Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 74.4% → 88.5%

Time: 18.9s

Alternatives: 19

Speedup: 0.8×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Initial Program: 74.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Alternative 1: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t_1\right)\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ t_4 := \frac{x}{t_2} + \frac{y \cdot z}{t \cdot t_2}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{t}{\frac{{b}^{2}}{z \cdot \left(a + 1\right)}}\right)}{y}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_4 (+ (/ x t_2) (/ (* y z) (* t t_2)))))
   (if (<= t_3 -2e-290)
     t_4
     (if (<= t_3 0.0)
       (-
        (/ z b)
        (/ (fma -1.0 (/ t (/ b x)) (/ t (/ (pow b 2.0) (* z (+ a 1.0))))) y))
       (if (<= t_3 INFINITY) t_4 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -2e-290) {
		tmp = t_4;
	} else if (t_3 <= 0.0) {
		tmp = (z / b) - (fma(-1.0, (t / (b / x)), (t / (pow(b, 2.0) / (z * (a + 1.0))))) / y);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(Float64(x / t_2) + Float64(Float64(y * z) / Float64(t * t_2)))
	tmp = 0.0
	if (t_3 <= -2e-290)
		tmp = t_4;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(z / b) - Float64(fma(-1.0, Float64(t / Float64(b / x)), Float64(t / Float64((b ^ 2.0) / Float64(z * Float64(a + 1.0))))) / y));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-290], t$95$4, If[LessEqual[t$95$3, 0.0], N[(N[(z / b), $MachinePrecision] - N[(N[(-1.0 * N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[Power[b, 2.0], $MachinePrecision] / N[(z * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 2: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t_1\right)\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ t_4 := \frac{x}{t_2} + \frac{y \cdot z}{t \cdot t_2}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-213}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 10^{-312}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_4 (+ (/ x t_2) (/ (* y z) (* t t_2)))))
   (if (<= t_3 -2e-213)
     t_4
     (if (<= t_3 1e-312)
       (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (* b (/ y t)))))
       (if (<= t_3 INFINITY) t_4 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -2e-213) {
		tmp = t_4;
	} else if (t_3 <= 1e-312) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -2e-213) {
		tmp = t_4;
	} else if (t_3 <= 1e-312) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_4 = (x / t_2) + ((y * z) / (t * t_2))
	tmp = 0
	if t_3 <= -2e-213:
		tmp = t_4
	elif t_3 <= 1e-312:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))))
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(Float64(x / t_2) + Float64(Float64(y * z) / Float64(t * t_2)))
	tmp = 0.0
	if (t_3 <= -2e-213)
		tmp = t_4;
	elseif (t_3 <= 1e-312)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = 1.0 + (a + t_1);
	t_3 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_4 = (x / t_2) + ((y * z) / (t * t_2));
	tmp = 0.0;
	if (t_3 <= -2e-213)
		tmp = t_4;
	elseif (t_3 <= 1e-312)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-213], t$95$4, If[LessEqual[t$95$3, 1e-312], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 3: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 0.0)
     (/ (+ x (* y (/ z t))) (+ 1.0 (+ a (* y (/ b t)))))
     (if (<= t_1 5e+286) t_1 (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else {
		tmp = z / 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) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    if (t_1 <= 0.0d0) then
        tmp = (x + (y * (z / t))) / (1.0d0 + (a + (y * (b / t))))
    else if (t_1 <= 5d+286) then
        tmp = t_1
    else
        tmp = z / 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 t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= 0.0:
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))))
	elif t_1 <= 5e+286:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

