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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 7

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x \cdot y + x\right) + y \]
2. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft1-in 100.0%

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

   3. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y + 1, x, y\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + 1, x, y\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 100.0%

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

   2. distribute-lft1-in 100.0%

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

   3. *-commutative 100.0%

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

   4. +-commutative 100.0%

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

   5. associate-+r+ 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto x + \left(y + y \cdot x\right) \]
8. Add Preprocessing

Alternative 2: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* y x)
   (if (<= y 1.85e-59) x (if (<= y 3.4e+188) y (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.85e-59) {
		tmp = x;
	} else if (y <= 3.4e+188) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = y * x
    else if (y <= 1.85d-59) then
        tmp = x
    else if (y <= 3.4d+188) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * x;
	} else if (y <= 1.85e-59) {
		tmp = x;
	} else if (y <= 3.4e+188) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = y * x
	elif y <= 1.85e-59:
		tmp = x
	elif y <= 3.4e+188:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y * x);
	elseif (y <= 1.85e-59)
		tmp = x;
	elseif (y <= 3.4e+188)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = y * x;
	elseif (y <= 1.85e-59)
		tmp = x;
	elseif (y <= 3.4e+188)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.85e-59], x, If[LessEqual[y, 3.4e+188], y, N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.39999999999999995e188 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.1%

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

   5. Simplified 56.1%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in 56.1%

         \[\leadsto \color{blue}{y \cdot x + 1 \cdot x} \]

      2. *-un-lft-identity 56.1%

         \[\leadsto y \cdot x + \color{blue}{x} \]

   7. Applied egg-rr 56.1%

      \[\leadsto \color{blue}{y \cdot x + x} \]

   8. Taylor expanded in y around inf 55.3%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -1 < y < 1.85e-59

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.3%

      \[\leadsto \color{blue}{x} \]

   if 1.85e-59 < y < 3.39999999999999995e188

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 51.8%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-120) (+ x (* y x)) (if (<= x 1.0) y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-120) {
		tmp = x + (y * x);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-7d-120)) then
        tmp = x + (y * x)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7e-120) {
		tmp = x + (y * x);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e-120:
		tmp = x + (y * x)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-120)
		tmp = Float64(x + Float64(y * x));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e-120)
		tmp = x + (y * x);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-120], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7e-120

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 90.7%

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

   5. Simplified 90.7%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in 90.7%

         \[\leadsto \color{blue}{y \cdot x + 1 \cdot x} \]

      2. *-un-lft-identity 90.7%

         \[\leadsto y \cdot x + \color{blue}{x} \]

   7. Applied egg-rr 90.7%

      \[\leadsto \color{blue}{y \cdot x + x} \]

   if -7e-120 < x < 1

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{y} \]

   if 1 < x

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in 98.4%

         \[\leadsto \color{blue}{y \cdot x + 1 \cdot x} \]

      2. *-un-lft-identity 98.4%

         \[\leadsto y \cdot x + \color{blue}{x} \]

   7. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{y \cdot x + x} \]

   8. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e-120) (* x (+ y 1.0)) (if (<= x 1.0) y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e-120) {
		tmp = x * (y + 1.0);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-7d-120)) then
        tmp = x * (y + 1.0d0)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7e-120) {
		tmp = x * (y + 1.0);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e-120:
		tmp = x * (y + 1.0)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e-120)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e-120)
		tmp = x * (y + 1.0);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e-120], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7e-120

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 90.7%

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

   5. Simplified 90.7%

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

   if -7e-120 < x < 1

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{y} \]

   if 1 < x

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in 98.4%

         \[\leadsto \color{blue}{y \cdot x + 1 \cdot x} \]

      2. *-un-lft-identity 98.4%

         \[\leadsto y \cdot x + \color{blue}{x} \]

   7. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{y \cdot x + x} \]

   8. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.45e-58) (* x (+ y 1.0)) (+ y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.45e-58) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y + (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.45d-58) then
        tmp = x * (y + 1.0d0)
    else
        tmp = y + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.45e-58) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.45e-58:
		tmp = x * (y + 1.0)
	else:
		tmp = y + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.45e-58)
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.45e-58)
		tmp = x * (y + 1.0);
	else
		tmp = y + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.45e-58], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.44999999999999995e-58

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if 1.44999999999999995e-58 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.8%

      \[\leadsto \color{blue}{x \cdot y} + y \]
   4. Step-by-step derivation

      1. *-commutative 93.8%

         \[\leadsto \color{blue}{y \cdot x} + y \]

   5. Simplified 93.8%

      \[\leadsto \color{blue}{y \cdot x} + y \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -6.8e-120) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-120) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.8d-120)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-120) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.8e-120:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-120)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.8e-120)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.8e-120], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000002e-120

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.0%

      \[\leadsto \color{blue}{x} \]

   if -6.8000000000000002e-120 < x

   1. Initial program 100.0%

      \[\left(x \cdot y + x\right) + y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 50.4%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 39.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x \cdot y + x\right) + y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 40.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024150 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))