Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 20

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (((x + y) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (- 1.0 (log t))) (fma (+ a -0.5) b (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (z * (1.0 - log(t))) + fma((a + -0.5), b, (x + y));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(z * Float64(1.0 - log(t))) + fma(Float64(a + -0.5), b, Float64(x + y)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+112} \lor \neg \left(t_1 \leq 2 \cdot 10^{+102}\right):\\ \;\;\;\;t_1 + \left(x + \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+112) (not (<= t_1 2e+102)))
     (+ t_1 (+ x (+ z y)))
     (+ x (+ (* z (- 1.0 (log t))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+112) || !(t_1 <= 2e+102)) {
		tmp = t_1 + (x + (z + y));
	} else {
		tmp = x + ((z * (1.0 - log(t))) + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+112)) .or. (.not. (t_1 <= 2d+102))) then
        tmp = t_1 + (x + (z + y))
    else
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+112) || !(t_1 <= 2e+102)) {
		tmp = t_1 + (x + (z + y));
	} else {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+112) or not (t_1 <= 2e+102):
		tmp = t_1 + (x + (z + y))
	else:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+112) || !(t_1 <= 2e+102))
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+112) || ~((t_1 <= 2e+102)))
		tmp = t_1 + (x + (z + y));
	else
		tmp = x + ((z * (1.0 - log(t))) + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+112], N[Not[LessEqual[t$95$1, 2e+102]], $MachinePrecision]], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 3: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+112}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x + \left(t_2 + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (* z (- 1.0 (log t)))))
   (if (<= t_1 -1e+112)
     (+ t_2 t_1)
     (if (<= t_1 2e+102) (+ x (+ t_2 y)) (+ t_1 (+ x (+ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = z * (1.0 - log(t));
	double tmp;
	if (t_1 <= -1e+112) {
		tmp = t_2 + t_1;
	} else if (t_1 <= 2e+102) {
		tmp = x + (t_2 + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = z * (1.0d0 - log(t))
    if (t_1 <= (-1d+112)) then
        tmp = t_2 + t_1
    else if (t_1 <= 2d+102) then
        tmp = x + (t_2 + y)
    else
        tmp = t_1 + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = z * (1.0 - Math.log(t));
	double tmp;
	if (t_1 <= -1e+112) {
		tmp = t_2 + t_1;
	} else if (t_1 <= 2e+102) {
		tmp = x + (t_2 + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = z * (1.0 - math.log(t))
	tmp = 0
	if t_1 <= -1e+112:
		tmp = t_2 + t_1
	elif t_1 <= 2e+102:
		tmp = x + (t_2 + y)
	else:
		tmp = t_1 + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (t_1 <= -1e+112)
		tmp = Float64(t_2 + t_1);
	elseif (t_1 <= 2e+102)
		tmp = Float64(x + Float64(t_2 + y));
	else
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = z * (1.0 - log(t));
	tmp = 0.0;
	if (t_1 <= -1e+112)
		tmp = t_2 + t_1;
	elseif (t_1 <= 2e+102)
		tmp = x + (t_2 + y);
	else
		tmp = t_1 + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+112], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], N[(x + N[(t$95$2 + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+112}:\\ \;\;\;\;\left(z + t_1\right) - z \cdot \log t\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -1e+112)
     (- (+ z t_1) (* z (log t)))
     (if (<= t_1 2e+102)
       (+ x (+ (* z (- 1.0 (log t))) y))
       (+ t_1 (+ x (+ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+112) {
		tmp = (z + t_1) - (z * log(t));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-1d+112)) then
        tmp = (z + t_1) - (z * log(t))
    else if (t_1 <= 2d+102) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = t_1 + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+112) {
		tmp = (z + t_1) - (z * Math.log(t));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -1e+112:
		tmp = (z + t_1) - (z * math.log(t))
	elif t_1 <= 2e+102:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = t_1 + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+112)
		tmp = Float64(Float64(z + t_1) - Float64(z * log(t)));
	elseif (t_1 <= 2e+102)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+112)
		tmp = (z + t_1) - (z * log(t));
	elseif (t_1 <= 2e+102)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = t_1 + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+112], N[(N[(z + t$95$1), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t_1 + \left(\left(z + y\right) - z \cdot \log t\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+43)
     (+ t_1 (- (+ z y) (* z (log t))))
     (if (<= t_1 2e+102)
       (+ x (+ (* z (- 1.0 (log t))) y))
       (+ t_1 (+ x (+ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = t_1 + ((z + y) - (z * log(t)));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-2d+43)) then
        tmp = t_1 + ((z + y) - (z * log(t)))
    else if (t_1 <= 2d+102) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = t_1 + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = t_1 + ((z + y) - (z * Math.log(t)));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+43:
		tmp = t_1 + ((z + y) - (z * math.log(t)))
	elif t_1 <= 2e+102:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = t_1 + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+43)
		tmp = Float64(t_1 + Float64(Float64(z + y) - Float64(z * log(t))));
	elseif (t_1 <= 2e+102)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -2e+43)
		tmp = t_1 + ((z + y) - (z * log(t)));
	elseif (t_1 <= 2e+102)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = t_1 + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+43], N[(t$95$1 + N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 6: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\left(y + \left(z + t_1\right)\right) - z \cdot \log t\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+43)
     (- (+ y (+ z t_1)) (* z (log t)))
     (if (<= t_1 2e+102)
       (+ x (+ (* z (- 1.0 (log t))) y))
       (+ t_1 (+ x (+ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (y + (z + t_1)) - (z * log(t));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-2d+43)) then
