Migdal et al, Equation (64)

Percentage Accurate: 99.5% → 99.6%

Time: 11.3s

Alternatives: 16

Speedup: 2.0×

• 43.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\cos th}{\sqrt{2}}\\ t_1 \cdot \left(a1 \cdot a1\right) + t_1 \cdot \left(a2 \cdot a2\right) \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 th)
 :precision binary64
 (let* ((t_1 (/ (cos th) (sqrt 2.0))))
   (+ (* t_1 (* a1 a1)) (* t_1 (* a2 a2)))))

C

double code(double a1, double a2, double th) {
	double t_1 = cos(th) / sqrt(2.0);
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
}

Fortran

real(8) function code(a1, a2, th)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: t_1
    t_1 = cos(th) / sqrt(2.0d0)
    code = (t_1 * (a1 * a1)) + (t_1 * (a2 * a2))
end function

Java

public static double code(double a1, double a2, double th) {
	double t_1 = Math.cos(th) / Math.sqrt(2.0);
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
}

Python

def code(a1, a2, th):
	t_1 = math.cos(th) / math.sqrt(2.0)
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2))

Julia

function code(a1, a2, th)
	t_1 = Float64(cos(th) / sqrt(2.0))
	return Float64(Float64(t_1 * Float64(a1 * a1)) + Float64(t_1 * Float64(a2 * a2)))
end

MATLAB

function tmp = code(a1, a2, th)
	t_1 = cos(th) / sqrt(2.0);
	tmp = (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
end

Wolfram

code[a1_, a2_, th_] := Block[{t$95$1 = N[(N[Cos[th], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$1 * N[(a1 * a1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(a2 * a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\cos th}{\sqrt{2}}\\ t_1 \cdot \left(a1 \cdot a1\right) + t_1 \cdot \left(a2 \cdot a2\right) \end{array} \end{array} \]

FPCore

(FPCore (a1 a2 th)
 :precision binary64
 (let* ((t_1 (/ (cos th) (sqrt 2.0))))
   (+ (* t_1 (* a1 a1)) (* t_1 (* a2 a2)))))

C

double code(double a1, double a2, double th) {
	double t_1 = cos(th) / sqrt(2.0);
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
}

Fortran

real(8) function code(a1, a2, th)
    real(8), intent (in) :: a1
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: t_1
    t_1 = cos(th) / sqrt(2.0d0)
    code = (t_1 * (a1 * a1)) + (t_1 * (a2 * a2))
end function

Java

public static double code(double a1, double a2, double th) {
	double t_1 = Math.cos(th) / Math.sqrt(2.0);
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
}

Python

def code(a1, a2, th):
	t_1 = math.cos(th) / math.sqrt(2.0)
	return (t_1 * (a1 * a1)) + (t_1 * (a2 * a2))

Julia

function code(a1, a2, th)
	t_1 = Float64(cos(th) / sqrt(2.0))
	return Float64(Float64(t_1 * Float64(a1 * a1)) + Float64(t_1 * Float64(a2 * a2)))
end

MATLAB

function tmp = code(a1, a2, th)
	t_1 = cos(th) / sqrt(2.0);
	tmp = (t_1 * (a1 * a1)) + (t_1 * (a2 * a2));
end

Wolfram

code[a1_, a2_, th_] := Block[{t$95$1 = N[(N[Cos[th], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$1 * N[(a1 * a1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(a2 * a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} t_1 := \frac{\cos th}{\sqrt{2}}\\ \mathsf{fma}\left(t_1 \cdot a2, a2, t_1 \cdot {a1_m}^{2}\right) \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (let* ((t_1 (/ (cos th) (sqrt 2.0))))
   (fma (* t_1 a2) a2 (* t_1 (pow a1_m 2.0)))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double t_1 = cos(th) / sqrt(2.0);
	return fma((t_1 * a2), a2, (t_1 * pow(a1_m, 2.0)));
}

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	t_1 = Float64(cos(th) / sqrt(2.0))
	return fma(Float64(t_1 * a2), a2, Float64(t_1 * (a1_m ^ 2.0)))
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := Block[{t$95$1 = N[(N[Cos[th], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$1 * a2), $MachinePrecision] * a2 + N[(t$95$1 * N[Power[a1$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \cos th \cdot \frac{{\left(\mathsf{hypot}\left(a1_m, a2\right)\right)}^{2}}{\sqrt{2}} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (* (cos th) (/ (pow (hypot a1_m a2) 2.0) (sqrt 2.0))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return cos(th) * (pow(hypot(a1_m, a2), 2.0) / sqrt(2.0));
}