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

Alternative 4: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-212} \lor \neg \left(t \leq 5.4 \cdot 10^{-182}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -3.5e-88)
     t_1
     (if (<= t -1.95e-199)
       (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
       (if (or (<= t -5.6e-212) (not (<= t 5.4e-182))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -3.5e-88) {
		tmp = t_1;
	} else if (t <= -1.95e-199) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if ((t <= -5.6e-212) || !(t <= 5.4e-182)) {
		tmp = t_1;
	} else {
		tmp = z / 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) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-3.5d-88)) then
        tmp = t_1
    else if (t <= (-1.95d-199)) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if ((t <= (-5.6d-212)) .or. (.not. (t <= 5.4d-182))) then
        tmp = t_1
    else
        tmp = z / 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 t_1 = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -3.5e-88) {
		tmp = t_1;
	} else if (t <= -1.95e-199) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if ((t <= -5.6e-212) || !(t <= 5.4e-182)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -3.5e-88:
		tmp = t_1
	elif t <= -1.95e-199:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif (t <= -5.6e-212) or not (t <= 5.4e-182):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -3.5e-88)
		tmp = t_1;
	elseif (t <= -1.95e-199)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif ((t <= -5.6e-212) || !(t <= 5.4e-182))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -3.5e-88)
		tmp = t_1;
	elseif (t <= -1.95e-199)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif ((t <= -5.6e-212) || ~((t <= 5.4e-182)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-88], t$95$1, If[LessEqual[t, -1.95e-199], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -5.6e-212], N[Not[LessEqual[t, 5.4e-182]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -2100:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-216}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* b (/ y t))))) (t_2 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -2100.0)
     t_2
     (if (<= a -2.5e-65)
       t_1
       (if (<= a -1.3e-216)
         (/ z b)
         (if (<= a 3.6e-255)
           t_1
           (if (<= a 1.7e-81)
             (+ x (/ (* y z) t))
             (if (<= a 3.5e+61) (/ z b) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -2100.0) {
		tmp = t_2;
	} else if (a <= -2.5e-65) {
		tmp = t_1;
	} else if (a <= -1.3e-216) {
		tmp = z / b;
	} else if (a <= 3.6e-255) {
		tmp = t_1;
	} else if (a <= 1.7e-81) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3.5e+61) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	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 = x / (1.0d0 + (b * (y / t)))
    t_2 = (x + (z * (y / t))) / a
    if (a <= (-2100.0d0)) then
        tmp = t_2
    else if (a <= (-2.5d-65)) then
        tmp = t_1
    else if (a <= (-1.3d-216)) then
        tmp = z / b
    else if (a <= 3.6d-255) then
        tmp = t_1
    else if (a <= 1.7d-81) then
        tmp = x + ((y * z) / t)
    else if (a <= 3.5d+61) then
        tmp = z / b
    else
        tmp = t_2
    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 = x / (1.0 + (b * (y / t)));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -2100.0) {
		tmp = t_2;
	} else if (a <= -2.5e-65) {
		tmp = t_1;
	} else if (a <= -1.3e-216) {
		tmp = z / b;
	} else if (a <= 3.6e-255) {
		tmp = t_1;
	} else if (a <= 1.7e-81) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3.5e+61) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (b * (y / t)))
	t_2 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -2100.0:
		tmp = t_2
	elif a <= -2.5e-65:
		tmp = t_1
	elif a <= -1.3e-216:
		tmp = z / b
	elif a <= 3.6e-255:
		tmp = t_1
	elif a <= 1.7e-81:
		tmp = x + ((y * z) / t)
	elif a <= 3.5e+61:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))))
	t_2 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -2100.0)
		tmp = t_2;
	elseif (a <= -2.5e-65)
		tmp = t_1;
	elseif (a <= -1.3e-216)
		tmp = Float64(z / b);
	elseif (a <= 3.6e-255)
		tmp = t_1;
	elseif (a <= 1.7e-81)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 3.5e+61)
		tmp = Float64(z / b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (b * (y / t)));
	t_2 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -2100.0)
		tmp = t_2;
	elseif (a <= -2.5e-65)
		tmp = t_1;
	elseif (a <= -1.3e-216)
		tmp = z / b;
	elseif (a <= 3.6e-255)
		tmp = t_1;
	elseif (a <= 1.7e-81)
		tmp = x + ((y * z) / t);
	elseif (a <= 3.5e+61)
		tmp = z / b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2100.0], t$95$2, If[LessEqual[a, -2.5e-65], t$95$1, If[LessEqual[a, -1.3e-216], N[(z / b), $MachinePrecision], If[LessEqual[a, 3.6e-255], t$95$1, If[LessEqual[a, 1.7e-81], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+61], N[(z / b), $MachinePrecision], t$95$2]]]]]]]]

