math.cos on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 9

Speedup: 1.0×

• 51.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 50.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot {im}^{2}\\ t_1 := 0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{if}\;\cos re \leq 0.5:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.68:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.72:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.73:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\cos re \leq 0.765:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.82:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.826:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.88:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.9:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.91:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.912:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.92:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.94:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.942:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\cos re \leq 0.96:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.965:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.97:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.99:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\cos re \leq 0.999:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.9995:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\cos re \leq 1:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (pow im 2.0))) (t_1 (* 0.5 (+ (exp (- im)) (exp im)))))
   (if (<= (cos re) 0.5)
     (cos re)
     (if (<= (cos re) 0.68)
       t_1
       (if (<= (cos re) 0.72)
         (cos re)
         (if (<= (cos re) 0.73)
           t_0
           (if (<= (cos re) 0.765)
             (cos re)
             (if (<= (cos re) 0.82)
               t_1
               (if (<= (cos re) 0.826)
                 (cos re)
                 (if (<= (cos re) 0.88)
                   t_1
                   (if (<= (cos re) 0.9)
                     (cos re)
                     (if (<= (cos re) 0.91)
                       t_1
                       (if (<= (cos re) 0.912)
                         (cos re)
                         (if (<= (cos re) 0.92)
                           t_1
                           (if (<= (cos re) 0.94)
                             (cos re)
                             (if (<= (cos re) 0.942)
                               t_0
                               (if (<= (cos re) 0.96)
                                 (cos re)
                                 (if (<= (cos re) 0.965)
                                   t_1
                                   (if (<= (cos re) 0.97)
                                     (cos re)
                                     (if (<= (cos re) 0.99)
                                       t_1
                                       (if (<= (cos re) 0.999)
                                         (cos re)
                                         (if (<= (cos re) 0.9995)
                                           t_0
                                           (if (<= (cos re) 1.0)
                                             (cos re)
                                             t_1)))))))))))))))))))))))

C

double code(double re, double im) {
	double t_0 = 0.5 * pow(im, 2.0);
	double t_1 = 0.5 * (exp(-im) + exp(im));
	double tmp;
	if (cos(re) <= 0.5) {
		tmp = cos(re);
	} else if (cos(re) <= 0.68) {
		tmp = t_1;
	} else if (cos(re) <= 0.72) {
		tmp = cos(re);
	} else if (cos(re) <= 0.73) {
		tmp = t_0;
	} else if (cos(re) <= 0.765) {
		tmp = cos(re);
	} else if (cos(re) <= 0.82) {
		tmp = t_1;
	} else if (cos(re) <= 0.826) {
		tmp = cos(re);
	} else if (cos(re) <= 0.88) {
		tmp = t_1;
	} else if (cos(re) <= 0.9) {
		tmp = cos(re);
	} else if (cos(re) <= 0.91) {
		tmp = t_1;
	} else if (cos(re) <= 0.912) {
		tmp = cos(re);
	} else if (cos(re) <= 0.92) {
		tmp = t_1;
	} else if (cos(re) <= 0.94) {
		tmp = cos(re);
	} else if (cos(re) <= 0.942) {
		tmp = t_0;
	} else if (cos(re) <= 0.96) {
		tmp = cos(re);
	} else if (cos(re) <= 0.965) {
		tmp = t_1;
	} else if (cos(re) <= 0.97) {
		tmp = cos(re);
	} else if (cos(re) <= 0.99) {
		tmp = t_1;
	} else if (cos(re) <= 0.999) {
		tmp = cos(re);
	} else if (cos(re) <= 0.9995) {
		tmp = t_0;
	} else if (cos(re) <= 1.0) {
		tmp = cos(re);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (im ** 2.0d0)
    t_1 = 0.5d0 * (exp(-im) + exp(im))
    if (cos(re) <= 0.5d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.68d0) then
        tmp = t_1
    else if (cos(re) <= 0.72d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.73d0) then
        tmp = t_0
    else if (cos(re) <= 0.765d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.82d0) then
        tmp = t_1
    else if (cos(re) <= 0.826d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.88d0) then
        tmp = t_1
    else if (cos(re) <= 0.9d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.91d0) then
        tmp = t_1
    else if (cos(re) <= 0.912d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.92d0) then
        tmp = t_1
    else if (cos(re) <= 0.94d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.942d0) then
        tmp = t_0
    else if (cos(re) <= 0.96d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.965d0) then
        tmp = t_1
    else if (cos(re) <= 0.97d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.99d0) then
        tmp = t_1
    else if (cos(re) <= 0.999d0) then
        tmp = cos(re)
    else if (cos(re) <= 0.9995d0) then
        tmp = t_0
    else if (cos(re) <= 1.0d0) then
        tmp = cos(re)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = 0.5 * Math.pow(im, 2.0);
	double t_1 = 0.5 * (Math.exp(-im) + Math.exp(im));
	double tmp;
	if (Math.cos(re) <= 0.5) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.68) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.72) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.73) {
		tmp = t_0;
	} else if (Math.cos(re) <= 0.765) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.82) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.826) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.88) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.9) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.91) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.912) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.92) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.94) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.942) {
		tmp = t_0;
	} else if (Math.cos(re) <= 0.96) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.965) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.97) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.99) {
		tmp = t_1;
	} else if (Math.cos(re) <= 0.999) {
		tmp = Math.cos(re);
	} else if (Math.cos(re) <= 0.9995) {
		tmp = t_0;
	} else if (Math.cos(re) <= 1.0) {
		tmp = Math.cos(re);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = 0.5 * math.pow(im, 2.0)
	t_1 = 0.5 * (math.exp(-im) + math.exp(im))
	tmp = 0
	if math.cos(re) <= 0.5:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.68:
		tmp = t_1
	elif math.cos(re) <= 0.72:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.73:
		tmp = t_0
	elif math.cos(re) <= 0.765:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.82:
		tmp = t_1
	elif math.cos(re) <= 0.826:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.88:
		tmp = t_1
	elif math.cos(re) <= 0.9:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.91:
		tmp = t_1
	elif math.cos(re) <= 0.912:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.92:
		tmp = t_1
	elif math.cos(re) <= 0.94:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.942:
		tmp = t_0
	elif math.cos(re) <= 0.96:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.965:
		tmp = t_1
	elif math.cos(re) <= 0.97:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.99:
		tmp = t_1
	elif math.cos(re) <= 0.999:
		tmp = math.cos(re)
	elif math.cos(re) <= 0.9995:
		tmp = t_0
	elif math.cos(re) <= 1.0:
		tmp = math.cos(re)
	else:
		tmp = t_1
	return tmp