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return Math.cos(th) * (Math.pow(Math.hypot(a1_m, a2), 2.0) / Math.sqrt(2.0));
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return math.cos(th) * (math.pow(math.hypot(a1_m, a2), 2.0) / math.sqrt(2.0))

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(cos(th) * Float64((hypot(a1_m, a2) ^ 2.0) / sqrt(2.0)))
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = cos(th) * ((hypot(a1_m, a2) ^ 2.0) / sqrt(2.0));
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(N[Cos[th], $MachinePrecision] * N[(N[Power[N[Sqrt[a1$95$m ^ 2 + a2 ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \frac{\cos th}{\sqrt{2} \cdot {\left(\mathsf{hypot}\left(a1_m, a2\right)\right)}^{-2}} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (/ (cos th) (* (sqrt 2.0) (pow (hypot a1_m a2) -2.0))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return cos(th) / (sqrt(2.0) * pow(hypot(a1_m, a2), -2.0));
}

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return Math.cos(th) / (Math.sqrt(2.0) * Math.pow(Math.hypot(a1_m, a2), -2.0));
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return math.cos(th) / (math.sqrt(2.0) * math.pow(math.hypot(a1_m, a2), -2.0))

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(cos(th) / Float64(sqrt(2.0) * (hypot(a1_m, a2) ^ -2.0)))
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = cos(th) / (sqrt(2.0) * (hypot(a1_m, a2) ^ -2.0));
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(N[Cos[th], $MachinePrecision] / N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[Sqrt[a1$95$m ^ 2 + a2 ^ 2], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 79.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;\cos th \leq 0.7:\\ \;\;\;\;\cos th \cdot \left(\left(a2 + a1_m\right) \cdot \left(a2 + a1_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a1_m \cdot a1_m + a2 \cdot a2\right) \cdot {0.25}^{0.25}\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= (cos th) 0.7)
   (* (cos th) (* (+ a2 a1_m) (+ a2 a1_m)))
   (* (+ (* a1_m a1_m) (* a2 a2)) (pow 0.25 0.25))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (cos(th) <= 0.7) {
		tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	} else {
		tmp = ((a1_m * a1_m) + (a2 * a2)) * pow(0.25, 0.25);
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (cos(th) <= 0.7d0) then
        tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m))
    else
        tmp = ((a1_m * a1_m) + (a2 * a2)) * (0.25d0 ** 0.25d0)
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (Math.cos(th) <= 0.7) {
		tmp = Math.cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	} else {
		tmp = ((a1_m * a1_m) + (a2 * a2)) * Math.pow(0.25, 0.25);
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if math.cos(th) <= 0.7:
		tmp = math.cos(th) * ((a2 + a1_m) * (a2 + a1_m))
	else:
		tmp = ((a1_m * a1_m) + (a2 * a2)) * math.pow(0.25, 0.25)
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (cos(th) <= 0.7)
		tmp = Float64(cos(th) * Float64(Float64(a2 + a1_m) * Float64(a2 + a1_m)));
	else
		tmp = Float64(Float64(Float64(a1_m * a1_m) + Float64(a2 * a2)) * (0.25 ^ 0.25));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (cos(th) <= 0.7)
		tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	else
		tmp = ((a1_m * a1_m) + (a2 * a2)) * (0.25 ^ 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[N[Cos[th], $MachinePrecision], 0.7], N[(N[Cos[th], $MachinePrecision] * N[(N[(a2 + a1$95$m), $MachinePrecision] * N[(a2 + a1$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision] * N[Power[0.25, 0.25], $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 79.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} t_1 := a1_m \cdot a1_m + a2 \cdot a2\\ \mathbf{if}\;\cos th \leq 0.7:\\ \;\;\;\;\cos th \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot {0.25}^{0.25}\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (let* ((t_1 (+ (* a1_m a1_m) (* a2 a2))))
   (if (<= (cos th) 0.7) (* (cos th) t_1) (* t_1 (pow 0.25 0.25)))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double t_1 = (a1_m * a1_m) + (a2 * a2);
	double tmp;
	if (cos(th) <= 0.7) {
		tmp = cos(th) * t_1;
	} else {
		tmp = t_1 * pow(0.25, 0.25);
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a1_m * a1_m) + (a2 * a2)
    if (cos(th) <= 0.7d0) then
        tmp = cos(th) * t_1
    else
        tmp = t_1 * (0.25d0 ** 0.25d0)
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double t_1 = (a1_m * a1_m) + (a2 * a2);
	double tmp;
	if (Math.cos(th) <= 0.7) {
		tmp = Math.cos(th) * t_1;
	} else {
		tmp = t_1 * Math.pow(0.25, 0.25);
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	t_1 = (a1_m * a1_m) + (a2 * a2)
	tmp = 0
	if math.cos(th) <= 0.7:
		tmp = math.cos(th) * t_1
	else:
		tmp = t_1 * math.pow(0.25, 0.25)
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	t_1 = Float64(Float64(a1_m * a1_m) + Float64(a2 * a2))
	tmp = 0.0
	if (cos(th) <= 0.7)
		tmp = Float64(cos(th) * t_1);
	else
		tmp = Float64(t_1 * (0.25 ^ 0.25));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	t_1 = (a1_m * a1_m) + (a2 * a2);
	tmp = 0.0;
	if (cos(th) <= 0.7)
		tmp = cos(th) * t_1;
	else
		tmp = t_1 * (0.25 ^ 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := Block[{t$95$1 = N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[th], $MachinePrecision], 0.7], N[(N[Cos[th], $MachinePrecision] * t$95$1), $MachinePrecision], N[(t$95$1 * N[Power[0.25, 0.25], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 99.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \left(\cos th \cdot {2}^{-0.5}\right) \cdot \left(a1_m \cdot a1_m + a2 \cdot a2\right) \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (* (* (cos th) (pow 2.0 -0.5)) (+ (* a1_m a1_m) (* a2 a2))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return (cos(th) * pow(2.0, -0.5)) * ((a1_m * a1_m) + (a2 * a2));
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    code = (cos(th) * (2.0d0 ** (-0.5d0))) * ((a1_m * a1_m) + (a2 * a2))
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return (Math.cos(th) * Math.pow(2.0, -0.5)) * ((a1_m * a1_m) + (a2 * a2));
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return (math.cos(th) * math.pow(2.0, -0.5)) * ((a1_m * a1_m) + (a2 * a2))