        tmp = (y + (z + t_1)) - (z * log(t))
    else if (t_1 <= 2d+102) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = t_1 + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (y + (z + t_1)) - (z * Math.log(t));
	} else if (t_1 <= 2e+102) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+43:
		tmp = (y + (z + t_1)) - (z * math.log(t))
	elif t_1 <= 2e+102:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = t_1 + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+43)
		tmp = Float64(Float64(y + Float64(z + t_1)) - Float64(z * log(t)));
	elseif (t_1 <= 2e+102)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -2e+43)
		tmp = (y + (z + t_1)) - (z * log(t));
	elseif (t_1 <= 2e+102)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = t_1 + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+43], N[(N[(y + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ z (+ x y)) (* z (log t))) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * Math.log(t))) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return ((z + (x + y)) - (z * math.log(t))) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 8: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+252}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+202}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.35e+252)
   (* z (- 1.0 (log t)))
   (if (<= z 1.32e+202)
     (+ (* b (- a 0.5)) (+ x (+ z y)))
     (- (+ z y) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e+252) {
		tmp = z * (1.0 - log(t));
	} else if (z <= 1.32e+202) {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	} else {
		tmp = (z + y) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.35d+252)) then
        tmp = z * (1.0d0 - log(t))
    else if (z <= 1.32d+202) then
        tmp = (b * (a - 0.5d0)) + (x + (z + y))
    else
        tmp = (z + y) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e+252) {
		tmp = z * (1.0 - Math.log(t));
	} else if (z <= 1.32e+202) {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	} else {
		tmp = (z + y) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.35e+252:
		tmp = z * (1.0 - math.log(t))
	elif z <= 1.32e+202:
		tmp = (b * (a - 0.5)) + (x + (z + y))
	else:
		tmp = (z + y) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.35e+252)
		tmp = Float64(z * Float64(1.0 - log(t)));
	elseif (z <= 1.32e+202)
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	else
		tmp = Float64(Float64(z + y) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.35e+252)
		tmp = z * (1.0 - log(t));
	elseif (z <= 1.32e+202)
		tmp = (b * (a - 0.5)) + (x + (z + y));
	else
		tmp = (z + y) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.35e+252], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+202], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 9: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+249} \lor \neg \left(z \leq 1.3 \cdot 10^{+253}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85e+249) (not (<= z 1.3e+253)))
   (* z (- 1.0 (log t)))
   (+ (* b (- a 0.5)) (+ x (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+249) || !(z <= 1.3e+253)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.85d+249)) .or. (.not. (z <= 1.3d+253))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (b * (a - 0.5d0)) + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+249) || !(z <= 1.3e+253)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e+249) or not (z <= 1.3e+253):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (b * (a - 0.5)) + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85e+249) || !(z <= 1.3e+253))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.85e+249) || ~((z <= 1.3e+253)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (b * (a - 0.5)) + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85e+249], N[Not[LessEqual[z, 1.3e+253]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 38.0% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1250000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-290}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-229}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1250000000000.0)
   (* a b)
   (if (<= a -1.05e-290)
     y
     (if (<= a 2.55e-229)
       (* -0.5 b)
       (if (<= a 2.3e-174) x (if (<= a 3.5e-17) (* -0.5 b) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1250000000000.0) {
		tmp = a * b;
	} else if (a <= -1.05e-290) {
		tmp = y;
	} else if (a <= 2.55e-229) {
		tmp = -0.5 * b;
	} else if (a <= 2.3e-174) {
		tmp = x;
	} else if (a <= 3.5e-17) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1250000000000.0d0)) then
        tmp = a * b
    else if (a <= (-1.05d-290)) then
        tmp = y
    else if (a <= 2.55d-229) then
        tmp = (-0.5d0) * b
    else if (a <= 2.3d-174) then
        tmp = x
    else if (a <= 3.5d-17) then
        tmp = (-0.5d0) * b
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1250000000000.0) {
		tmp = a * b;
	} else if (a <= -1.05e-290) {
		tmp = y;
	} else if (a <= 2.55e-229) {
		tmp = -0.5 * b;
	} else if (a <= 2.3e-174) {
		tmp = x;
	} else if (a <= 3.5e-17) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1250000000000.0:
		tmp = a * b
	elif a <= -1.05e-290:
		tmp = y
	elif a <= 2.55e-229:
		tmp = -0.5 * b
	elif a <= 2.3e-174:
		tmp = x
	elif a <= 3.5e-17:
		tmp = -0.5 * b
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1250000000000.0)
		tmp = Float64(a * b);
	elseif (a <= -1.05e-290)
		tmp = y;
	elseif (a <= 2.55e-229)
		tmp = Float64(-0.5 * b);
	elseif (a <= 2.3e-174)
		tmp = x;
	elseif (a <= 3.5e-17)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1250000000000.0)
		tmp = a * b;
	elseif (a <= -1.05e-290)
		tmp = y;
	elseif (a <= 2.55e-229)
		tmp = -0.5 * b;
	elseif (a <= 2.3e-174)
		tmp = x;
	elseif (a <= 3.5e-17)
		tmp = -0.5 * b;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1250000000000.0], N[(a * b), $MachinePrecision], If[LessEqual[a, -1.05e-290], y, If[LessEqual[a, 2.55e-229], N[(-0.5 * b), $MachinePrecision], If[LessEqual[a, 2.3e-174], x, If[LessEqual[a, 3.5e-17], N[(-0.5 * b), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