Julia

function code(re, im)
	t_0 = Float64(0.5 * (im ^ 2.0))
	t_1 = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)))
	tmp = 0.0
	if (cos(re) <= 0.5)
		tmp = cos(re);
	elseif (cos(re) <= 0.68)
		tmp = t_1;
	elseif (cos(re) <= 0.72)
		tmp = cos(re);
	elseif (cos(re) <= 0.73)
		tmp = t_0;
	elseif (cos(re) <= 0.765)
		tmp = cos(re);
	elseif (cos(re) <= 0.82)
		tmp = t_1;
	elseif (cos(re) <= 0.826)
		tmp = cos(re);
	elseif (cos(re) <= 0.88)
		tmp = t_1;
	elseif (cos(re) <= 0.9)
		tmp = cos(re);
	elseif (cos(re) <= 0.91)
		tmp = t_1;
	elseif (cos(re) <= 0.912)
		tmp = cos(re);
	elseif (cos(re) <= 0.92)
		tmp = t_1;
	elseif (cos(re) <= 0.94)
		tmp = cos(re);
	elseif (cos(re) <= 0.942)
		tmp = t_0;
	elseif (cos(re) <= 0.96)
		tmp = cos(re);
	elseif (cos(re) <= 0.965)
		tmp = t_1;
	elseif (cos(re) <= 0.97)
		tmp = cos(re);
	elseif (cos(re) <= 0.99)
		tmp = t_1;
	elseif (cos(re) <= 0.999)
		tmp = cos(re);
	elseif (cos(re) <= 0.9995)
		tmp = t_0;
	elseif (cos(re) <= 1.0)
		tmp = cos(re);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = 0.5 * (im ^ 2.0);
	t_1 = 0.5 * (exp(-im) + exp(im));
	tmp = 0.0;
	if (cos(re) <= 0.5)
		tmp = cos(re);
	elseif (cos(re) <= 0.68)
		tmp = t_1;
	elseif (cos(re) <= 0.72)
		tmp = cos(re);
	elseif (cos(re) <= 0.73)
		tmp = t_0;
	elseif (cos(re) <= 0.765)
		tmp = cos(re);
	elseif (cos(re) <= 0.82)
		tmp = t_1;
	elseif (cos(re) <= 0.826)
		tmp = cos(re);
	elseif (cos(re) <= 0.88)
		tmp = t_1;
	elseif (cos(re) <= 0.9)
		tmp = cos(re);
	elseif (cos(re) <= 0.91)
		tmp = t_1;
	elseif (cos(re) <= 0.912)
		tmp = cos(re);
	elseif (cos(re) <= 0.92)
		tmp = t_1;
	elseif (cos(re) <= 0.94)
		tmp = cos(re);
	elseif (cos(re) <= 0.942)
		tmp = t_0;
	elseif (cos(re) <= 0.96)
		tmp = cos(re);
	elseif (cos(re) <= 0.965)
		tmp = t_1;
	elseif (cos(re) <= 0.97)
		tmp = cos(re);
	elseif (cos(re) <= 0.99)
		tmp = t_1;
	elseif (cos(re) <= 0.999)
		tmp = cos(re);
	elseif (cos(re) <= 0.9995)
		tmp = t_0;
	elseif (cos(re) <= 1.0)
		tmp = cos(re);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[re], $MachinePrecision], 0.5], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.68], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.72], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.73], t$95$0, If[LessEqual[N[Cos[re], $MachinePrecision], 0.765], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.82], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.826], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.88], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.9], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.91], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.912], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.92], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.94], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.942], t$95$0, If[LessEqual[N[Cos[re], $MachinePrecision], 0.96], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.965], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.97], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.99], t$95$1, If[LessEqual[N[Cos[re], $MachinePrecision], 0.999], N[Cos[re], $MachinePrecision], If[LessEqual[N[Cos[re], $MachinePrecision], 0.9995], t$95$0, If[LessEqual[N[Cos[re], $MachinePrecision], 1.0], N[Cos[re], $MachinePrecision], t$95$1]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (cos.f64 re) < 0.5 or 0.680000000000000049 < (cos.f64 re) < 0.71999999999999997 or 0.72999999999999998 < (cos.f64 re) < 0.765000000000000013 or 0.819999999999999951 < (cos.f64 re) < 0.825999999999999956 or 0.880000000000000004 < (cos.f64 re) < 0.900000000000000022 or 0.910000000000000031 < (cos.f64 re) < 0.912000000000000033 or 0.92000000000000004 < (cos.f64 re) < 0.93999999999999995 or 0.94199999999999995 < (cos.f64 re) < 0.95999999999999996 or 0.964999999999999969 < (cos.f64 re) < 0.96999999999999997 or 0.98999999999999999 < (cos.f64 re) < 0.998999999999999999 or 0.99950000000000006 < (cos.f64 re) < 1