Derivation

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

Alternative 6: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{if}\;a \leq -2100:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-216}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* b (/ y t))))))
   (if (<= a -2100.0)
     (/ (+ x (/ y (/ t z))) a)
     (if (<= a -2.5e-65)
       t_1
       (if (<= a -3e-216)
         (/ z b)
         (if (<= a 1.45e-283)
           t_1
           (if (<= a 6.5e-88)
             (+ x (/ (* y z) t))
             (if (<= a 3e+61) (/ z b) (/ (+ x (* z (/ y t))) a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double tmp;
	if (a <= -2100.0) {
		tmp = (x + (y / (t / z))) / a;
	} else if (a <= -2.5e-65) {
		tmp = t_1;
	} else if (a <= -3e-216) {
		tmp = z / b;
	} else if (a <= 1.45e-283) {
		tmp = t_1;
	} else if (a <= 6.5e-88) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3e+61) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	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 = x / (1.0d0 + (b * (y / t)))
    if (a <= (-2100.0d0)) then
        tmp = (x + (y / (t / z))) / a
    else if (a <= (-2.5d-65)) then
        tmp = t_1
    else if (a <= (-3d-216)) then
        tmp = z / b
    else if (a <= 1.45d-283) then
        tmp = t_1
    else if (a <= 6.5d-88) then
        tmp = x + ((y * z) / t)
    else if (a <= 3d+61) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / a
    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 = x / (1.0 + (b * (y / t)));
	double tmp;
	if (a <= -2100.0) {
		tmp = (x + (y / (t / z))) / a;
	} else if (a <= -2.5e-65) {
		tmp = t_1;
	} else if (a <= -3e-216) {
		tmp = z / b;
	} else if (a <= 1.45e-283) {
		tmp = t_1;
	} else if (a <= 6.5e-88) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3e+61) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (b * (y / t)))
	tmp = 0
	if a <= -2100.0:
		tmp = (x + (y / (t / z))) / a
	elif a <= -2.5e-65:
		tmp = t_1
	elif a <= -3e-216:
		tmp = z / b
	elif a <= 1.45e-283:
		tmp = t_1
	elif a <= 6.5e-88:
		tmp = x + ((y * z) / t)
	elif a <= 3e+61:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (a <= -2100.0)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	elseif (a <= -2.5e-65)
		tmp = t_1;
	elseif (a <= -3e-216)
		tmp = Float64(z / b);
	elseif (a <= 1.45e-283)
		tmp = t_1;
	elseif (a <= 6.5e-88)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 3e+61)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (b * (y / t)));
	tmp = 0.0;
	if (a <= -2100.0)
		tmp = (x + (y / (t / z))) / a;
	elseif (a <= -2.5e-65)
		tmp = t_1;
	elseif (a <= -3e-216)
		tmp = z / b;
	elseif (a <= 1.45e-283)
		tmp = t_1;
	elseif (a <= 6.5e-88)
		tmp = x + ((y * z) / t);
	elseif (a <= 3e+61)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2100.0], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -2.5e-65], t$95$1, If[LessEqual[a, -3e-216], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.45e-283], t$95$1, If[LessEqual[a, 6.5e-88], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+61], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 7: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{if}\;a \leq -1.8:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* b (/ y t))))))
   (if (<= a -1.8)
     (/ (+ x (/ y (/ t z))) a)
     (if (<= a -3.4e-65)
       t_1
       (if (<= a -2.6e-216)
         (/ z b)
         (if (<= a 6e-256)
           t_1
           (if (<= a 3.7e-79)
             (+ x (/ (* y (/ z t)) (+ a 1.0)))
             (if (<= a 3e+61) (/ z b) (/ (+ x (* z (/ y t))) a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double tmp;
	if (a <= -1.8) {
		tmp = (x + (y / (t / z))) / a;
	} else if (a <= -3.4e-65) {
		tmp = t_1;
	} else if (a <= -2.6e-216) {
		tmp = z / b;
	} else if (a <= 6e-256) {
		tmp = t_1;
	} else if (a <= 3.7e-79) {
		tmp = x + ((y * (z / t)) / (a + 1.0));
	} else if (a <= 3e+61) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	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 = x / (1.0d0 + (b * (y / t)))
    if (a <= (-1.8d0)) then
        tmp = (x + (y / (t / z))) / a
    else if (a <= (-3.4d-65)) then
        tmp = t_1
    else if (a <= (-2.6d-216)) then
        tmp = z / b
    else if (a <= 6d-256) then
        tmp = t_1
    else if (a <= 3.7d-79) then
        tmp = x + ((y * (z / t)) / (a + 1.0d0))
    else if (a <= 3d+61) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / a
