math.exp on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 8

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ e^{re} \cdot \cos im \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* (exp re) (cos im)))

C

double code(double re, double im) {
	return exp(re) * cos(im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * cos(im)
end function

Java

public static double code(double re, double im) {
	return Math.exp(re) * Math.cos(im);
}

Python

def code(re, im):
	return math.exp(re) * math.cos(im)

Julia

function code(re, im)
	return Float64(exp(re) * cos(im))
end

MATLAB

function tmp = code(re, im)
	tmp = exp(re) * cos(im);
end

Wolfram

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Cos[im], $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{re} \cdot \cos im \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* (exp re) (cos im)))

C

double code(double re, double im) {
	return exp(re) * cos(im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * cos(im)
end function

Java

public static double code(double re, double im) {
	return Math.exp(re) * Math.cos(im);
}

Python

def code(re, im):
	return math.exp(re) * math.cos(im)

Julia

function code(re, im)
	return Float64(exp(re) * cos(im))
end

MATLAB

function tmp = code(re, im)
	tmp = exp(re) * cos(im);
end

Wolfram

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Cos[im], $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{re} \cdot \cos im \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* (exp re) (cos im)))

C

double code(double re, double im) {
	return exp(re) * cos(im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = exp(re) * cos(im)
end function

Java

public static double code(double re, double im) {
	return Math.exp(re) * Math.cos(im);
}

Python

def code(re, im):
	return math.exp(re) * math.cos(im)

Julia

function code(re, im)
	return Float64(exp(re) * cos(im))
end

MATLAB

function tmp = code(re, im)
	tmp = exp(re) * cos(im);
end

Wolfram

code[re_, im_] := N[(N[Exp[re], $MachinePrecision] * N[Cos[im], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{re} \cdot \cos im \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 2\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= (exp re) 0.0) (not (<= (exp re) 2.0)))
   (exp re)
   (* (cos im) (+ re 1.0))))

C

double code(double re, double im) {
	double tmp;
	if ((exp(re) <= 0.0) || !(exp(re) <= 2.0)) {
		tmp = exp(re);
	} else {
		tmp = cos(im) * (re + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if ((exp(re) <= 0.0d0) .or. (.not. (exp(re) <= 2.0d0))) then
        tmp = exp(re)
    else
        tmp = cos(im) * (re + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if ((Math.exp(re) <= 0.0) || !(Math.exp(re) <= 2.0)) {
		tmp = Math.exp(re);
	} else {
		tmp = Math.cos(im) * (re + 1.0);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (math.exp(re) <= 0.0) or not (math.exp(re) <= 2.0):
		tmp = math.exp(re)
	else:
		tmp = math.cos(im) * (re + 1.0)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((exp(re) <= 0.0) || !(exp(re) <= 2.0))
		tmp = exp(re);
	else
		tmp = Float64(cos(im) * Float64(re + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((exp(re) <= 0.0) || ~((exp(re) <= 2.0)))
		tmp = exp(re);
	else
		tmp = cos(im) * (re + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[N[Exp[re], $MachinePrecision], 0.0], N[Not[LessEqual[N[Exp[re], $MachinePrecision], 2.0]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[(N[Cos[im], $MachinePrecision] * N[(re + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 re) < 0.0 or 2 < (exp.f64 re)

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 86.4%

      \[\leadsto \color{blue}{e^{re}} \]

   if 0.0 < (exp.f64 re) < 2

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 99.6%

      \[\leadsto \color{blue}{\cos im + re \cdot \cos im} \]
   4. Step-by-step derivation

      1. distribute-rgt1-in 99.6%

         \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 2\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 2\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= (exp re) 0.0) (not (<= (exp re) 2.0))) (exp re) (cos im)))