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(Float64(cos(th) * (2.0 ^ -0.5)) * Float64(Float64(a1_m * a1_m) + Float64(a2 * a2)))
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = (cos(th) * (2.0 ^ -0.5)) * ((a1_m * a1_m) + (a2 * a2));
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(N[(N[Cos[th], $MachinePrecision] * N[Power[2.0, -0.5], $MachinePrecision]), $MachinePrecision] * N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 67.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;\cos th \leq 0.7:\\ \;\;\;\;\cos th \cdot \left(\left(a2 + a1_m\right) \cdot \left(a2 + a1_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a2}{\sqrt{2}}\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= (cos th) 0.7)
   (* (cos th) (* (+ a2 a1_m) (+ a2 a1_m)))
   (* a2 (/ a2 (sqrt 2.0)))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (cos(th) <= 0.7) {
		tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	} else {
		tmp = a2 * (a2 / sqrt(2.0));
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (cos(th) <= 0.7d0) then
        tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m))
    else
        tmp = a2 * (a2 / sqrt(2.0d0))
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (Math.cos(th) <= 0.7) {
		tmp = Math.cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	} else {
		tmp = a2 * (a2 / Math.sqrt(2.0));
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if math.cos(th) <= 0.7:
		tmp = math.cos(th) * ((a2 + a1_m) * (a2 + a1_m))
	else:
		tmp = a2 * (a2 / math.sqrt(2.0))
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (cos(th) <= 0.7)
		tmp = Float64(cos(th) * Float64(Float64(a2 + a1_m) * Float64(a2 + a1_m)));
	else
		tmp = Float64(a2 * Float64(a2 / sqrt(2.0)));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (cos(th) <= 0.7)
		tmp = cos(th) * ((a2 + a1_m) * (a2 + a1_m));
	else
		tmp = a2 * (a2 / sqrt(2.0));
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[N[Cos[th], $MachinePrecision], 0.7], N[(N[Cos[th], $MachinePrecision] * N[(N[(a2 + a1$95$m), $MachinePrecision] * N[(a2 + a1$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a2 / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 99.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \frac{\cos th}{\sqrt{2}} \cdot \left(a1_m \cdot a1_m + a2 \cdot a2\right) \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (* (/ (cos th) (sqrt 2.0)) (+ (* a1_m a1_m) (* a2 a2))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return (cos(th) / sqrt(2.0)) * ((a1_m * a1_m) + (a2 * a2));
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    code = (cos(th) / sqrt(2.0d0)) * ((a1_m * a1_m) + (a2 * a2))
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return (Math.cos(th) / Math.sqrt(2.0)) * ((a1_m * a1_m) + (a2 * a2));
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return (math.cos(th) / math.sqrt(2.0)) * ((a1_m * a1_m) + (a2 * a2))

