Logistic regression 2

Percentage Accurate: 99.4% → 99.5%

Time: 9.7s

Alternatives: 9

Speedup: 1.0×

• could not determine a ground truth

  1. x = 7.58643144968146e+46
  2. y = 5.1912155786919385e+237

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (- (log (+ 1.0 (exp x))) (* x y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = log((1.0d0 + exp(x))) - (x * y)
end function

Java

public static double code(double x, double y) {
	return Math.log((1.0 + Math.exp(x))) - (x * y);
}

Python

def code(x, y):
	return math.log((1.0 + math.exp(x))) - (x * y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (- (log (+ 1.0 (exp x))) (* x y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = log((1.0d0 + exp(x))) - (x * y)
end function

Java

public static double code(double x, double y) {
	return Math.log((1.0 + Math.exp(x))) - (x * y);
}

Python

def code(x, y):
	return math.log((1.0 + math.exp(x))) - (x * y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{log1p}\left(e^{x}\right) - x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (log1p (exp x)) (* x y)))

C

double code(double x, double y) {
	return log1p(exp(x)) - (x * y);
}

Java

public static double code(double x, double y) {
	return Math.log1p(Math.exp(x)) - (x * y);
}

Python

def code(x, y):
	return math.log1p(math.exp(x)) - (x * y)

Julia

function code(x, y)
	return Float64(log1p(exp(x)) - Float64(x * y))
end

Wolfram

code[x_, y_] := N[(N[Log[1 + N[Exp[x], $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Final simplification 98.8%

   \[\leadsto \mathsf{log1p}\left(e^{x}\right) - x \cdot y \]

Alternative 2: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-87} \lor \neg \left(x \leq 6.5 \cdot 10^{-78}\right) \land x \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;\log \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.2e-5)
   (* x (- y))
   (if (or (<= x 3.4e-87) (and (not (<= x 6.5e-78)) (<= x 6.5e-10)))
     (log (+ x 2.0))
     (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.2e-5) {
		tmp = x * -y;
	} else if ((x <= 3.4e-87) || (!(x <= 6.5e-78) && (x <= 6.5e-10))) {
		tmp = log((x + 2.0));
	} else {
		tmp = x * (0.5 - 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 <= (-5.2d-5)) then
        tmp = x * -y
    else if ((x <= 3.4d-87) .or. (.not. (x <= 6.5d-78)) .and. (x <= 6.5d-10)) then
        tmp = log((x + 2.0d0))
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.2e-5) {
		tmp = x * -y;
	} else if ((x <= 3.4e-87) || (!(x <= 6.5e-78) && (x <= 6.5e-10))) {
		tmp = Math.log((x + 2.0));
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.2e-5:
		tmp = x * -y
	elif (x <= 3.4e-87) or (not (x <= 6.5e-78) and (x <= 6.5e-10)):
		tmp = math.log((x + 2.0))
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.2e-5)
		tmp = Float64(x * Float64(-y));
	elseif ((x <= 3.4e-87) || (!(x <= 6.5e-78) && (x <= 6.5e-10)))
		tmp = log(Float64(x + 2.0));
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.2e-5)
		tmp = x * -y;
	elseif ((x <= 3.4e-87) || (~((x <= 6.5e-78)) && (x <= 6.5e-10)))
		tmp = log((x + 2.0));
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.2e-5], N[(x * (-y)), $MachinePrecision], If[Or[LessEqual[x, 3.4e-87], And[N[Not[LessEqual[x, 6.5e-78]], $MachinePrecision], LessEqual[x, 6.5e-10]]], N[Log[N[(x + 2.0), $MachinePrecision]], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.19999999999999968e-5

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-rgt-neg-out 98.8%

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

   6. Simplified 98.8%

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

   if -5.19999999999999968e-5 < x < 3.3999999999999999e-87 or 6.5000000000000003e-78 < x < 6.5000000000000003e-10

   1. Initial program 99.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]
   4. Step-by-step derivation

      1. add-log-exp 83.1%

         \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   6. Taylor expanded in y around 0 81.7%

      \[\leadsto \log \color{blue}{\left(1 + e^{x}\right)} \]

   7. Taylor expanded in x around 0 81.1%

      \[\leadsto \log \color{blue}{\left(2 + x\right)} \]

   if 3.3999999999999999e-87 < x < 6.5000000000000003e-78 or 6.5000000000000003e-10 < x

   1. Initial program 87.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 88.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