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

Alternative 11: 49.8% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+43}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-289}:\\ \;\;\;\;y + -0.5 \cdot b\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{-34}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6e+43)
   (* a b)
   (if (<= a -5.6e-289)
     (+ y (* -0.5 b))
     (if (<= a 3.75e-34) (+ x (* -0.5 b)) (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6e+43) {
		tmp = a * b;
	} else if (a <= -5.6e-289) {
		tmp = y + (-0.5 * b);
	} else if (a <= 3.75e-34) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6d+43)) then
        tmp = a * b
    else if (a <= (-5.6d-289)) then
        tmp = y + ((-0.5d0) * b)
    else if (a <= 3.75d-34) then
        tmp = x + ((-0.5d0) * b)
    else
        tmp = b * (a - 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6e+43) {
		tmp = a * b;
	} else if (a <= -5.6e-289) {
		tmp = y + (-0.5 * b);
	} else if (a <= 3.75e-34) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6e+43:
		tmp = a * b
	elif a <= -5.6e-289:
		tmp = y + (-0.5 * b)
	elif a <= 3.75e-34:
		tmp = x + (-0.5 * b)
	else:
		tmp = b * (a - 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6e+43)
		tmp = Float64(a * b);
	elseif (a <= -5.6e-289)
		tmp = Float64(y + Float64(-0.5 * b));
	elseif (a <= 3.75e-34)
		tmp = Float64(x + Float64(-0.5 * b));
	else
		tmp = Float64(b * Float64(a - 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6e+43)
		tmp = a * b;
	elseif (a <= -5.6e-289)
		tmp = y + (-0.5 * b);
	elseif (a <= 3.75e-34)
		tmp = x + (-0.5 * b);
	else
		tmp = b * (a - 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6e+43], N[(a * b), $MachinePrecision], If[LessEqual[a, -5.6e-289], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.75e-34], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 12: 59.7% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 5 \cdot 10^{-108}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) 5e-108) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 5e-108) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= 5d-108) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 5e-108) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 5e-108:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 5e-108)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 5e-108)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 5e-108], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