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(Float64(cos(th) / sqrt(2.0)) * Float64(Float64(a1_m * a1_m) + Float64(a2 * a2)))
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = (cos(th) / sqrt(2.0)) * ((a1_m * a1_m) + (a2 * a2));
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(N[(N[Cos[th], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 63.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;\cos th \leq -1 \cdot 10^{-310}:\\ \;\;\;\;-0.5 \cdot {a2}^{2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \left(a2 \cdot {2}^{-0.5}\right)\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= (cos th) -1e-310) (* -0.5 (pow a2 2.0)) (* a2 (* a2 (pow 2.0 -0.5)))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (cos(th) <= -1e-310) {
		tmp = -0.5 * pow(a2, 2.0);
	} else {
		tmp = a2 * (a2 * pow(2.0, -0.5));
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (cos(th) <= (-1d-310)) then
        tmp = (-0.5d0) * (a2 ** 2.0d0)
    else
        tmp = a2 * (a2 * (2.0d0 ** (-0.5d0)))
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (Math.cos(th) <= -1e-310) {
		tmp = -0.5 * Math.pow(a2, 2.0);
	} else {
		tmp = a2 * (a2 * Math.pow(2.0, -0.5));
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if math.cos(th) <= -1e-310:
		tmp = -0.5 * math.pow(a2, 2.0)
	else:
		tmp = a2 * (a2 * math.pow(2.0, -0.5))
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (cos(th) <= -1e-310)
		tmp = Float64(-0.5 * (a2 ^ 2.0));
	else
		tmp = Float64(a2 * Float64(a2 * (2.0 ^ -0.5)));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (cos(th) <= -1e-310)
		tmp = -0.5 * (a2 ^ 2.0);
	else
		tmp = a2 * (a2 * (2.0 ^ -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[N[Cos[th], $MachinePrecision], -1e-310], N[(-0.5 * N[Power[a2, 2.0], $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a2 * N[Power[2.0, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 63.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;\cos th \leq -1 \cdot 10^{-310}:\\ \;\;\;\;-0.5 \cdot {a2}^{2}\\ \mathbf{else}:\\ \;\;\;\;a2 \cdot \frac{a2}{\sqrt{2}}\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= (cos th) -1e-310) (* -0.5 (pow a2 2.0)) (* a2 (/ a2 (sqrt 2.0)))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (cos(th) <= -1e-310) {
		tmp = -0.5 * pow(a2, 2.0);
	} else {
		tmp = a2 * (a2 / sqrt(2.0));
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (cos(th) <= (-1d-310)) then
        tmp = (-0.5d0) * (a2 ** 2.0d0)
    else
        tmp = a2 * (a2 / sqrt(2.0d0))
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (Math.cos(th) <= -1e-310) {
		tmp = -0.5 * Math.pow(a2, 2.0);
	} else {
		tmp = a2 * (a2 / Math.sqrt(2.0));
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if math.cos(th) <= -1e-310:
		tmp = -0.5 * math.pow(a2, 2.0)
	else:
		tmp = a2 * (a2 / math.sqrt(2.0))
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (cos(th) <= -1e-310)
		tmp = Float64(-0.5 * (a2 ^ 2.0));
	else
		tmp = Float64(a2 * Float64(a2 / sqrt(2.0)));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (cos(th) <= -1e-310)
		tmp = -0.5 * (a2 ^ 2.0);
	else
		tmp = a2 * (a2 / sqrt(2.0));
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[N[Cos[th], $MachinePrecision], -1e-310], N[(-0.5 * N[Power[a2, 2.0], $MachinePrecision]), $MachinePrecision], N[(a2 * N[(a2 / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 57.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;\cos th \leq -1 \cdot 10^{-310}:\\ \;\;\;\;-0.5 \cdot {a2}^{2}\\ \mathbf{else}:\\ \;\;\;\;\left(a1_m \cdot a1_m + a2 \cdot a2\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= (cos th) -1e-310)
   (* -0.5 (pow a2 2.0))
   (* (+ (* a1_m a1_m) (* a2 a2)) 0.5)))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (cos(th) <= -1e-310) {
		tmp = -0.5 * pow(a2, 2.0);
	} else {
