math.exp on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 9

Speedup: 1.0×

• 23.8% 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

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1. Add Preprocessing

Alternative 2: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 1.00000000000001\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im \cdot \left(re + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= (exp re) 0.0) (not (<= (exp re) 1.00000000000001)))
   (exp re)
   (* (cos im) (+ re 1.0))))

C

double code(double re, double im) {
	double tmp;
	if ((exp(re) <= 0.0) || !(exp(re) <= 1.00000000000001)) {
		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) <= 1.00000000000001d0))) 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) <= 1.00000000000001)) {
		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) <= 1.00000000000001):
		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) <= 1.00000000000001))
		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) <= 1.00000000000001)))
		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], 1.00000000000001]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[(N[Cos[im], $MachinePrecision] * N[(re + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 92.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{re} \leq 0 \lor \neg \left(e^{re} \leq 1.00000000000001\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;re + \cos im\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= (exp re) 0.0) (not (<= (exp re) 1.00000000000001)))
   (exp re)
   (+ re (cos im))))

C

double code(double re, double im) {
	double tmp;
	if ((exp(re) <= 0.0) || !(exp(re) <= 1.00000000000001)) {
		tmp = exp(re);
	} else {
		tmp = re + 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) <= 1.00000000000001d0))) then
        tmp = exp(re)
    else
        tmp = re + 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) <= 1.00000000000001)) {
		tmp = Math.exp(re);
	} else {
		tmp = re + Math.cos(im);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (math.exp(re) <= 0.0) or not (math.exp(re) <= 1.00000000000001):
		tmp = math.exp(re)
	else:
		tmp = re + math.cos(im)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((exp(re) <= 0.0) || !(exp(re) <= 1.00000000000001))
		tmp = exp(re);
	else
		tmp = Float64(re + cos(im));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((exp(re) <= 0.0) || ~((exp(re) <= 1.00000000000001)))
		tmp = exp(re);
	else
		tmp = re + 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], 1.00000000000001]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[(re + N[Cos[im], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 4: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{re} \leq 1 \lor \neg \left(e^{re} \leq 1.00000000000001\right):\\ \;\;\;\;e^{re}\\ \mathbf{else}:\\ \;\;\;\;\cos im\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= (exp re) 1.0) (not (<= (exp re) 1.00000000000001)))
   (exp re)
   (cos im)))

C

double code(double re, double im) {
	double tmp;
	if ((exp(re) <= 1.0) || !(exp(re) <= 1.00000000000001)) {
		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) <= 1.0d0) .or. (.not. (exp(re) <= 1.00000000000001d0))) 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) <= 1.0) || !(Math.exp(re) <= 1.00000000000001)) {
		tmp = Math.exp(re);
	} else {
		tmp = Math.cos(im);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (math.exp(re) <= 1.0) or not (math.exp(re) <= 1.00000000000001):
		tmp = math.exp(re)
	else:
		tmp = math.cos(im)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((exp(re) <= 1.0) || !(exp(re) <= 1.00000000000001))
		tmp = exp(re);
	else
		tmp = cos(im);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((exp(re) <= 1.0) || ~((exp(re) <= 1.00000000000001)))
		tmp = exp(re);
	else
		tmp = cos(im);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[N[Exp[re], $MachinePrecision], 1.0], N[Not[LessEqual[N[Exp[re], $MachinePrecision], 1.00000000000001]], $MachinePrecision]], N[Exp[re], $MachinePrecision], N[Cos[im], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 60.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -0.5 \cdot \left(im \cdot im\right)\\ \mathbf{if}\;re \leq -480:\\ \;\;\;\;\left(re + 1\right) \cdot t_0\\ \mathbf{elif}\;re \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;\cos im\\ \mathbf{else}:\\ \;\;\;\;\left(re + 1\right) \cdot \left(1 + t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* -0.5 (* im im))))
   (if (<= re -480.0)
     (* (+ re 1.0) t_0)
     (if (<= re 1.2e-14) (cos im) (* (+ re 1.0) (+ 1.0 t_0))))))

C

double code(double re, double im) {
	double t_0 = -0.5 * (im * im);
	double tmp;
	if (re <= -480.0) {
		tmp = (re + 1.0) * t_0;
	} else if (re <= 1.2e-14) {
		tmp = cos(im);
	} else {
		tmp = (re + 1.0) * (1.0 + t_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) :: tmp
    t_0 = (-0.5d0) * (im * im)
    if (re <= (-480.0d0)) then
        tmp = (re + 1.0d0) * t_0
    else if (re <= 1.2d-14) then
        tmp = cos(im)
    else
        tmp = (re + 1.0d0) * (1.0d0 + t_0)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = -0.5 * (im * im);
	double tmp;
	if (re <= -480.0) {
		tmp = (re + 1.0) * t_0;
	} else if (re <= 1.2e-14) {
		tmp = Math.cos(im);
	} else {
		tmp = (re + 1.0) * (1.0 + t_0);
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = -0.5 * (im * im)
	tmp = 0
	if re <= -480.0:
		tmp = (re + 1.0) * t_0
	elif re <= 1.2e-14:
		tmp = math.cos(im)
	else:
		tmp = (re + 1.0) * (1.0 + t_0)
	return tmp