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

Alternative 13: 80.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (* b (- a 0.5)) (+ x (+ z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (x + (z + y));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (b * (a - 0.5d0)) + (x + (z + y))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (x + (z + y));
}

Python

def code(x, y, z, t, a, b):
	return (b * (a - 0.5)) + (x + (z + y))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a - 0.5)) + (x + (z + y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 14: 42.0% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.1e+153) x (if (<= x 3.8e+173) (* b (- a 0.5)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.1e+153) {
		tmp = x;
	} else if (x <= 3.8e+173) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.1d+153)) then
        tmp = x
    else if (x <= 3.8d+173) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.1e+153) {
		tmp = x;
	} else if (x <= 3.8e+173) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.1e+153:
		tmp = x
	elif x <= 3.8e+173:
		tmp = b * (a - 0.5)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.1e+153)
		tmp = x;
	elseif (x <= 3.8e+173)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.1e+153)
		tmp = x;
	elseif (x <= 3.8e+173)
		tmp = b * (a - 0.5);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.1e+153], x, If[LessEqual[x, 3.8e+173], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], y]]

Derivation

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

Alternative 15: 50.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.7e+71)
   (* a b)
   (if (<= a 3.5e-17) (+ x (* -0.5 b)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.7e+71) {
		tmp = a * b;
	} else if (a <= 3.5e-17) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.7d+71)) then
        tmp = a * b
    else if (a <= 3.5d-17) then
        tmp = x + ((-0.5d0) * b)
    else
        tmp = b * (a - 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.7e+71) {
		tmp = a * b;
	} else if (a <= 3.5e-17) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = b * (a - 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.7e+71:
		tmp = a * b
	elif a <= 3.5e-17:
		tmp = x + (-0.5 * b)
	else:
		tmp = b * (a - 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.7e+71)
		tmp = Float64(a * b);
	elseif (a <= 3.5e-17)
		tmp = Float64(x + Float64(-0.5 * b));
	else
		tmp = Float64(b * Float64(a - 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.7e+71)
		tmp = a * b;
	elseif (a <= 3.5e-17)
		tmp = x + (-0.5 * b);
	else
		tmp = b * (a - 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.7e+71], N[(a * b), $MachinePrecision], If[LessEqual[a, 3.5e-17], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 16: 62.3% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+232}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.6e+232) (+ x (* b (- a 0.5))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.6e+232) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.6d+232) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.6e+232) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.6e+232:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.6e+232)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.6e+232)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.6e+232], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]

Derivation

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

Alternative 17: 79.7% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ x y) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (a - 0.5));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + y) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return (x + y) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + y) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 18: 28.3% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 3.1e-17) x (if (<= y 1.7e+23) (* -0.5 b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.1e-17) {
		tmp = x;
	} else if (y <= 1.7e+23) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 3.1d-17) then
        tmp = x
    else if (y <= 1.7d+23) then
        tmp = (-0.5d0) * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.1e-17) {
		tmp = x;
	} else if (y <= 1.7e+23) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.1e-17:
		tmp = x
	elif y <= 1.7e+23:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.1e-17)
		tmp = x;
	elseif (y <= 1.7e+23)
		tmp = Float64(-0.5 * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.1e-17)
		tmp = x;
	elseif (y <= 1.7e+23)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.1e-17], x, If[LessEqual[y, 1.7e+23], N[(-0.5 * b), $MachinePrecision], y]]

Derivation

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

Alternative 19: 28.6% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.22e+23) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.22e+23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.22d+23) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.22e+23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.22e+23:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.22e+23)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.22e+23)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.22e+23], x, y]

Derivation

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

Alternative 20: 22.5% accurate, 115.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

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

Developer target: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + y) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))