		tmp = ((a1_m * a1_m) + (a2 * a2)) * 0.5;
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (cos(th) <= (-1d-310)) then
        tmp = (-0.5d0) * (a2 ** 2.0d0)
    else
        tmp = ((a1_m * a1_m) + (a2 * a2)) * 0.5d0
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (Math.cos(th) <= -1e-310) {
		tmp = -0.5 * Math.pow(a2, 2.0);
	} else {
		tmp = ((a1_m * a1_m) + (a2 * a2)) * 0.5;
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if math.cos(th) <= -1e-310:
		tmp = -0.5 * math.pow(a2, 2.0)
	else:
		tmp = ((a1_m * a1_m) + (a2 * a2)) * 0.5
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (cos(th) <= -1e-310)
		tmp = Float64(-0.5 * (a2 ^ 2.0));
	else
		tmp = Float64(Float64(Float64(a1_m * a1_m) + Float64(a2 * a2)) * 0.5);
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (cos(th) <= -1e-310)
		tmp = -0.5 * (a2 ^ 2.0);
	else
		tmp = ((a1_m * a1_m) + (a2 * a2)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[N[Cos[th], $MachinePrecision], -1e-310], N[(-0.5 * N[Power[a2, 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 59.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} t_1 := a1_m \cdot a1_m + a2 \cdot a2\\ \mathbf{if}\;\cos th \leq -1 \cdot 10^{-310}:\\ \;\;\;\;-0.5 \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot 0.5\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (let* ((t_1 (+ (* a1_m a1_m) (* a2 a2))))
   (if (<= (cos th) -1e-310) (* -0.5 t_1) (* t_1 0.5))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double t_1 = (a1_m * a1_m) + (a2 * a2);
	double tmp;
	if (cos(th) <= -1e-310) {
		tmp = -0.5 * t_1;
	} else {
		tmp = t_1 * 0.5;
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a1_m * a1_m) + (a2 * a2)
    if (cos(th) <= (-1d-310)) then
        tmp = (-0.5d0) * t_1
    else
        tmp = t_1 * 0.5d0
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double t_1 = (a1_m * a1_m) + (a2 * a2);
	double tmp;
	if (Math.cos(th) <= -1e-310) {
		tmp = -0.5 * t_1;
	} else {
		tmp = t_1 * 0.5;
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	t_1 = (a1_m * a1_m) + (a2 * a2)
	tmp = 0
	if math.cos(th) <= -1e-310:
		tmp = -0.5 * t_1
	else:
		tmp = t_1 * 0.5
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	t_1 = Float64(Float64(a1_m * a1_m) + Float64(a2 * a2))
	tmp = 0.0
	if (cos(th) <= -1e-310)
		tmp = Float64(-0.5 * t_1);
	else
		tmp = Float64(t_1 * 0.5);
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	t_1 = (a1_m * a1_m) + (a2 * a2);
	tmp = 0.0;
	if (cos(th) <= -1e-310)
		tmp = -0.5 * t_1;
	else
		tmp = t_1 * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := Block[{t$95$1 = N[(N[(a1$95$m * a1$95$m), $MachinePrecision] + N[(a2 * a2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[th], $MachinePrecision], -1e-310], N[(-0.5 * t$95$1), $MachinePrecision], N[(t$95$1 * 0.5), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 9.2% accurate, 58.8× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \begin{array}{l} \mathbf{if}\;th \leq 26.5:\\ \;\;\;\;a2 + a1_m\\ \mathbf{else}:\\ \;\;\;\;a1_m - a2 \cdot a2\\ \end{array} \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th)
 :precision binary64
 (if (<= th 26.5) (+ a2 a1_m) (- a1_m (* a2 a2))))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	double tmp;
	if (th <= 26.5) {
		tmp = a2 + a1_m;
	} else {
		tmp = a1_m - (a2 * a2);
	}
	return tmp;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    real(8) :: tmp
    if (th <= 26.5d0) then
        tmp = a2 + a1_m
    else
        tmp = a1_m - (a2 * a2)
    end if
    code = tmp
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	double tmp;
	if (th <= 26.5) {
		tmp = a2 + a1_m;
	} else {
		tmp = a1_m - (a2 * a2);
	}
	return tmp;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	tmp = 0
	if th <= 26.5:
		tmp = a2 + a1_m
	else:
		tmp = a1_m - (a2 * a2)
	return tmp