C

double code(double re, double im) {
	double tmp;
	if ((exp(re) <= 0.0) || !(exp(re) <= 2.0)) {
		tmp = exp(re);
	} else {
		tmp = cos(im);
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if ((exp(re) <= 0.0d0) .or. (.not. (exp(re) <= 2.0d0))) then
        tmp = exp(re)
    else
        tmp = cos(im)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if ((Math.exp(re) <= 0.0) || !(Math.exp(re) <= 2.0)) {
		tmp = Math.exp(re);
	} else {
		tmp = Math.cos(im);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (math.exp(re) <= 0.0) or not (math.exp(re) <= 2.0):
		tmp = math.exp(re)
	else:
		tmp = math.cos(im)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((exp(re) <= 0.0) || !(exp(re) <= 2.0))
		tmp = exp(re);
	else
		tmp = cos(im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((exp(re) <= 0.0) || ~((exp(re) <= 2.0)))
		tmp = exp(re);
	else
		tmp = cos(im);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[N[Exp[re], $MachinePrecision], 0.0], N[Not[LessEqual[N[Exp[re], $MachinePrecision], 2.0]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[Cos[im], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 re) < 0.0 or 2 < (exp.f64 re)

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 86.4%

      \[\leadsto \color{blue}{e^{re}} \]

   if 0.0 < (exp.f64 re) < 2

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 98.6%

      \[\leadsto \color{blue}{\cos im} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 2\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;re \leq -0.0235 \lor \neg \left(re \leq 350\right) \land re \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= re -0.0235) (and (not (<= re 350.0)) (<= re 1.25e+150)))
   (exp re)
   (* (cos im) (+ (+ re 1.0) (* re (* re 0.5))))))

C

double code(double re, double im) {
	double tmp;
	if ((re <= -0.0235) || (!(re <= 350.0) && (re <= 1.25e+150))) {
		tmp = exp(re);
	} else {
		tmp = cos(im) * ((re + 1.0) + (re * (re * 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if ((re <= (-0.0235d0)) .or. (.not. (re <= 350.0d0)) .and. (re <= 1.25d+150)) then
        tmp = exp(re)
    else
        tmp = cos(im) * ((re + 1.0d0) + (re * (re * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if ((re <= -0.0235) || (!(re <= 350.0) && (re <= 1.25e+150))) {
		tmp = Math.exp(re);
	} else {
		tmp = Math.cos(im) * ((re + 1.0) + (re * (re * 0.5)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (re <= -0.0235) or (not (re <= 350.0) and (re <= 1.25e+150)):
		tmp = math.exp(re)
	else:
		tmp = math.cos(im) * ((re + 1.0) + (re * (re * 0.5)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((re <= -0.0235) || (!(re <= 350.0) && (re <= 1.25e+150)))
		tmp = exp(re);
	else
		tmp = Float64(cos(im) * Float64(Float64(re + 1.0) + Float64(re * Float64(re * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((re <= -0.0235) || (~((re <= 350.0)) && (re <= 1.25e+150)))
		tmp = exp(re);
	else
		tmp = cos(im) * ((re + 1.0) + (re * (re * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[re, -0.0235], And[N[Not[LessEqual[re, 350.0]], $MachinePrecision], LessEqual[re, 1.25e+150]]], N[Exp[re], $MachinePrecision], N[(N[Cos[im], $MachinePrecision] * N[(N[(re + 1.0), $MachinePrecision] + N[(re * N[(re * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if re < -0.0235 or 350 < re < 1.25000000000000002e150

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 95.0%

      \[\leadsto \color{blue}{e^{re}} \]

   if -0.0235 < re < 350 or 1.25000000000000002e150 < re

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{e^{re} \cdot \cos im} \cdot \sqrt[3]{e^{re} \cdot \cos im}\right) \cdot \sqrt[3]{e^{re} \cdot \cos im}} \]

      2. pow3 99.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{e^{re} \cdot \cos im}\right)}^{3}} \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{e^{re} \cdot \cos im}\right)}^{3}} \]

   5. Taylor expanded in re around 0 98.1%

      \[\leadsto \color{blue}{\cos im + re \cdot \left(\cos im + 0.5 \cdot \left(re \cdot \cos im\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in 98.1%

         \[\leadsto \cos im + \color{blue}{\left(re \cdot \cos im + re \cdot \left(0.5 \cdot \left(re \cdot \cos im\right)\right)\right)} \]

      2. associate-+r+ 98.1%

         \[\leadsto \color{blue}{\left(\cos im + re \cdot \cos im\right) + re \cdot \left(0.5 \cdot \left(re \cdot \cos im\right)\right)} \]

