math.sin on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 9

Speedup: 1.0×

• 49.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * sin(re)) * (exp((0.0d0 - im)) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.sin(re)) * (Math.exp((0.0 - im)) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.sin(re)) * (math.exp((0.0 - im)) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * sin(re)) * Float64(exp(Float64(0.0 - im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * sin(re)) * (exp((0.0d0 - im)) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.sin(re)) * (Math.exp((0.0 - im)) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.sin(re)) * (math.exp((0.0 - im)) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * sin(re)) * Float64(exp(Float64(0.0 - im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * sin(re)) * (exp((0.0 - im)) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \sin re \cdot \mathsf{fma}\left(0.5, e^{im_m}, \frac{0.5}{e^{im_m}}\right) \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (* (sin re) (fma 0.5 (exp im_m) (/ 0.5 (exp im_m)))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	return sin(re) * fma(0.5, exp(im_m), (0.5 / exp(im_m)));
}

Julia

im_m = abs(im)
function code(re, im_m)
	return Float64(sin(re) * fma(0.5, exp(im_m), Float64(0.5 / exp(im_m))))
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := N[(N[Sin[re], $MachinePrecision] * N[(0.5 * N[Exp[im$95$m], $MachinePrecision] + N[(0.5 / N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 2: 100.0% accurate, 1.0× speedup

Math

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

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (* (* (sin re) 0.5) (+ (exp im_m) (exp (- im_m)))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	return (sin(re) * 0.5) * (exp(im_m) + exp(-im_m));
}

Fortran

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

Java

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

Python

im_m = math.fabs(im)
def code(re, im_m):
	return (math.sin(re) * 0.5) * (math.exp(im_m) + math.exp(-im_m))

Julia

im_m = abs(im)
function code(re, im_m)
	return Float64(Float64(sin(re) * 0.5) * Float64(exp(im_m) + exp(Float64(-im_m))))
end

MATLAB

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

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := N[(N[(N[Sin[re], $MachinePrecision] * 0.5), $MachinePrecision] * N[(N[Exp[im$95$m], $MachinePrecision] + N[Exp[(-im$95$m)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 3: 74.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \begin{array}{l} \mathbf{if}\;im_m \leq 0.000135:\\ \;\;\;\;\sin re\\ \mathbf{elif}\;im_m \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;re \cdot \cosh im_m\\ \mathbf{else}:\\ \;\;\;\;0.001388888888888889 \cdot \left(\sin re \cdot {im_m}^{6}\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (if (<= im_m 0.000135)
   (sin re)
   (if (<= im_m 2.4e+51)
     (* re (cosh im_m))
     (* 0.001388888888888889 (* (sin re) (pow im_m 6.0))))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	double tmp;
	if (im_m <= 0.000135) {
		tmp = sin(re);
	} else if (im_m <= 2.4e+51) {
		tmp = re * cosh(im_m);
	} else {
		tmp = 0.001388888888888889 * (sin(re) * pow(im_m, 6.0));
	}
	return tmp;
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 0.000135d0) then
        tmp = sin(re)
    else if (im_m <= 2.4d+51) then
        tmp = re * cosh(im_m)
    else
        tmp = 0.001388888888888889d0 * (sin(re) * (im_m ** 6.0d0))
    end if
    code = tmp
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	double tmp;
	if (im_m <= 0.000135) {
		tmp = Math.sin(re);
	} else if (im_m <= 2.4e+51) {
		tmp = re * Math.cosh(im_m);
	} else {
		tmp = 0.001388888888888889 * (Math.sin(re) * Math.pow(im_m, 6.0));
	}
	return tmp;
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	tmp = 0
	if im_m <= 0.000135:
		tmp = math.sin(re)
	elif im_m <= 2.4e+51:
		tmp = re * math.cosh(im_m)
	else:
		tmp = 0.001388888888888889 * (math.sin(re) * math.pow(im_m, 6.0))
	return tmp

Julia

im_m = abs(im)
function code(re, im_m)
	tmp = 0.0
	if (im_m <= 0.000135)
		tmp = sin(re);
	elseif (im_m <= 2.4e+51)
		tmp = Float64(re * cosh(im_m));
	else
		tmp = Float64(0.001388888888888889 * Float64(sin(re) * (im_m ^ 6.0)));
	end
	return tmp
end

