x < 1.8e6

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -340:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y -340.0) (* y x) (if (<= y 1.0) (+ x y) (* y (+ 1.0 x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -340.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 + x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-340.0d0)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = x + y
    else
        tmp = y * (1.0d0 + x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= -340.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 + x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= -340.0:
		tmp = y * x
	elif y <= 1.0:
		tmp = x + y
	else:
		tmp = y * (1.0 + x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= -340.0)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 + x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -340.0)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = x + y;
	else
		tmp = y * (1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, -340.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], N[(x + y), $MachinePrecision], N[(y * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -340

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -340 < y < 1

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= x -2.2e-45) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.2d-45)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-45) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -2.2e-45:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -2.2e-45)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e-45)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[x, -2.2e-45], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999993e-45

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.19999999999999993e-45 < x

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 38.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 x)

C

assert(x < y);
double code(double x, double y) {
	return x;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

assert x < y;
public static double code(double x, double y) {
	return x;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	return x

Julia

x, y = sort([x, y])
function code(x, y)
	return x
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))