Julia

function code(re, im)
	t_0 = Float64(-0.5 * Float64(im * im))
	tmp = 0.0
	if (re <= -480.0)
		tmp = Float64(Float64(re + 1.0) * t_0);
	elseif (re <= 1.2e-14)
		tmp = cos(im);
	else
		tmp = Float64(Float64(re + 1.0) * Float64(1.0 + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = -0.5 * (im * im);
	tmp = 0.0;
	if (re <= -480.0)
		tmp = (re + 1.0) * t_0;
	elseif (re <= 1.2e-14)
		tmp = cos(im);
	else
		tmp = (re + 1.0) * (1.0 + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(-0.5 * N[(im * im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[re, -480.0], N[(N[(re + 1.0), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[re, 1.2e-14], N[Cos[im], $MachinePrecision], N[(N[(re + 1.0), $MachinePrecision] * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 38.0% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -0.5 \cdot \left(im \cdot im\right)\\ \mathbf{if}\;re \leq -15.6:\\ \;\;\;\;\left(re + 1\right) \cdot t_0\\ \mathbf{elif}\;re \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;re + 1\\ \mathbf{else}:\\ \;\;\;\;\left(re + 1\right) \cdot \left(1 + t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* -0.5 (* im im))))
   (if (<= re -15.6)
     (* (+ re 1.0) t_0)
     (if (<= re 6.8e+109) (+ re 1.0) (* (+ re 1.0) (+ 1.0 t_0))))))

C

double code(double re, double im) {
	double t_0 = -0.5 * (im * im);
	double tmp;
	if (re <= -15.6) {
		tmp = (re + 1.0) * t_0;
	} else if (re <= 6.8e+109) {
		tmp = re + 1.0;
	} else {
		tmp = (re + 1.0) * (1.0 + t_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) :: tmp
    t_0 = (-0.5d0) * (im * im)
    if (re <= (-15.6d0)) then
        tmp = (re + 1.0d0) * t_0
    else if (re <= 6.8d+109) then
        tmp = re + 1.0d0
    else
        tmp = (re + 1.0d0) * (1.0d0 + t_0)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = -0.5 * (im * im);
	double tmp;
	if (re <= -15.6) {
		tmp = (re + 1.0) * t_0;
	} else if (re <= 6.8e+109) {
		tmp = re + 1.0;
	} else {
		tmp = (re + 1.0) * (1.0 + t_0);
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = -0.5 * (im * im)
	tmp = 0
	if re <= -15.6:
		tmp = (re + 1.0) * t_0
	elif re <= 6.8e+109:
		tmp = re + 1.0
	else:
		tmp = (re + 1.0) * (1.0 + t_0)
	return tmp

Julia

function code(re, im)
	t_0 = Float64(-0.5 * Float64(im * im))
	tmp = 0.0
	if (re <= -15.6)
		tmp = Float64(Float64(re + 1.0) * t_0);
	elseif (re <= 6.8e+109)
		tmp = Float64(re + 1.0);
	else
		tmp = Float64(Float64(re + 1.0) * Float64(1.0 + t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = -0.5 * (im * im);
	tmp = 0.0;
	if (re <= -15.6)
		tmp = (re + 1.0) * t_0;
	elseif (re <= 6.8e+109)
		tmp = re + 1.0;
	else
		tmp = (re + 1.0) * (1.0 + t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(-0.5 * N[(im * im), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[re, -15.6], N[(N[(re + 1.0), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[re, 6.8e+109], N[(re + 1.0), $MachinePrecision], N[(N[(re + 1.0), $MachinePrecision] * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 37.6% accurate, 15.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;re \leq -41 \lor \neg \left(re \leq 1.38 \cdot 10^{+110}\right):\\ \;\;\;\;\left(re + 1\right) \cdot \left(-0.5 \cdot \left(im \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;re + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (or (<= re -41.0) (not (<= re 1.38e+110)))
   (* (+ re 1.0) (* -0.5 (* im im)))
   (+ re 1.0)))

C

double code(double re, double im) {
	double tmp;
	if ((re <= -41.0) || !(re <= 1.38e+110)) {
		tmp = (re + 1.0) * (-0.5 * (im * im));
	} else {
		tmp = 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 <= (-41.0d0)) .or. (.not. (re <= 1.38d+110))) then
        tmp = (re + 1.0d0) * ((-0.5d0) * (im * im))
    else
        tmp = re + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if ((re <= -41.0) || !(re <= 1.38e+110)) {
		tmp = (re + 1.0) * (-0.5 * (im * im));
	} else {
		tmp = re + 1.0;
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if (re <= -41.0) or not (re <= 1.38e+110):
		tmp = (re + 1.0) * (-0.5 * (im * im))
	else:
		tmp = re + 1.0
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if ((re <= -41.0) || !(re <= 1.38e+110))
		tmp = Float64(Float64(re + 1.0) * Float64(-0.5 * Float64(im * im)));
	else
		tmp = Float64(re + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if ((re <= -41.0) || ~((re <= 1.38e+110)))
		tmp = (re + 1.0) * (-0.5 * (im * im));
	else
		tmp = re + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Or[LessEqual[re, -41.0], N[Not[LessEqual[re, 1.38e+110]], $MachinePrecision]], N[(N[(re + 1.0), $MachinePrecision] * N[(-0.5 * N[(im * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(re + 1.0), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 28.7% 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

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1. Add Preprocessing

Alternative 9: 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

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023347 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))