    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 = x / (1.0 + (b * (y / t)));
	double tmp;
	if (a <= -1.8) {
		tmp = (x + (y / (t / z))) / a;
	} else if (a <= -3.4e-65) {
		tmp = t_1;
	} else if (a <= -2.6e-216) {
		tmp = z / b;
	} else if (a <= 6e-256) {
		tmp = t_1;
	} else if (a <= 3.7e-79) {
		tmp = x + ((y * (z / t)) / (a + 1.0));
	} else if (a <= 3e+61) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (b * (y / t)))
	tmp = 0
	if a <= -1.8:
		tmp = (x + (y / (t / z))) / a
	elif a <= -3.4e-65:
		tmp = t_1
	elif a <= -2.6e-216:
		tmp = z / b
	elif a <= 6e-256:
		tmp = t_1
	elif a <= 3.7e-79:
		tmp = x + ((y * (z / t)) / (a + 1.0))
	elif a <= 3e+61:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (a <= -1.8)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	elseif (a <= -3.4e-65)
		tmp = t_1;
	elseif (a <= -2.6e-216)
		tmp = Float64(z / b);
	elseif (a <= 6e-256)
		tmp = t_1;
	elseif (a <= 3.7e-79)
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0)));
	elseif (a <= 3e+61)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (b * (y / t)));
	tmp = 0.0;
	if (a <= -1.8)
		tmp = (x + (y / (t / z))) / a;
	elseif (a <= -3.4e-65)
		tmp = t_1;
	elseif (a <= -2.6e-216)
		tmp = z / b;
	elseif (a <= 6e-256)
		tmp = t_1;
	elseif (a <= 3.7e-79)
		tmp = x + ((y * (z / t)) / (a + 1.0));
	elseif (a <= 3e+61)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -3.4e-65], t$95$1, If[LessEqual[a, -2.6e-216], N[(z / b), $MachinePrecision], If[LessEqual[a, 6e-256], t$95$1, If[LessEqual[a, 3.7e-79], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+61], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 8: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-186}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= t -6.5e-218)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 1.26e-186) (/ z b) (/ (+ x (* z (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -6.5e-218) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 1.26e-186) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / 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 = 1.0d0 + (a + (y * (b / t)))
    if (t <= (-6.5d-218)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 1.26d-186) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / 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 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -6.5e-218) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 1.26e-186) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if t <= -6.5e-218:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 1.26e-186:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -6.5e-218)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 1.26e-186)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (t <= -6.5e-218)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 1.26e-186)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-218], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.26e-186], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

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

Alternative 9: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-185}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= t -6.8e-218)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 3.4e-185) (/ z b) (/ (+ x (/ z (/ t y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -6.8e-218) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 3.4e-185) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / 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 = 1.0d0 + (a + (y * (b / t)))
    if (t <= (-6.8d-218)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 3.4d-185) then
        tmp = z / b
    else
        tmp = (x + (z / (t / 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 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -6.8e-218) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 3.4e-185) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if t <= -6.8e-218:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 3.4e-185:
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -6.8e-218)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 3.4e-185)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (t <= -6.8e-218)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 3.4e-185)
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-218], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 3.4e-185], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