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	tmp = 0.0
	if (th <= 26.5)
		tmp = Float64(a2 + a1_m);
	else
		tmp = Float64(a1_m - Float64(a2 * a2));
	end
	return tmp
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp_2 = code(a1_m, a2, th)
	tmp = 0.0;
	if (th <= 26.5)
		tmp = a2 + a1_m;
	else
		tmp = a1_m - (a2 * a2);
	end
	tmp_2 = tmp;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := If[LessEqual[th, 26.5], N[(a2 + a1$95$m), $MachinePrecision], N[(a1$95$m - N[(a2 * a2), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 46.3% accurate, 59.3× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ \left(a2 + a1_m\right) \cdot \left(a2 + a1_m\right) \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th) :precision binary64 (* (+ a2 a1_m) (+ a2 a1_m)))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return (a2 + a1_m) * (a2 + a1_m);
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    code = (a2 + a1_m) * (a2 + a1_m)
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return (a2 + a1_m) * (a2 + a1_m);
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return (a2 + a1_m) * (a2 + a1_m)

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(Float64(a2 + a1_m) * Float64(a2 + a1_m))
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = (a2 + a1_m) * (a2 + a1_m);
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(N[(a2 + a1$95$m), $MachinePrecision] * N[(a2 + a1$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 4.7% accurate, 138.3× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ a2 + a1_m \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th) :precision binary64 (+ a2 a1_m))

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return a2 + a1_m;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    code = a2 + a1_m
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return a2 + a1_m;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return a2 + a1_m

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return Float64(a2 + a1_m)
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = a2 + a1_m;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := N[(a2 + a1$95$m), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 3.5% accurate, 415.0× speedup

Math

\[\begin{array}{l} a1_m = \left|a1\right| \\ [a1_m, a2, th] = \mathsf{sort}([a1_m, a2, th])\\ \\ 1 \end{array} \]

FPCore

a1_m = (fabs.f64 a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
(FPCore (a1_m a2 th) :precision binary64 1.0)

C

a1_m = fabs(a1);
assert(a1_m < a2 && a2 < th);
double code(double a1_m, double a2, double th) {
	return 1.0;
}

Fortran

a1_m = abs(a1)
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
real(8) function code(a1_m, a2, th)
    real(8), intent (in) :: a1_m
    real(8), intent (in) :: a2
    real(8), intent (in) :: th
    code = 1.0d0
end function

Java

a1_m = Math.abs(a1);
assert a1_m < a2 && a2 < th;
public static double code(double a1_m, double a2, double th) {
	return 1.0;
}

Python

a1_m = math.fabs(a1)
[a1_m, a2, th] = sort([a1_m, a2, th])
def code(a1_m, a2, th):
	return 1.0

Julia

a1_m = abs(a1)
a1_m, a2, th = sort([a1_m, a2, th])
function code(a1_m, a2, th)
	return 1.0
end

MATLAB

a1_m = abs(a1);
a1_m, a2, th = num2cell(sort([a1_m, a2, th])){:}
function tmp = code(a1_m, a2, th)
	tmp = 1.0;
end

Wolfram

a1_m = N[Abs[a1], $MachinePrecision]
NOTE: a1_m, a2, and th should be sorted in increasing order before calling this function.
code[a1$95$m_, a2_, th_] := 1.0

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023347 
(FPCore (a1 a2 th)
  :name "Migdal et al, Equation (64)"
  :precision binary64
  (+ (* (/ (cos th) (sqrt 2.0)) (* a1 a1)) (* (/ (cos th) (sqrt 2.0)) (* a2 a2))))