      3. distribute-rgt1-in 98.1%

         \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} + re \cdot \left(0.5 \cdot \left(re \cdot \cos im\right)\right) \]

      4. +-commutative 98.1%

         \[\leadsto \color{blue}{\left(1 + re\right)} \cdot \cos im + re \cdot \left(0.5 \cdot \left(re \cdot \cos im\right)\right) \]

      5. associate-*r* 98.1%

         \[\leadsto \left(1 + re\right) \cdot \cos im + re \cdot \color{blue}{\left(\left(0.5 \cdot re\right) \cdot \cos im\right)} \]

      6. associate-*r* 98.1%

         \[\leadsto \left(1 + re\right) \cdot \cos im + \color{blue}{\left(re \cdot \left(0.5 \cdot re\right)\right) \cdot \cos im} \]

      7. distribute-rgt-out 98.1%

         \[\leadsto \color{blue}{\cos im \cdot \left(\left(1 + re\right) + re \cdot \left(0.5 \cdot re\right)\right)} \]

      8. +-commutative 98.1%

         \[\leadsto \cos im \cdot \left(\color{blue}{\left(re + 1\right)} + re \cdot \left(0.5 \cdot re\right)\right) \]

      9. *-commutative 98.1%

         \[\leadsto \cos im \cdot \left(\left(re + 1\right) + re \cdot \color{blue}{\left(re \cdot 0.5\right)}\right) \]

   7. Simplified 98.1%

      \[\leadsto \color{blue}{\cos im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \leq -0.0235 \lor \neg \left(re \leq 350\right) \land re \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(\left(re + 1\right) + re \cdot \left(re \cdot 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;re \leq -0.00122 \lor \neg \left(re \leq 0.000405\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos im}{\left(-re\right) - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= re -0.00122) (not (<= re 0.000405)))
   (exp re)
   (/ (cos im) (- (- re) -1.0))))

C

double code(double re, double im) {
	double tmp;
	if ((re <= -0.00122) || !(re <= 0.000405)) {
		tmp = exp(re);
	} else {
		tmp = cos(im) / (-re - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if ((re <= (-0.00122d0)) .or. (.not. (re <= 0.000405d0))) then
        tmp = exp(re)
    else
        tmp = cos(im) / (-re - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if ((re <= -0.00122) || !(re <= 0.000405)) {
		tmp = Math.exp(re);
	} else {
		tmp = Math.cos(im) / (-re - -1.0);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (re <= -0.00122) or not (re <= 0.000405):
		tmp = math.exp(re)
	else:
		tmp = math.cos(im) / (-re - -1.0)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((re <= -0.00122) || !(re <= 0.000405))
		tmp = exp(re);
	else
		tmp = Float64(cos(im) / Float64(Float64(-re) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((re <= -0.00122) || ~((re <= 0.000405)))
		tmp = exp(re);
	else
		tmp = cos(im) / (-re - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[re, -0.00122], N[Not[LessEqual[re, 0.000405]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[(N[Cos[im], $MachinePrecision] / N[((-re) - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if re < -0.00121999999999999995 or 4.0499999999999998e-4 < re

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 86.4%

      \[\leadsto \color{blue}{e^{re}} \]

   if -0.00121999999999999995 < re < 4.0499999999999998e-4

   1. Initial program 100.0%

      \[e^{re} \cdot \cos im \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 99.6%

      \[\leadsto \color{blue}{\cos im + re \cdot \cos im} \]
   4. Step-by-step derivation

      1. distribute-rgt1-in 99.6%

         \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

   5. Simplified 99.6%

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

      1. flip-+ 99.6%

         \[\leadsto \color{blue}{\frac{re \cdot re - 1 \cdot 1}{re - 1}} \cdot \cos im \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{\left(re \cdot re - 1 \cdot 1\right) \cdot \cos im}{re - 1}} \]

      3. metadata-eval 99.6%

         \[\leadsto \frac{\left(re \cdot re - \color{blue}{1}\right) \cdot \cos im}{re - 1} \]

      4. fma-neg 99.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(re, re, -1\right)} \cdot \cos im}{re - 1} \]