MATLAB

im_m = abs(im);
function tmp_2 = code(re, im_m)
	tmp = 0.0;
	if (im_m <= 0.000135)
		tmp = sin(re);
	elseif (im_m <= 2.4e+51)
		tmp = re * cosh(im_m);
	else
		tmp = 0.001388888888888889 * (sin(re) * (im_m ^ 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := If[LessEqual[im$95$m, 0.000135], N[Sin[re], $MachinePrecision], If[LessEqual[im$95$m, 2.4e+51], N[(re * N[Cosh[im$95$m], $MachinePrecision]), $MachinePrecision], N[(0.001388888888888889 * N[(N[Sin[re], $MachinePrecision] * N[Power[im$95$m, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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Alternative 4: 98.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \sin re \cdot \left(0.5 + 0.5 \cdot e^{im_m}\right) \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m) :precision binary64 (* (sin re) (+ 0.5 (* 0.5 (exp im_m)))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	return sin(re) * (0.5 + (0.5 * exp(im_m)));
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    code = sin(re) * (0.5d0 + (0.5d0 * exp(im_m)))
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	return Math.sin(re) * (0.5 + (0.5 * Math.exp(im_m)));
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	return math.sin(re) * (0.5 + (0.5 * math.exp(im_m)))

Julia

im_m = abs(im)
function code(re, im_m)
	return Float64(sin(re) * Float64(0.5 + Float64(0.5 * exp(im_m))))
end

MATLAB

im_m = abs(im);
function tmp = code(re, im_m)
	tmp = sin(re) * (0.5 + (0.5 * exp(im_m)));
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := N[(N[Sin[re], $MachinePrecision] * N[(0.5 + N[(0.5 * N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 5: 68.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \begin{array}{l} \mathbf{if}\;im_m \leq 0.000165:\\ \;\;\;\;\sin re\\ \mathbf{else}:\\ \;\;\;\;re \cdot \cosh im_m\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (if (<= im_m 0.000165) (sin re) (* re (cosh im_m))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	double tmp;
	if (im_m <= 0.000165) {
		tmp = sin(re);
	} else {
		tmp = re * cosh(im_m);
	}
	return tmp;
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 0.000165d0) then
        tmp = sin(re)
    else
        tmp = re * cosh(im_m)
    end if
    code = tmp
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	double tmp;
	if (im_m <= 0.000165) {
		tmp = Math.sin(re);
	} else {
		tmp = re * Math.cosh(im_m);
	}
	return tmp;
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	tmp = 0
	if im_m <= 0.000165:
		tmp = math.sin(re)
	else:
		tmp = re * math.cosh(im_m)
	return tmp

Julia

im_m = abs(im)
function code(re, im_m)
	tmp = 0.0
	if (im_m <= 0.000165)
		tmp = sin(re);
	else
		tmp = Float64(re * cosh(im_m));
	end
	return tmp
end

MATLAB

im_m = abs(im);
function tmp_2 = code(re, im_m)
	tmp = 0.0;
	if (im_m <= 0.000165)
		tmp = sin(re);
	else
		tmp = re * cosh(im_m);
	end
	tmp_2 = tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := If[LessEqual[im$95$m, 0.000165], N[Sin[re], $MachinePrecision], N[(re * N[Cosh[im$95$m], $MachinePrecision]), $MachinePrecision]]

Derivation

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Alternative 6: 53.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \begin{array}{l} \mathbf{if}\;im_m \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;\sin re\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(0.5 \cdot im_m\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (if (<= im_m 1.1e+46) (sin re) (* re (* 0.5 im_m))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	double tmp;
	if (im_m <= 1.1e+46) {
		tmp = sin(re);
	} else {
		tmp = re * (0.5 * im_m);
	}
	return tmp;
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 1.1d+46) then
        tmp = sin(re)
    else
        tmp = re * (0.5d0 * im_m)
    end if
    code = tmp
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	double tmp;
	if (im_m <= 1.1e+46) {
		tmp = Math.sin(re);
	} else {
		tmp = re * (0.5 * im_m);
	}
	return tmp;
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	tmp = 0
	if im_m <= 1.1e+46:
		tmp = math.sin(re)
	else:
		tmp = re * (0.5 * im_m)
	return tmp