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 55.9%

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

   if 0.5 < (cos.f64 re) < 0.680000000000000049 or 0.765000000000000013 < (cos.f64 re) < 0.819999999999999951 or 0.825999999999999956 < (cos.f64 re) < 0.880000000000000004 or 0.900000000000000022 < (cos.f64 re) < 0.910000000000000031 or 0.912000000000000033 < (cos.f64 re) < 0.92000000000000004 or 0.95999999999999996 < (cos.f64 re) < 0.964999999999999969 or 0.96999999999999997 < (cos.f64 re) < 0.98999999999999999 or 1 < (cos.f64 re)

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 89.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{im} + e^{-im}\right)} \]

   if 0.71999999999999997 < (cos.f64 re) < 0.72999999999999998 or 0.93999999999999995 < (cos.f64 re) < 0.94199999999999995 or 0.998999999999999999 < (cos.f64 re) < 0.99950000000000006

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 100.0%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 100.0%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   6. Taylor expanded in im around inf 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   9. Taylor expanded in re around 0 100.0%

      \[\leadsto \color{blue}{0.5 \cdot {im}^{2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos re \leq 0.5:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.68:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.72:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.73:\\ \;\;\;\;0.5 \cdot {im}^{2}\\ \mathbf{elif}\;\cos re \leq 0.765:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.82:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.826:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.88:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.9:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.91:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.912:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.92:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.94:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.942:\\ \;\;\;\;0.5 \cdot {im}^{2}\\ \mathbf{elif}\;\cos re \leq 0.96:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.965:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.97:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.99:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;\cos re \leq 0.999:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;\cos re \leq 0.9995:\\ \;\;\;\;0.5 \cdot {im}^{2}\\ \mathbf{elif}\;\cos re \leq 1:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos re \leq 1:\\ \;\;\;\;\cos re \cdot \left(1 + 0.5 \cdot {im}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= (cos re) 1.0)
   (* (cos re) (+ 1.0 (* 0.5 (pow im 2.0))))
   (* 0.5 (+ (exp (- im)) (exp im)))))

C

double code(double re, double im) {
	double tmp;
	if (cos(re) <= 1.0) {
		tmp = cos(re) * (1.0 + (0.5 * pow(im, 2.0)));
	} else {
		tmp = 0.5 * (exp(-im) + exp(im));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (cos(re) <= 1.0d0) then
        tmp = cos(re) * (1.0d0 + (0.5d0 * (im ** 2.0d0)))
    else
        tmp = 0.5d0 * (exp(-im) + exp(im))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (Math.cos(re) <= 1.0) {
		tmp = Math.cos(re) * (1.0 + (0.5 * Math.pow(im, 2.0)));
	} else {
		tmp = 0.5 * (Math.exp(-im) + Math.exp(im));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if math.cos(re) <= 1.0:
		tmp = math.cos(re) * (1.0 + (0.5 * math.pow(im, 2.0)))
	else:
		tmp = 0.5 * (math.exp(-im) + math.exp(im))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (cos(re) <= 1.0)
		tmp = Float64(cos(re) * Float64(1.0 + Float64(0.5 * (im ^ 2.0))));
	else
		tmp = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (cos(re) <= 1.0)
		tmp = cos(re) * (1.0 + (0.5 * (im ^ 2.0)));
	else
		tmp = 0.5 * (exp(-im) + exp(im));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[N[Cos[re], $MachinePrecision], 1.0], N[(N[Cos[re], $MachinePrecision] * N[(1.0 + N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 re) < 1

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 77.8%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 77.8%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 77.8%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 77.8%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   if 1 < (cos.f64 re)