      5. metadata-eval 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(re, re, \color{blue}{-1}\right) \cdot \cos im}{re - 1} \]

      6. sub-neg 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(re, re, -1\right) \cdot \cos im}{\color{blue}{re + \left(-1\right)}} \]

      7. metadata-eval 99.6%

         \[\leadsto \frac{\mathsf{fma}\left(re, re, -1\right) \cdot \cos im}{re + \color{blue}{-1}} \]

   7. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(re, re, -1\right) \cdot \cos im}{re + -1}} \]

   8. Taylor expanded in re around 0 99.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \cos im}}{re + -1} \]
   9. Step-by-step derivation

      1. neg-mul-1 99.6%

         \[\leadsto \frac{\color{blue}{-\cos im}}{re + -1} \]

   10. Simplified 99.6%

       \[\leadsto \frac{\color{blue}{-\cos im}}{re + -1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \leq -0.00122 \lor \neg \left(re \leq 0.000405\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos im}{\left(-re\right) - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \cos im \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (cos im))

C

double code(double re, double im) {
	return cos(im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = cos(im)
end function

Java

public static double code(double re, double im) {
	return Math.cos(im);
}

Python

def code(re, im):
	return math.cos(im)

Julia

function code(re, im)
	return cos(im)
end

MATLAB

function tmp = code(re, im)
	tmp = cos(im);
end

Wolfram

code[re_, im_] := N[Cos[im], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{re} \cdot \cos im \]
2. Add Preprocessing

3. Taylor expanded in re around 0 47.2%

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

Alternative 7: 29.0% accurate, 67.7× speedup

Math

\[\begin{array}{l} \\ re + 1 \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (+ re 1.0))

C

double code(double re, double im) {
	return re + 1.0;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = re + 1.0d0
end function

Java

public static double code(double re, double im) {
	return re + 1.0;
}

Python

def code(re, im):
	return re + 1.0

Julia

function code(re, im)
	return Float64(re + 1.0)
end

MATLAB

function tmp = code(re, im)
	tmp = re + 1.0;
end

Wolfram

code[re_, im_] := N[(re + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{re} \cdot \cos im \]
2. Add Preprocessing

3. Taylor expanded in re around 0 48.0%

   \[\leadsto \color{blue}{\cos im + re \cdot \cos im} \]
4. Step-by-step derivation

   1. distribute-rgt1-in 48.0%

      \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

5. Simplified 48.0%

   \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

6. Taylor expanded in im around 0 25.7%

   \[\leadsto \color{blue}{1 + re} \]
7. Step-by-step derivation

   1. +-commutative 25.7%

      \[\leadsto \color{blue}{re + 1} \]

8. Simplified 25.7%

   \[\leadsto \color{blue}{re + 1} \]
9. Add Preprocessing

Alternative 8: 3.5% accurate, 203.0× speedup

Math

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

FPCore

(FPCore (re im) :precision binary64 re)

C

double code(double re, double im) {
	return re;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = re
end function

Java

public static double code(double re, double im) {
	return re;
}

Python

def code(re, im):
	return re

Julia

function code(re, im)
	return re
end

MATLAB

function tmp = code(re, im)
	tmp = re;
end

Wolfram

code[re_, im_] := re

Derivation

1. Initial program 100.0%

   \[e^{re} \cdot \cos im \]
2. Add Preprocessing

3. Taylor expanded in re around 0 48.0%

   \[\leadsto \color{blue}{\cos im + re \cdot \cos im} \]
4. Step-by-step derivation

   1. distribute-rgt1-in 48.0%

      \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

5. Simplified 48.0%

   \[\leadsto \color{blue}{\left(re + 1\right) \cdot \cos im} \]

6. Taylor expanded in re around inf 3.7%

   \[\leadsto \color{blue}{re \cdot \cos im} \]
7. Step-by-step derivation

   1. *-commutative 3.7%

      \[\leadsto \color{blue}{\cos im \cdot re} \]

8. Simplified 3.7%

   \[\leadsto \color{blue}{\cos im \cdot re} \]

9. Taylor expanded in im around 0 3.4%

   \[\leadsto \color{blue}{re} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))