   5. Taylor expanded in x around inf 85.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-87} \lor \neg \left(x \leq 6.5 \cdot 10^{-78}\right) \land x \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;\log \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 3: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-86} \lor \neg \left(x \leq 6.6 \cdot 10^{-77}\right) \land x \leq 8 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6e-5)
   (* x (- y))
   (if (or (<= x 1.1e-86) (and (not (<= x 6.6e-77)) (<= x 8e-9)))
     (log1p (+ x 1.0))
     (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-5) {
		tmp = x * -y;
	} else if ((x <= 1.1e-86) || (!(x <= 6.6e-77) && (x <= 8e-9))) {
		tmp = log1p((x + 1.0));
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-5) {
		tmp = x * -y;
	} else if ((x <= 1.1e-86) || (!(x <= 6.6e-77) && (x <= 8e-9))) {
		tmp = Math.log1p((x + 1.0));
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6e-5:
		tmp = x * -y
	elif (x <= 1.1e-86) or (not (x <= 6.6e-77) and (x <= 8e-9)):
		tmp = math.log1p((x + 1.0))
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6e-5)
		tmp = Float64(x * Float64(-y));
	elseif ((x <= 1.1e-86) || (!(x <= 6.6e-77) && (x <= 8e-9)))
		tmp = log1p(Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6e-5], N[(x * (-y)), $MachinePrecision], If[Or[LessEqual[x, 1.1e-86], And[N[Not[LessEqual[x, 6.6e-77]], $MachinePrecision], LessEqual[x, 8e-9]]], N[Log[1 + N[(x + 1.0), $MachinePrecision]], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e-5

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-rgt-neg-out 98.8%

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

   6. Simplified 98.8%

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

   if -4.6e-5 < x < 1.1000000000000001e-86 or 6.59999999999999982e-77 < x < 8.0000000000000005e-9

   1. Initial program 99.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]
   4. Step-by-step derivation

      1. add-log-exp 83.1%

         \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   6. Taylor expanded in y around 0 81.7%

      \[\leadsto \log \color{blue}{\left(1 + e^{x}\right)} \]

   7. Taylor expanded in x around 0 81.1%

      \[\leadsto \log \color{blue}{\left(2 + x\right)} \]
   8. Step-by-step derivation

      1. log1p-expm1-u 81.1%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(2 + x\right)\right)\right)} \]

      2. expm1-udef 81.1%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{e^{\log \left(2 + x\right)} - 1}\right) \]

      3. add-exp-log 81.1%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{\left(2 + x\right)} - 1\right) \]

      4. +-commutative 81.1%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{\left(x + 2\right)} - 1\right) \]

   9. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\left(x + 2\right) - 1\right)} \]
   10. Step-by-step derivation

       1. associate--l+ 81.1%

          \[\leadsto \mathsf{log1p}\left(\color{blue}{x + \left(2 - 1\right)}\right) \]

       2. metadata-eval 81.1%

          \[\leadsto \mathsf{log1p}\left(x + \color{blue}{1}\right) \]

   11. Simplified 81.1%

       \[\leadsto \color{blue}{\mathsf{log1p}\left(x + 1\right)} \]

   if 1.1000000000000001e-86 < x < 6.59999999999999982e-77 or 8.0000000000000005e-9 < x

   1. Initial program 87.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 88.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

   5. Taylor expanded in x around inf 85.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-86} \lor \neg \left(x \leq 6.6 \cdot 10^{-77}\right) \land x \leq 8 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-77} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6e-5)
   (* x (- y))
   (if (<= x 1.7e-86)
     (+ (log 2.0) (* x 0.5))
     (if (or (<= x 4.5e-77) (not (<= x 3.3e-9)))
       (* x (- 0.5 y))
       (log1p (+ x 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-5) {
		tmp = x * -y;
	} else if (x <= 1.7e-86) {
		tmp = log(2.0) + (x * 0.5);
	} else if ((x <= 4.5e-77) || !(x <= 3.3e-9)) {
		tmp = x * (0.5 - y);
	} else {
		tmp = log1p((x + 1.0));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-5) {
		tmp = x * -y;
	} else if (x <= 1.7e-86) {
		tmp = Math.log(2.0) + (x * 0.5);
	} else if ((x <= 4.5e-77) || !(x <= 3.3e-9)) {
		tmp = x * (0.5 - y);
	} else {
		tmp = Math.log1p((x + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6e-5:
		tmp = x * -y
	elif x <= 1.7e-86:
		tmp = math.log(2.0) + (x * 0.5)
	elif (x <= 4.5e-77) or not (x <= 3.3e-9):
		tmp = x * (0.5 - y)
	else:
		tmp = math.log1p((x + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6e-5)
		tmp = Float64(x * Float64(-y));
	elseif (x <= 1.7e-86)
		tmp = Float64(log(2.0) + Float64(x * 0.5));
	elseif ((x <= 4.5e-77) || !(x <= 3.3e-9))
		tmp = Float64(x * Float64(0.5 - y));
	else
		tmp = log1p(Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6e-5], N[(x * (-y)), $MachinePrecision], If[LessEqual[x, 1.7e-86], N[(N[Log[2.0], $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.5e-77], N[Not[LessEqual[x, 3.3e-9]], $MachinePrecision]], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision], N[Log[1 + N[(x + 1.0), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.6e-5