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 62.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos re \leq 1:\\ \;\;\;\;\cos re \cdot \left(1 + 0.5 \cdot {im}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 250:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.3 \cdot 10^{+18} \lor \neg \left(im \leq 7.8 \cdot 10^{+18}\right) \land \left(im \leq 9.5 \cdot 10^{+34} \lor \neg \left(im \leq 10^{+35}\right) \land \left(im \leq 8.5 \cdot 10^{+79} \lor \neg \left(im \leq 8.6 \cdot 10^{+79}\right) \land \left(im \leq 7.2 \cdot 10^{+130} \lor \neg \left(im \leq 7.5 \cdot 10^{+130}\right) \land \left(im \leq 1.05 \cdot 10^{+144} \lor \neg \left(im \leq 1.06 \cdot 10^{+144}\right) \land \left(im \leq 3.8 \cdot 10^{+146} \lor \neg \left(im \leq 6.4 \cdot 10^{+151}\right) \land im \leq 1.4 \cdot 10^{+154}\right)\right)\right)\right)\right):\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(0.5 \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 250.0)
   (cos re)
   (if (or (<= im 2.3e+18)
           (and (not (<= im 7.8e+18))
                (or (<= im 9.5e+34)
                    (and (not (<= im 1e+35))
                         (or (<= im 8.5e+79)
                             (and (not (<= im 8.6e+79))
                                  (or (<= im 7.2e+130)
                                      (and (not (<= im 7.5e+130))
                                           (or (<= im 1.05e+144)
                                               (and (not (<= im 1.06e+144))
                                                    (or (<= im 3.8e+146)
                                                        (and (not
                                                              (<= im 6.4e+151))
                                                             (<=
                                                              im
                                                              1.4e+154)))))))))))))
     (* 0.5 (+ (exp (- im)) (exp im)))
     (* (cos re) (* 0.5 (pow im 2.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 250.0) {
		tmp = cos(re);
	} else if ((im <= 2.3e+18) || (!(im <= 7.8e+18) && ((im <= 9.5e+34) || (!(im <= 1e+35) && ((im <= 8.5e+79) || (!(im <= 8.6e+79) && ((im <= 7.2e+130) || (!(im <= 7.5e+130) && ((im <= 1.05e+144) || (!(im <= 1.06e+144) && ((im <= 3.8e+146) || (!(im <= 6.4e+151) && (im <= 1.4e+154))))))))))))) {
		tmp = 0.5 * (exp(-im) + exp(im));
	} else {
		tmp = cos(re) * (0.5 * pow(im, 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 250.0d0) then
        tmp = cos(re)
    else if ((im <= 2.3d+18) .or. (.not. (im <= 7.8d+18)) .and. (im <= 9.5d+34) .or. (.not. (im <= 1d+35)) .and. (im <= 8.5d+79) .or. (.not. (im <= 8.6d+79)) .and. (im <= 7.2d+130) .or. (.not. (im <= 7.5d+130)) .and. (im <= 1.05d+144) .or. (.not. (im <= 1.06d+144)) .and. (im <= 3.8d+146) .or. (.not. (im <= 6.4d+151)) .and. (im <= 1.4d+154)) then
        tmp = 0.5d0 * (exp(-im) + exp(im))
    else
        tmp = cos(re) * (0.5d0 * (im ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 250.0) {
		tmp = Math.cos(re);
	} else if ((im <= 2.3e+18) || (!(im <= 7.8e+18) && ((im <= 9.5e+34) || (!(im <= 1e+35) && ((im <= 8.5e+79) || (!(im <= 8.6e+79) && ((im <= 7.2e+130) || (!(im <= 7.5e+130) && ((im <= 1.05e+144) || (!(im <= 1.06e+144) && ((im <= 3.8e+146) || (!(im <= 6.4e+151) && (im <= 1.4e+154))))))))))))) {
		tmp = 0.5 * (Math.exp(-im) + Math.exp(im));
	} else {
		tmp = Math.cos(re) * (0.5 * Math.pow(im, 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 250.0:
		tmp = math.cos(re)
	elif (im <= 2.3e+18) or (not (im <= 7.8e+18) and ((im <= 9.5e+34) or (not (im <= 1e+35) and ((im <= 8.5e+79) or (not (im <= 8.6e+79) and ((im <= 7.2e+130) or (not (im <= 7.5e+130) and ((im <= 1.05e+144) or (not (im <= 1.06e+144) and ((im <= 3.8e+146) or (not (im <= 6.4e+151) and (im <= 1.4e+154)))))))))))):
		tmp = 0.5 * (math.exp(-im) + math.exp(im))
	else:
		tmp = math.cos(re) * (0.5 * math.pow(im, 2.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 250.0)
		tmp = cos(re);
	elseif ((im <= 2.3e+18) || (!(im <= 7.8e+18) && ((im <= 9.5e+34) || (!(im <= 1e+35) && ((im <= 8.5e+79) || (!(im <= 8.6e+79) && ((im <= 7.2e+130) || (!(im <= 7.5e+130) && ((im <= 1.05e+144) || (!(im <= 1.06e+144) && ((im <= 3.8e+146) || (!(im <= 6.4e+151) && (im <= 1.4e+154)))))))))))))
		tmp = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)));
	else
		tmp = Float64(cos(re) * Float64(0.5 * (im ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 250.0)
		tmp = cos(re);
	elseif ((im <= 2.3e+18) || (~((im <= 7.8e+18)) && ((im <= 9.5e+34) || (~((im <= 1e+35)) && ((im <= 8.5e+79) || (~((im <= 8.6e+79)) && ((im <= 7.2e+130) || (~((im <= 7.5e+130)) && ((im <= 1.05e+144) || (~((im <= 1.06e+144)) && ((im <= 3.8e+146) || (~((im <= 6.4e+151)) && (im <= 1.4e+154)))))))))))))
		tmp = 0.5 * (exp(-im) + exp(im));
	else
		tmp = cos(re) * (0.5 * (im ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 250.0], N[Cos[re], $MachinePrecision], If[Or[LessEqual[im, 2.3e+18], And[N[Not[LessEqual[im, 7.8e+18]], $MachinePrecision], Or[LessEqual[im, 9.5e+34], And[N[Not[LessEqual[im, 1e+35]], $MachinePrecision], Or[LessEqual[im, 8.5e+79], And[N[Not[LessEqual[im, 8.6e+79]], $MachinePrecision], Or[LessEqual[im, 7.2e+130], And[N[Not[LessEqual[im, 7.5e+130]], $MachinePrecision], Or[LessEqual[im, 1.05e+144], And[N[Not[LessEqual[im, 1.06e+144]], $MachinePrecision], Or[LessEqual[im, 3.8e+146], And[N[Not[LessEqual[im, 6.4e+151]], $MachinePrecision], LessEqual[im, 1.4e+154]]]]]]]]]]]]], N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if im < 250

