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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

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

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

FPCore

(FPCore (x y) :precision binary64 (+ x (* y (+ x 1.0))))

C

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

Fortran

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

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

Python

def code(x, y):
	return x + (y * (x + 1.0))

Julia

function code(x, y)
	return Float64(x + Float64(y * Float64(x + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y * (x + 1.0));
end

Wolfram

code[x_, y_] := N[(x + N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

   5. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

   8. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + y \cdot \left(x + 1\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+232}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* x y)
   (if (<= y 7e-93) x (if (<= y 3.7e+32) y (if (<= y 1.14e+232) (* x y) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 7e-93) {
		tmp = x;
	} else if (y <= 3.7e+32) {
		tmp = y;
	} else if (y <= 1.14e+232) {
		tmp = x * y;
	} 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 (y <= (-1.0d0)) then
        tmp = x * y
    else if (y <= 7d-93) then
        tmp = x
    else if (y <= 3.7d+32) then
        tmp = y
    else if (y <= 1.14d+232) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 7e-93) {
		tmp = x;
	} else if (y <= 3.7e+32) {
		tmp = y;
	} else if (y <= 1.14e+232) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 7e-93:
		tmp = x
	elif y <= 3.7e+32:
		tmp = y
	elif y <= 1.14e+232:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * y);
	elseif (y <= 7e-93)
		tmp = x;
	elseif (y <= 3.7e+32)
		tmp = y;
	elseif (y <= 1.14e+232)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * y;
	elseif (y <= 7e-93)
		tmp = x;
	elseif (y <= 3.7e+32)
		tmp = y;
	elseif (y <= 1.14e+232)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 7e-93], x, If[LessEqual[y, 3.7e+32], y, If[LessEqual[y, 1.14e+232], N[(x * y), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.7e32 < y < 1.14e232

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 57.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   7. Simplified 57.5%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   10. Simplified 57.1%

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

   if -1 < y < 7e-93

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 77.2%

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

   if 7e-93 < y < 3.7e32 or 1.14e232 < y

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 58.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+232}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -265000:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -265000.0)
   (* x (+ y 1.0))
   (if (<= x 3.2e-67) (+ x y) (* y (+ x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -265000.0) {
		tmp = x * (y + 1.0);
	} else if (x <= 3.2e-67) {
		tmp = x + y;
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-265000.0d0)) then
        tmp = x * (y + 1.0d0)
    else if (x <= 3.2d-67) then
        tmp = x + y
    else
        tmp = y * (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -265000.0) {
		tmp = x * (y + 1.0);
	} else if (x <= 3.2e-67) {
		tmp = x + y;
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -265000.0:
		tmp = x * (y + 1.0)
	elif x <= 3.2e-67:
		tmp = x + y
	else:
		tmp = y * (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -265000.0)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (x <= 3.2e-67)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -265000.0)
		tmp = x * (y + 1.0);
	elseif (x <= 3.2e-67)
		tmp = x + y;
	else
		tmp = y * (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -265000.0], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-67], N[(x + y), $MachinePrecision], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -265000

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   7. Simplified 100.0%

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

   if -265000 < x < 3.20000000000000021e-67

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 97.8%

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

   if 3.20000000000000021e-67 < x

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 56.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 56.6%

      \[\leadsto \color{blue}{y \cdot \left(x + 1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -265000:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -265000.0) (* x (+ y 1.0)) (if (<= x 3900.0) (+ x y) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -265000.0) {
		tmp = x * (y + 1.0);
	} else if (x <= 3900.0) {
		tmp = x + y;
	} else {
		tmp = x * 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 <= (-265000.0d0)) then
        tmp = x * (y + 1.0d0)
    else if (x <= 3900.0d0) then
        tmp = x + y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -265000.0) {
		tmp = x * (y + 1.0);
	} else if (x <= 3900.0) {
		tmp = x + y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -265000.0:
		tmp = x * (y + 1.0)
	elif x <= 3900.0:
		tmp = x + y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -265000.0)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (x <= 3900.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -265000.0)
		tmp = x * (y + 1.0);
	elseif (x <= 3900.0)
		tmp = x + y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -265000.0], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3900.0], N[(x + y), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -265000

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   7. Simplified 100.0%

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

   if -265000 < x < 3900

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 97.4%

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

   if 3900 < x

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 97.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   7. Simplified 97.5%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   10. Simplified 57.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -265000:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+204) (* x y) (if (<= x 3900.0) (+ x y) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+204) {
		tmp = x * y;
	} else if (x <= 3900.0) {
		tmp = x + y;
	} else {
		tmp = x * 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 <= (-2d+204)) then
        tmp = x * y
    else if (x <= 3900.0d0) then
        tmp = x + y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2e+204) {
		tmp = x * y;
	} else if (x <= 3900.0) {
		tmp = x + y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+204:
		tmp = x * y
	elif x <= 3900.0:
		tmp = x + y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+204)
		tmp = Float64(x * y);
	elseif (x <= 3900.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+204)
		tmp = x * y;
	elseif (x <= 3900.0)
		tmp = x + y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+204], N[(x * y), $MachinePrecision], If[LessEqual[x, 3900.0], N[(x + y), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999998e204 or 3900 < x

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 98.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   7. Simplified 98.2%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 59.2%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   10. Simplified 59.2%

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

   if -1.99999999999999998e204 < x < 3900

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 86.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.1 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7.1e-93) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.1e-93) {
		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 (y <= 7.1d-93) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7.1e-93) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.1e-93:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.1e-93)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7.1e-93)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.1e-93], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 7.1e-93

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 47.4%

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

   if 7.1e-93 < y

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 48.1%

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

Alternative 7: 38.0% 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. Step-by-step derivation

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + x \cdot y\right)}\right) \]

   5. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(x + 1\right) \cdot \color{blue}{y}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(x + 1\right)}\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(x + 1\right)}\right)\right) \]

   8. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 36.5%

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

Reproduce

herbie shell --seed 2024164 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))