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

Alternative 10: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+111} \lor \neg \left(y \leq 5.8 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+111) (not (<= y 5.8e+138)))
   (/ z b)
   (+ (/ x (+ a 1.0)) (* (/ y t) (/ z (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+111) || !(y <= 5.8e+138)) {
		tmp = z / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	}
	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 <= (-4d+111)) .or. (.not. (y <= 5.8d+138))) then
        tmp = z / b
    else
        tmp = (x / (a + 1.0d0)) + ((y / t) * (z / (a + 1.0d0)))
    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 <= -4e+111) || !(y <= 5.8e+138)) {
		tmp = z / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e+111) or not (y <= 5.8e+138):
		tmp = z / b
	else:
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+111) || !(y <= 5.8e+138))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e+111) || ~((y <= 5.8e+138)))
		tmp = z / b;
	else
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+111], N[Not[LessEqual[y, 5.8e+138]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+80} \lor \neg \left(y \leq 4.9 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+80) (not (<= y 4.9e+138)))
   (/ z b)
   (+ (/ x (+ a 1.0)) (/ (* y z) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+80) || !(y <= 4.9e+138)) {
		tmp = z / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y * z) / (t * (a + 1.0)));
	}
	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 <= (-4.1d+80)) .or. (.not. (y <= 4.9d+138))) then
        tmp = z / b
    else
        tmp = (x / (a + 1.0d0)) + ((y * z) / (t * (a + 1.0d0)))
    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 <= -4.1e+80) || !(y <= 4.9e+138)) {
		tmp = z / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y * z) / (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.1e+80) or not (y <= 4.9e+138):
		tmp = z / b
	else:
		tmp = (x / (a + 1.0)) + ((y * z) / (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.1e+80) || !(y <= 4.9e+138))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y * z) / Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.1e+80) || ~((y <= 4.9e+138)))
		tmp = z / b;
	else
		tmp = (x / (a + 1.0)) + ((y * z) / (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.1e+80], N[Not[LessEqual[y, 4.9e+138]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -250:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e+111)
   (/ z b)
   (if (<= y -250.0)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y 5.8e+138) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+111) {
		tmp = z / b;
	} else if (y <= -250.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 5.8e+138) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / 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 (y <= (-1.8d+111)) then
        tmp = z / b
    else if (y <= (-250.0d0)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 5.8d+138) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = z / 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 (y <= -1.8e+111) {
		tmp = z / b;
	} else if (y <= -250.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 5.8e+138) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e+111:
		tmp = z / b
	elif y <= -250.0:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 5.8e+138:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e+111)
		tmp = Float64(z / b);
	elseif (y <= -250.0)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 5.8e+138)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e+111)
		tmp = z / b;
	elseif (y <= -250.0)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 5.8e+138)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e+111], N[(z / b), $MachinePrecision], If[LessEqual[y, -250.0], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+138], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