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 67.1%

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

   if 250 < im < 2.3e18 or 7.8e18 < im < 9.4999999999999999e34 or 9.9999999999999997e34 < im < 8.4999999999999998e79 or 8.6000000000000006e79 < im < 7.2000000000000002e130 or 7.5000000000000003e130 < im < 1.04999999999999998e144 or 1.06e144 < im < 3.79999999999999979e146 or 6.39999999999999988e151 < im < 1.4e154

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{im} + e^{-im}\right)} \]

   if 2.3e18 < im < 7.8e18 or 9.4999999999999999e34 < im < 9.9999999999999997e34 or 8.4999999999999998e79 < im < 8.6000000000000006e79 or 7.2000000000000002e130 < im < 7.5000000000000003e130 or 1.04999999999999998e144 < im < 1.06e144 or 3.79999999999999979e146 < im < 6.39999999999999988e151 or 1.4e154 < im

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 84.2%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 84.2%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 84.2%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   6. Taylor expanded in im around inf 84.2%

      \[\leadsto \color{blue}{0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 84.2%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. *-commutative 84.2%

         \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   8. Simplified 84.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 250:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.3 \cdot 10^{+18} \lor \neg \left(im \leq 7.8 \cdot 10^{+18}\right) \land \left(im \leq 9.5 \cdot 10^{+34} \lor \neg \left(im \leq 10^{+35}\right) \land \left(im \leq 8.5 \cdot 10^{+79} \lor \neg \left(im \leq 8.6 \cdot 10^{+79}\right) \land \left(im \leq 7.2 \cdot 10^{+130} \lor \neg \left(im \leq 7.5 \cdot 10^{+130}\right) \land \left(im \leq 1.05 \cdot 10^{+144} \lor \neg \left(im \leq 1.06 \cdot 10^{+144}\right) \land \left(im \leq 3.8 \cdot 10^{+146} \lor \neg \left(im \leq 6.4 \cdot 10^{+151}\right) \land im \leq 1.4 \cdot 10^{+154}\right)\right)\right)\right)\right):\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(0.5 \cdot {im}^{2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ t_1 := 0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{if}\;im \leq 250:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 8.6 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 7.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 7.5 \cdot 10^{+130}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 9 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 1.06 \cdot 10^{+144}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 3.8 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;im \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;im \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(0.5 \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* (pow im 2.0) (* -0.25 (pow re 2.0))))
        (t_1 (* 0.5 (+ (exp (- im)) (exp im)))))
   (if (<= im 250.0)
     (cos re)
     (if (<= im 2.3e+18)
       t_1
       (if (<= im 7.8e+18)
         t_0
         (if (<= im 9.5e+34)
           t_1
           (if (<= im 1e+35)
             t_0
             (if (<= im 8.5e+79)
               t_1
               (if (<= im 8.6e+79)
                 t_0
                 (if (<= im 7.2e+130)
                   t_1
                   (if (<= im 7.5e+130)
                     t_0
                     (if (<= im 9e+143)
                       t_1
                       (if (<= im 1.06e+144)
                         t_0
                         (if (<= im 3.8e+146)
                           t_1
                           (if (<= im 6.4e+151)
                             t_0
                             (if (<= im 1.4e+154)
                               t_1
                               (*
                                (cos re)
                                (* 0.5 (pow im 2.0)))))))))))))))))))