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-rgt-neg-out 98.8%

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

   6. Simplified 98.8%

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

   if -4.6e-5 < x < 1.7e-86

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 99.3%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

   5. Taylor expanded in y around 0 82.9%

      \[\leadsto \color{blue}{0.5 \cdot x} + \log 2 \]

   if 1.7e-86 < x < 4.5000000000000001e-77 or 3.30000000000000018e-9 < x

   1. Initial program 87.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 88.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

   5. Taylor expanded in x around inf 85.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x} \]

   if 4.5000000000000001e-77 < x < 3.30000000000000018e-9

   1. Initial program 99.8%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 99.9%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]
   4. Step-by-step derivation

      1. add-log-exp 68.4%

         \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   5. Applied egg-rr 68.4%

      \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \log \color{blue}{\left(1 + e^{x}\right)} \]

   7. Taylor expanded in x around 0 67.5%

      \[\leadsto \log \color{blue}{\left(2 + x\right)} \]
   8. Step-by-step derivation

      1. log1p-expm1-u 67.5%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(2 + x\right)\right)\right)} \]

      2. expm1-udef 67.5%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{e^{\log \left(2 + x\right)} - 1}\right) \]

      3. add-exp-log 67.5%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{\left(2 + x\right)} - 1\right) \]

      4. +-commutative 67.5%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{\left(x + 2\right)} - 1\right) \]

   9. Applied egg-rr 67.5%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\left(x + 2\right) - 1\right)} \]
   10. Step-by-step derivation

       1. associate--l+ 67.6%

          \[\leadsto \mathsf{log1p}\left(\color{blue}{x + \left(2 - 1\right)}\right) \]

       2. metadata-eval 67.6%

          \[\leadsto \mathsf{log1p}\left(x + \color{blue}{1}\right) \]

   11. Simplified 67.6%

       \[\leadsto \color{blue}{\mathsf{log1p}\left(x + 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-77} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \end{array} \]

Alternative 5: 82.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-86} \lor \neg \left(x \leq 3.8 \cdot 10^{-78}\right) \land x \leq 2.75 \cdot 10^{-9}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e-6)
   (* x (- y))
   (if (or (<= x 1.56e-86) (and (not (<= x 3.8e-78)) (<= x 2.75e-9)))
     (log 2.0)
     (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-6) {
		tmp = x * -y;
	} else if ((x <= 1.56e-86) || (!(x <= 3.8e-78) && (x <= 2.75e-9))) {
		tmp = log(2.0);
	} else {
		tmp = x * (0.5 - 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 <= (-2.2d-6)) then
        tmp = x * -y
    else if ((x <= 1.56d-86) .or. (.not. (x <= 3.8d-78)) .and. (x <= 2.75d-9)) then
        tmp = log(2.0d0)
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-6) {
		tmp = x * -y;
	} else if ((x <= 1.56e-86) || (!(x <= 3.8e-78) && (x <= 2.75e-9))) {
		tmp = Math.log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e-6:
		tmp = x * -y
	elif (x <= 1.56e-86) or (not (x <= 3.8e-78) and (x <= 2.75e-9)):
		tmp = math.log(2.0)
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e-6)
		tmp = Float64(x * Float64(-y));
	elseif ((x <= 1.56e-86) || (!(x <= 3.8e-78) && (x <= 2.75e-9)))
		tmp = log(2.0);
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e-6)
		tmp = x * -y;
	elseif ((x <= 1.56e-86) || (~((x <= 3.8e-78)) && (x <= 2.75e-9)))
		tmp = log(2.0);
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e-6], N[(x * (-y)), $MachinePrecision], If[Or[LessEqual[x, 1.56e-86], And[N[Not[LessEqual[x, 3.8e-78]], $MachinePrecision], LessEqual[x, 2.75e-9]]], N[Log[2.0], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e-6