Julia

im_m = abs(im)
function code(re, im_m)
	tmp = 0.0
	if (im_m <= 1.1e+46)
		tmp = sin(re);
	else
		tmp = Float64(re * Float64(0.5 * im_m));
	end
	return tmp
end

MATLAB

im_m = abs(im);
function tmp_2 = code(re, im_m)
	tmp = 0.0;
	if (im_m <= 1.1e+46)
		tmp = sin(re);
	else
		tmp = re * (0.5 * im_m);
	end
	tmp_2 = tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := If[LessEqual[im$95$m, 1.1e+46], N[Sin[re], $MachinePrecision], N[(re * N[(0.5 * im$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

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Alternative 7: 30.3% accurate, 43.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ \begin{array}{l} \mathbf{if}\;re \leq 8.8 \cdot 10^{+23}:\\ \;\;\;\;re\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(0.5 \cdot im_m\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m)
 :precision binary64
 (if (<= re 8.8e+23) re (* re (* 0.5 im_m))))

C

im_m = fabs(im);
double code(double re, double im_m) {
	double tmp;
	if (re <= 8.8e+23) {
		tmp = re;
	} else {
		tmp = re * (0.5 * im_m);
	}
	return tmp;
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (re <= 8.8d+23) then
        tmp = re
    else
        tmp = re * (0.5d0 * im_m)
    end if
    code = tmp
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	double tmp;
	if (re <= 8.8e+23) {
		tmp = re;
	} else {
		tmp = re * (0.5 * im_m);
	}
	return tmp;
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	tmp = 0
	if re <= 8.8e+23:
		tmp = re
	else:
		tmp = re * (0.5 * im_m)
	return tmp

Julia

im_m = abs(im)
function code(re, im_m)
	tmp = 0.0
	if (re <= 8.8e+23)
		tmp = re;
	else
		tmp = Float64(re * Float64(0.5 * im_m));
	end
	return tmp
end

MATLAB

im_m = abs(im);
function tmp_2 = code(re, im_m)
	tmp = 0.0;
	if (re <= 8.8e+23)
		tmp = re;
	else
		tmp = re * (0.5 * im_m);
	end
	tmp_2 = tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := If[LessEqual[re, 8.8e+23], re, N[(re * N[(0.5 * im$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

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Alternative 8: 32.9% accurate, 44.1× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ re \cdot \left(0.5 \cdot im_m + 1\right) \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m) :precision binary64 (* re (+ (* 0.5 im_m) 1.0)))

C

im_m = fabs(im);
double code(double re, double im_m) {
	return re * ((0.5 * im_m) + 1.0);
}

Fortran

im_m = abs(im)
real(8) function code(re, im_m)
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    code = re * ((0.5d0 * im_m) + 1.0d0)
end function

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	return re * ((0.5 * im_m) + 1.0);
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	return re * ((0.5 * im_m) + 1.0)

Julia

im_m = abs(im)
function code(re, im_m)
	return Float64(re * Float64(Float64(0.5 * im_m) + 1.0))
end

MATLAB

im_m = abs(im);
function tmp = code(re, im_m)
	tmp = re * ((0.5 * im_m) + 1.0);
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := N[(re * N[(N[(0.5 * im$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

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Alternative 9: 27.0% accurate, 309.0× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ re \end{array} \]

FPCore

im_m = (fabs.f64 im)
(FPCore (re im_m) :precision binary64 re)

C

im_m = fabs(im);
double code(double re, double im_m) {
	return re;
}

Fortran

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

Java

im_m = Math.abs(im);
public static double code(double re, double im_m) {
	return re;
}

Python

im_m = math.fabs(im)
def code(re, im_m):
	return re

Julia

im_m = abs(im)
function code(re, im_m)
	return re
end

MATLAB

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

Wolfram

im_m = N[Abs[im], $MachinePrecision]
code[re_, im$95$m_] := re

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023342 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))