C

double code(double re, double im) {
	double t_0 = pow(im, 2.0) * (-0.25 * pow(re, 2.0));
	double t_1 = 0.5 * (exp(-im) + exp(im));
	double tmp;
	if (im <= 250.0) {
		tmp = cos(re);
	} else if (im <= 2.3e+18) {
		tmp = t_1;
	} else if (im <= 7.8e+18) {
		tmp = t_0;
	} else if (im <= 9.5e+34) {
		tmp = t_1;
	} else if (im <= 1e+35) {
		tmp = t_0;
	} else if (im <= 8.5e+79) {
		tmp = t_1;
	} else if (im <= 8.6e+79) {
		tmp = t_0;
	} else if (im <= 7.2e+130) {
		tmp = t_1;
	} else if (im <= 7.5e+130) {
		tmp = t_0;
	} else if (im <= 9e+143) {
		tmp = t_1;
	} else if (im <= 1.06e+144) {
		tmp = t_0;
	} else if (im <= 3.8e+146) {
		tmp = t_1;
	} else if (im <= 6.4e+151) {
		tmp = t_0;
	} else if (im <= 1.4e+154) {
		tmp = t_1;
	} else {
		tmp = cos(re) * (0.5 * pow(im, 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (im ** 2.0d0) * ((-0.25d0) * (re ** 2.0d0))
    t_1 = 0.5d0 * (exp(-im) + exp(im))
    if (im <= 250.0d0) then
        tmp = cos(re)
    else if (im <= 2.3d+18) then
        tmp = t_1
    else if (im <= 7.8d+18) then
        tmp = t_0
    else if (im <= 9.5d+34) then
        tmp = t_1
    else if (im <= 1d+35) then
        tmp = t_0
    else if (im <= 8.5d+79) then
        tmp = t_1
    else if (im <= 8.6d+79) then
        tmp = t_0
    else if (im <= 7.2d+130) then
        tmp = t_1
    else if (im <= 7.5d+130) then
        tmp = t_0
    else if (im <= 9d+143) then
        tmp = t_1
    else if (im <= 1.06d+144) then
        tmp = t_0
    else if (im <= 3.8d+146) then
        tmp = t_1
    else if (im <= 6.4d+151) then
        tmp = t_0
    else if (im <= 1.4d+154) then
        tmp = t_1
    else
        tmp = cos(re) * (0.5d0 * (im ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = Math.pow(im, 2.0) * (-0.25 * Math.pow(re, 2.0));
	double t_1 = 0.5 * (Math.exp(-im) + Math.exp(im));
	double tmp;
	if (im <= 250.0) {
		tmp = Math.cos(re);
	} else if (im <= 2.3e+18) {
		tmp = t_1;
	} else if (im <= 7.8e+18) {
		tmp = t_0;
	} else if (im <= 9.5e+34) {
		tmp = t_1;
	} else if (im <= 1e+35) {
		tmp = t_0;
	} else if (im <= 8.5e+79) {
		tmp = t_1;
	} else if (im <= 8.6e+79) {
		tmp = t_0;
	} else if (im <= 7.2e+130) {
		tmp = t_1;
	} else if (im <= 7.5e+130) {
		tmp = t_0;
	} else if (im <= 9e+143) {
		tmp = t_1;
	} else if (im <= 1.06e+144) {
		tmp = t_0;
	} else if (im <= 3.8e+146) {
		tmp = t_1;
	} else if (im <= 6.4e+151) {
		tmp = t_0;
	} else if (im <= 1.4e+154) {
		tmp = t_1;
	} else {
		tmp = Math.cos(re) * (0.5 * Math.pow(im, 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = math.pow(im, 2.0) * (-0.25 * math.pow(re, 2.0))
	t_1 = 0.5 * (math.exp(-im) + math.exp(im))
	tmp = 0
	if im <= 250.0:
		tmp = math.cos(re)
	elif im <= 2.3e+18:
		tmp = t_1
	elif im <= 7.8e+18:
		tmp = t_0
	elif im <= 9.5e+34:
		tmp = t_1
	elif im <= 1e+35:
		tmp = t_0
	elif im <= 8.5e+79:
		tmp = t_1
	elif im <= 8.6e+79:
		tmp = t_0
	elif im <= 7.2e+130:
		tmp = t_1
	elif im <= 7.5e+130:
		tmp = t_0
	elif im <= 9e+143:
		tmp = t_1
	elif im <= 1.06e+144:
		tmp = t_0
	elif im <= 3.8e+146:
		tmp = t_1
	elif im <= 6.4e+151:
		tmp = t_0
	elif im <= 1.4e+154:
		tmp = t_1
	else:
		tmp = math.cos(re) * (0.5 * math.pow(im, 2.0))
	return tmp