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 96.5%

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

      1. mul-1-neg 96.5%

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

      2. distribute-rgt-neg-out 96.5%

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

   6. Simplified 96.5%

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

   if -2.2000000000000001e-6 < x < 1.5599999999999999e-86 or 3.7999999999999999e-78 < x < 2.7499999999999998e-9

   1. Initial program 99.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]
   4. Step-by-step derivation

      1. add-log-exp 83.4%

         \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   5. Applied egg-rr 83.4%

      \[\leadsto \color{blue}{\log \left(e^{\mathsf{log1p}\left(e^{x}\right) - x \cdot y}\right)} \]

   6. Taylor expanded in x around 0 80.7%

      \[\leadsto \log \color{blue}{2} \]

   if 1.5599999999999999e-86 < x < 3.7999999999999999e-78 or 2.7499999999999998e-9 < x

   1. Initial program 87.9%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 88.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

   5. Taylor expanded in x around inf 85.8%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-86} \lor \neg \left(x \leq 3.8 \cdot 10^{-78}\right) \land x \leq 2.75 \cdot 10^{-9}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 6: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right) + \log 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4) (* x (- y)) (+ (* x (- 0.5 y)) (log 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4) {
		tmp = x * -y;
	} else {
		tmp = (x * (0.5 - y)) + log(2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.4d0)) then
        tmp = x * -y
    else
        tmp = (x * (0.5d0 - y)) + log(2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.4) {
		tmp = x * -y;
	} else {
		tmp = (x * (0.5 - y)) + Math.log(2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4:
		tmp = x * -y
	else:
		tmp = (x * (0.5 - y)) + math.log(2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(Float64(x * Float64(0.5 - y)) + log(2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4)
		tmp = x * -y;
	else
		tmp = (x * (0.5 - y)) + log(2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4], N[(x * (-y)), $MachinePrecision], N[(N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision] + N[Log[2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   6. Simplified 100.0%

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

   if -1.3999999999999999 < x

   1. Initial program 98.3%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 98.4%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right) + \log 2\\ \end{array} \]

Alternative 7: 98.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -31:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -31.0) (* x (- y)) (- (log 2.0) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -31.0) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) - (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 <= (-31.0d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -31.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -31.0:
		tmp = x * -y
	else:
		tmp = math.log(2.0) - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -31.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -31.0)
		tmp = x * -y;
	else
		tmp = log(2.0) - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -31.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -31

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   6. Simplified 100.0%

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

   if -31 < x

   1. Initial program 98.3%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 98.4%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 96.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -31:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 - x \cdot y\\ \end{array} \]

Alternative 8: 53.1% accurate, 51.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Taylor expanded in x around inf 50.5%

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

   1. mul-1-neg 50.5%

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

   2. distribute-rgt-neg-out 50.5%

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

6. Simplified 50.5%

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

7. Final simplification 50.5%

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

Alternative 9: 3.6% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x 0.5))

C

double code(double x, double y) {
	return x * 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 0.5d0
end function

Java

public static double code(double x, double y) {
	return x * 0.5;
}

Python

def code(x, y):
	return x * 0.5

Julia

function code(x, y)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Taylor expanded in x around 0 84.6%

   \[\leadsto \color{blue}{\left(0.5 - y\right) \cdot x + \log 2} \]

5. Taylor expanded in y around 0 50.7%

   \[\leadsto \color{blue}{0.5 \cdot x} + \log 2 \]

6. Taylor expanded in x around inf 3.6%

   \[\leadsto \color{blue}{0.5 \cdot x} \]
7. Step-by-step derivation

   1. *-commutative 3.6%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

8. Simplified 3.6%

   \[\leadsto \color{blue}{x \cdot 0.5} \]

9. Final simplification 3.6%

   \[\leadsto x \cdot 0.5 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0)
   (- (log (+ 1.0 (exp x))) (* x y))
   (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0) {
		tmp = log((1.0 + exp(x))) - (x * y);
	} else {
		tmp = log((1.0 + exp(-x))) - (-x * (1.0 - 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 <= 0.0d0) then
        tmp = log((1.0d0 + exp(x))) - (x * y)
    else
        tmp = log((1.0d0 + exp(-x))) - (-x * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0) {
		tmp = Math.log((1.0 + Math.exp(x))) - (x * y);
	} else {
		tmp = Math.log((1.0 + Math.exp(-x))) - (-x * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0:
		tmp = math.log((1.0 + math.exp(x))) - (x * y)
	else:
		tmp = math.log((1.0 + math.exp(-x))) - (-x * (1.0 - y))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0], N[(N[Log[N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(1.0 + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[((-x) * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y))))

  (- (log (+ 1.0 (exp x))) (* x y)))