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

Alternative 13: 66.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+80} \lor \neg \left(y \leq 4.8 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.7e+80) (not (<= y 4.8e+138)))
   (/ z b)
   (/ (+ x (* z (/ y t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.7e+80) || !(y <= 4.8e+138)) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	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 <= (-4.7d+80)) .or. (.not. (y <= 4.8d+138))) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    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 <= -4.7e+80) || !(y <= 4.8e+138)) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.7e+80) or not (y <= 4.8e+138):
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.7e+80) || !(y <= 4.8e+138))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.7e+80) || ~((y <= 4.8e+138)))
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.7e+80], N[Not[LessEqual[y, 4.8e+138]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+79} \lor \neg \left(y \leq 5.2 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+79) (not (<= y 5.2e+138)))
   (/ z b)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+79) || !(y <= 5.2e+138)) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	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 <= (-9d+79)) .or. (.not. (y <= 5.2d+138))) then
        tmp = z / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    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 <= -9e+79) || !(y <= 5.2e+138)) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+79) or not (y <= 5.2e+138):
		tmp = z / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+79) || !(y <= 5.2e+138))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+79) || ~((y <= 5.2e+138)))
		tmp = z / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+79], N[Not[LessEqual[y, 5.2e+138]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 15: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-304}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0)
   (/ x a)
   (if (<= a -6e-65)
     x
     (if (<= a -3.8e-217)
       (/ z b)
       (if (<= a -1.7e-304) x (if (<= a 2.7e+107) (/ z b) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -6e-65) {
		tmp = x;
	} else if (a <= -3.8e-217) {
		tmp = z / b;
	} else if (a <= -1.7e-304) {
		tmp = x;
	} else if (a <= 2.7e+107) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= (-6d-65)) then
        tmp = x
    else if (a <= (-3.8d-217)) then
        tmp = z / b
    else if (a <= (-1.7d-304)) then
        tmp = x
    else if (a <= 2.7d+107) then
        tmp = z / b
    else
        tmp = x / a
    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 <= -1.0) {
		tmp = x / a;
	} else if (a <= -6e-65) {
		tmp = x;
	} else if (a <= -3.8e-217) {
		tmp = z / b;
	} else if (a <= -1.7e-304) {
		tmp = x;
	} else if (a <= 2.7e+107) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= -6e-65:
		tmp = x
	elif a <= -3.8e-217:
		tmp = z / b
	elif a <= -1.7e-304:
		tmp = x
	elif a <= 2.7e+107:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= -6e-65)
		tmp = x;
	elseif (a <= -3.8e-217)
		tmp = Float64(z / b);
	elseif (a <= -1.7e-304)
		tmp = x;
	elseif (a <= 2.7e+107)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x / a;
	elseif (a <= -6e-65)
		tmp = x;
	elseif (a <= -3.8e-217)
		tmp = z / b;
	elseif (a <= -1.7e-304)
		tmp = x;
	elseif (a <= 2.7e+107)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -6e-65], x, If[LessEqual[a, -3.8e-217], N[(z / b), $MachinePrecision], If[LessEqual[a, -1.7e-304], x, If[LessEqual[a, 2.7e+107], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]

Derivation

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

Alternative 16: 54.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-44}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+126}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+111)
   (/ z b)
   (if (<= y -1.25e-44)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y 1.82e+126) (/ x (+ a 1.0)) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+111) {
		tmp = z / b;
	} else if (y <= -1.25e-44) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.82e+126) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / 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 (y <= (-2.3d+111)) then
        tmp = z / b
    else if (y <= (-1.25d-44)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 1.82d+126) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / 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 (y <= -2.3e+111) {
		tmp = z / b;
	} else if (y <= -1.25e-44) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.82e+126) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.3e+111:
		tmp = z / b
	elif y <= -1.25e-44:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 1.82e+126:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+111)
		tmp = Float64(z / b);
	elseif (y <= -1.25e-44)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 1.82e+126)
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.3e+111)
		tmp = z / b;
	elseif (y <= -1.25e-44)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 1.82e+126)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+111], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.25e-44], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.82e+126], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

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

Alternative 17: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+53} \lor \neg \left(y \leq 1.36 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e+53) (not (<= y 1.36e+128))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+53) || !(y <= 1.36e+128)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	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 <= (-1d+53)) .or. (.not. (y <= 1.36d+128))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    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 <= -1e+53) || !(y <= 1.36e+128)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e+53) or not (y <= 1.36e+128):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e+53) || !(y <= 1.36e+128))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e+53) || ~((y <= 1.36e+128)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e+53], N[Not[LessEqual[y, 1.36e+128]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 18: 40.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	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 <= (-1.0d0)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    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 <= -1.0) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

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

Alternative 19: 19.4% accurate, 17.0× 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: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = 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 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = 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 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023347 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))