Julia

function code(re, im)
	t_0 = Float64((im ^ 2.0) * Float64(-0.25 * (re ^ 2.0)))
	t_1 = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)))
	tmp = 0.0
	if (im <= 250.0)
		tmp = cos(re);
	elseif (im <= 2.3e+18)
		tmp = t_1;
	elseif (im <= 7.8e+18)
		tmp = t_0;
	elseif (im <= 9.5e+34)
		tmp = t_1;
	elseif (im <= 1e+35)
		tmp = t_0;
	elseif (im <= 8.5e+79)
		tmp = t_1;
	elseif (im <= 8.6e+79)
		tmp = t_0;
	elseif (im <= 7.2e+130)
		tmp = t_1;
	elseif (im <= 7.5e+130)
		tmp = t_0;
	elseif (im <= 9e+143)
		tmp = t_1;
	elseif (im <= 1.06e+144)
		tmp = t_0;
	elseif (im <= 3.8e+146)
		tmp = t_1;
	elseif (im <= 6.4e+151)
		tmp = t_0;
	elseif (im <= 1.4e+154)
		tmp = t_1;
	else
		tmp = Float64(cos(re) * Float64(0.5 * (im ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = (im ^ 2.0) * (-0.25 * (re ^ 2.0));
	t_1 = 0.5 * (exp(-im) + exp(im));
	tmp = 0.0;
	if (im <= 250.0)
		tmp = cos(re);
	elseif (im <= 2.3e+18)
		tmp = t_1;
	elseif (im <= 7.8e+18)
		tmp = t_0;
	elseif (im <= 9.5e+34)
		tmp = t_1;
	elseif (im <= 1e+35)
		tmp = t_0;
	elseif (im <= 8.5e+79)
		tmp = t_1;
	elseif (im <= 8.6e+79)
		tmp = t_0;
	elseif (im <= 7.2e+130)
		tmp = t_1;
	elseif (im <= 7.5e+130)
		tmp = t_0;
	elseif (im <= 9e+143)
		tmp = t_1;
	elseif (im <= 1.06e+144)
		tmp = t_0;
	elseif (im <= 3.8e+146)
		tmp = t_1;
	elseif (im <= 6.4e+151)
		tmp = t_0;
	elseif (im <= 1.4e+154)
		tmp = t_1;
	else
		tmp = cos(re) * (0.5 * (im ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(N[Power[im, 2.0], $MachinePrecision] * N[(-0.25 * N[Power[re, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[im, 250.0], N[Cos[re], $MachinePrecision], If[LessEqual[im, 2.3e+18], t$95$1, If[LessEqual[im, 7.8e+18], t$95$0, If[LessEqual[im, 9.5e+34], t$95$1, If[LessEqual[im, 1e+35], t$95$0, If[LessEqual[im, 8.5e+79], t$95$1, If[LessEqual[im, 8.6e+79], t$95$0, If[LessEqual[im, 7.2e+130], t$95$1, If[LessEqual[im, 7.5e+130], t$95$0, If[LessEqual[im, 9e+143], t$95$1, If[LessEqual[im, 1.06e+144], t$95$0, If[LessEqual[im, 3.8e+146], t$95$1, If[LessEqual[im, 6.4e+151], t$95$0, If[LessEqual[im, 1.4e+154], t$95$1, N[(N[Cos[re], $MachinePrecision] * N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if im < 250

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 67.1%

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

   if 250 < im < 2.3e18 or 7.8e18 < im < 9.4999999999999999e34 or 9.9999999999999997e34 < im < 8.4999999999999998e79 or 8.6000000000000006e79 < im < 7.2000000000000002e130 or 7.5000000000000003e130 < im < 8.9999999999999993e143 or 1.06e144 < im < 3.79999999999999979e146 or 6.39999999999999988e151 < im < 1.4e154

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in re around 0 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{im} + e^{-im}\right)} \]

   if 2.3e18 < im < 7.8e18 or 9.4999999999999999e34 < im < 9.9999999999999997e34 or 8.4999999999999998e79 < im < 8.6000000000000006e79 or 7.2000000000000002e130 < im < 7.5000000000000003e130 or 8.9999999999999993e143 < im < 1.06e144 or 3.79999999999999979e146 < im < 6.39999999999999988e151

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 5.4%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 5.4%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 5.4%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 5.4%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   6. Taylor expanded in im around inf 5.4%

      \[\leadsto \color{blue}{0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 5.4%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. *-commutative 5.4%

         \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   8. Simplified 5.4%

      \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   9. Taylor expanded in re around 0 84.1%

      \[\leadsto \color{blue}{-0.25 \cdot \left({im}^{2} \cdot {re}^{2}\right) + 0.5 \cdot {im}^{2}} \]
   10. Step-by-step derivation

       1. *-commutative 84.1%

          \[\leadsto -0.25 \cdot \color{blue}{\left({re}^{2} \cdot {im}^{2}\right)} + 0.5 \cdot {im}^{2} \]

       2. associate-*r* 84.1%

          \[\leadsto \color{blue}{\left(-0.25 \cdot {re}^{2}\right) \cdot {im}^{2}} + 0.5 \cdot {im}^{2} \]

       3. distribute-rgt-out 84.1%

          \[\leadsto \color{blue}{{im}^{2} \cdot \left(-0.25 \cdot {re}^{2} + 0.5\right)} \]

       4. +-commutative 84.1%

          \[\leadsto {im}^{2} \cdot \color{blue}{\left(0.5 + -0.25 \cdot {re}^{2}\right)} \]

   11. Simplified 84.1%

       \[\leadsto \color{blue}{{im}^{2} \cdot \left(0.5 + -0.25 \cdot {re}^{2}\right)} \]

   12. Taylor expanded in re around inf 84.1%

       \[\leadsto \color{blue}{-0.25 \cdot \left({im}^{2} \cdot {re}^{2}\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 84.1%

          \[\leadsto \color{blue}{\left(-0.25 \cdot {im}^{2}\right) \cdot {re}^{2}} \]

       2. *-commutative 84.1%

          \[\leadsto \color{blue}{\left({im}^{2} \cdot -0.25\right)} \cdot {re}^{2} \]

       3. associate-*r* 84.1%

          \[\leadsto \color{blue}{{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)} \]

   14. Simplified 84.1%

       \[\leadsto \color{blue}{{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)} \]

   if 1.4e154 < im

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 100.0%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 100.0%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   6. Taylor expanded in im around inf 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\cos re \cdot \left(0.5 \cdot {im}^{2}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 250:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.3 \cdot 10^{+18}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 10^{+35}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 8.6 \cdot 10^{+79}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 7.2 \cdot 10^{+130}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 7.5 \cdot 10^{+130}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 9 \cdot 10^{+143}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 1.06 \cdot 10^{+144}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 3.8 \cdot 10^{+146}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{elif}\;im \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;{im}^{2} \cdot \left(-0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(0.5 \cdot {im}^{2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cos re \leq 0.999:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;1 + 0.5 \cdot {im}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= (cos re) 0.999) (cos re) (+ 1.0 (* 0.5 (pow im 2.0)))))

C

double code(double re, double im) {
	double tmp;
	if (cos(re) <= 0.999) {
		tmp = cos(re);
	} else {
		tmp = 1.0 + (0.5 * pow(im, 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (cos(re) <= 0.999d0) then
        tmp = cos(re)
    else
        tmp = 1.0d0 + (0.5d0 * (im ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (Math.cos(re) <= 0.999) {
		tmp = Math.cos(re);
	} else {
		tmp = 1.0 + (0.5 * Math.pow(im, 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if math.cos(re) <= 0.999:
		tmp = math.cos(re)
	else:
		tmp = 1.0 + (0.5 * math.pow(im, 2.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (cos(re) <= 0.999)
		tmp = cos(re);
	else
		tmp = Float64(1.0 + Float64(0.5 * (im ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (cos(re) <= 0.999)
		tmp = cos(re);
	else
		tmp = 1.0 + (0.5 * (im ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[N[Cos[re], $MachinePrecision], 0.999], N[Cos[re], $MachinePrecision], N[(1.0 + N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 re) < 0.998999999999999999

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 55.9%

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

   if 0.998999999999999999 < (cos.f64 re)

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in im around 0 71.7%

      \[\leadsto \color{blue}{\cos re + 0.5 \cdot \left({im}^{2} \cdot \cos re\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 71.7%

         \[\leadsto \cos re + \color{blue}{\left(0.5 \cdot {im}^{2}\right) \cdot \cos re} \]

      2. distribute-rgt1-in 71.7%

         \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{\left(0.5 \cdot {im}^{2} + 1\right) \cdot \cos re} \]

   6. Taylor expanded in re around 0 71.2%

      \[\leadsto \color{blue}{1 + 0.5 \cdot {im}^{2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 49.7% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
2. Add Preprocessing

3. Taylor expanded in im around 0 51.6%

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

Alternative 8: 28.0% accurate, 308.0× speedup

Math

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

FPCore

(FPCore (re im) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(re, im):
	return 1.0

Julia

function code(re, im)
	return 1.0
end

MATLAB

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

Wolfram

code[re_, im_] := 1.0

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
2. Add Preprocessing

4. Applied egg-rr 26.6%

   \[\leadsto \color{blue}{\frac{\cos re \cdot -2}{\cos re \cdot -2 + \left(\cos re \cdot -2 - \cos re \cdot -2\right)}} \]
5. Step-by-step derivation

   1. +-inverses 26.6%

      \[\leadsto \frac{\cos re \cdot -2}{\cos re \cdot -2 + \color{blue}{0}} \]

   2. +-rgt-identity 26.6%

      \[\leadsto \frac{\cos re \cdot -2}{\color{blue}{\cos re \cdot -2}} \]

   3. *-inverses 26.6%

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

6. Simplified 26.6%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Alternative 9: 2.3% accurate, 308.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (re im) :precision binary64 0.0)

C

double code(double re, double im) {
	return 0.0;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 0.0d0
end function

Java

public static double code(double re, double im) {
	return 0.0;
}

Python

def code(re, im):
	return 0.0

Julia

function code(re, im)
	return 0.0
end

MATLAB

function tmp = code(re, im)
	tmp = 0.0;
end

Wolfram

code[re_, im_] := 0.0

Derivation

1. Initial program 100.0%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
2. Add Preprocessing

4. Applied egg-rr 2.4%

   \[\leadsto \color{blue}{\log \left({1}^{\cos re}\right)} \]
5. Step-by-step derivation

   1. pow-base-1 2.4%

      \[\leadsto \log \color{blue}{1} \]

   2. metadata-eval 2.4%

      \[\leadsto \color{blue}{0} \]

6. Simplified 2.4%

   \[\leadsto \color{blue}{0} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))