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

Percentage Accurate: 75.1% → 85.7%

Time: 16.4s

Alternatives: 14

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: 75.1% 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: 85.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{t \cdot \frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{y}}{b}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e-303)
     (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 0.0)
       (/ (* t (/ (fma y (/ z t) x) y)) b)
       (if (<= t_1 4e+295) 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 <= -4e-303) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 0.0) {
		tmp = (t * (fma(y, (z / t), x) / y)) / b;
	} else if (t_1 <= 4e+295) {
		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 <= -4e-303)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t * Float64(fma(y, Float64(z / t), x) / y)) / b);
	elseif (t_1 <= 4e+295)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return 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, -4e-303], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t * N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 4e+295], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

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

Alternative 2: 85.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-290}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -1e-290)
     (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 0.0)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t_1 4e+295) 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 <= -1e-290) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 0.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t_1 <= 4e+295) {
		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 <= (-1d-290)) then
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (y / (t / b))))
    else if (t_1 <= 0.0d0) then
        tmp = (z + ((x * t) / y)) / b
    else if (t_1 <= 4d+295) 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 <= -1e-290) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 0.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t_1 <= 4e+295) {
		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 <= -1e-290:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))))
	elif t_1 <= 0.0:
		tmp = (z + ((x * t) / y)) / b
	elif t_1 <= 4e+295:
		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 <= -1e-290)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t_1 <= 4e+295)
		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 <= -1e-290)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	elseif (t_1 <= 0.0)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t_1 <= 4e+295)
		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, -1e-290], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 4e+295], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+109} \lor \neg \left(y \leq 1.02 \cdot 10^{+210}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+109) (not (<= y 1.02e+210)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+109) || !(y <= 1.02e+210)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / 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 ((y <= (-1.25d+109)) .or. (.not. (y <= 1.02d+210))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (b * (y / 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 ((y <= -1.25e+109) || !(y <= 1.02e+210)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+109) or not (y <= 1.02e+210):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+109) || !(y <= 1.02e+210))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+109) || ~((y <= 1.02e+210)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+109], N[Not[LessEqual[y, 1.02e+210]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], 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]]

Derivation

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

Alternative 4: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+94}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= b -4.6e+79)
     t_1
     (if (<= b 6e+94)
       (/ (+ x (/ y (/ t z))) (+ a 1.0))
       (if (<= b 2.45e+155)
         t_1
         (if (<= b 1.15e+234)
           (/ x (+ 1.0 (+ a (* b (/ y t)))))
           (* (/ t b) (+ (/ z t) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (b <= -4.6e+79) {
		tmp = t_1;
	} else if (b <= 6e+94) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (b <= 2.45e+155) {
		tmp = t_1;
	} else if (b <= 1.15e+234) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (t / b) * ((z / t) + (x / 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 = (z + ((x * t) / y)) / b
    if (b <= (-4.6d+79)) then
        tmp = t_1
    else if (b <= 6d+94) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (b <= 2.45d+155) then
        tmp = t_1
    else if (b <= 1.15d+234) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else
        tmp = (t / b) * ((z / t) + (x / 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 = (z + ((x * t) / y)) / b;
	double tmp;
	if (b <= -4.6e+79) {
		tmp = t_1;
	} else if (b <= 6e+94) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (b <= 2.45e+155) {
		tmp = t_1;
	} else if (b <= 1.15e+234) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if b <= -4.6e+79:
		tmp = t_1
	elif b <= 6e+94:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif b <= 2.45e+155:
		tmp = t_1
	elif b <= 1.15e+234:
		tmp = x / (1.0 + (a + (b * (y / t))))
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (b <= -4.6e+79)
		tmp = t_1;
	elseif (b <= 6e+94)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (b <= 2.45e+155)
		tmp = t_1;
	elseif (b <= 1.15e+234)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (b <= -4.6e+79)
		tmp = t_1;
	elseif (b <= 6e+94)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (b <= 2.45e+155)
		tmp = t_1;
	elseif (b <= 1.15e+234)
		tmp = x / (1.0 + (a + (b * (y / t))));
	else
		tmp = (t / b) * ((z / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[b, -4.6e+79], t$95$1, If[LessEqual[b, 6e+94], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.45e+155], t$95$1, If[LessEqual[b, 1.15e+234], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 41.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-102}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.46e-102)
   (/ z b)
   (if (<= y -2.3e-270)
     (/ x a)
     (if (<= y 1.35e-295)
       x
       (if (<= y 1.15e-192)
         (/ x a)
         (if (<= y 3e-78) (* x (- 1.0 a)) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.46e-102) {
		tmp = z / b;
	} else if (y <= -2.3e-270) {
		tmp = x / a;
	} else if (y <= 1.35e-295) {
		tmp = x;
	} else if (y <= 1.15e-192) {
		tmp = x / a;
	} else if (y <= 3e-78) {
		tmp = x * (1.0 - a);
	} 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 <= (-1.46d-102)) then
        tmp = z / b
    else if (y <= (-2.3d-270)) then
        tmp = x / a
    else if (y <= 1.35d-295) then
        tmp = x
    else if (y <= 1.15d-192) then
        tmp = x / a
    else if (y <= 3d-78) then
        tmp = x * (1.0d0 - a)
    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 <= -1.46e-102) {
		tmp = z / b;
	} else if (y <= -2.3e-270) {
		tmp = x / a;
	} else if (y <= 1.35e-295) {
		tmp = x;
	} else if (y <= 1.15e-192) {
		tmp = x / a;
	} else if (y <= 3e-78) {
		tmp = x * (1.0 - a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.46e-102:
		tmp = z / b
	elif y <= -2.3e-270:
		tmp = x / a
	elif y <= 1.35e-295:
		tmp = x
	elif y <= 1.15e-192:
		tmp = x / a
	elif y <= 3e-78:
		tmp = x * (1.0 - a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.46e-102)
		tmp = Float64(z / b);
	elseif (y <= -2.3e-270)
		tmp = Float64(x / a);
	elseif (y <= 1.35e-295)
		tmp = x;
	elseif (y <= 1.15e-192)
		tmp = Float64(x / a);
	elseif (y <= 3e-78)
		tmp = Float64(x * Float64(1.0 - a));
	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 <= -1.46e-102)
		tmp = z / b;
	elseif (y <= -2.3e-270)
		tmp = x / a;
	elseif (y <= 1.35e-295)
		tmp = x;
	elseif (y <= 1.15e-192)
		tmp = x / a;
	elseif (y <= 3e-78)
		tmp = x * (1.0 - a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.46e-102], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.3e-270], N[(x / a), $MachinePrecision], If[LessEqual[y, 1.35e-295], x, If[LessEqual[y, 1.15e-192], N[(x / a), $MachinePrecision], If[LessEqual[y, 3e-78], N[(x * N[(1.0 - a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 63.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-48} \lor \neg \left(y \leq 2.8 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-48) (not (<= y 2.8e+72)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ 1.0 (+ a (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-48) || !(y <= 2.8e+72)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / 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 ((y <= (-1.25d-48)) .or. (.not. (y <= 2.8d+72))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (1.0d0 + (a + (b * (y / 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 ((y <= -1.25e-48) || !(y <= 2.8e+72)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e-48) or not (y <= 2.8e+72):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (1.0 + (a + (b * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e-48) || !(y <= 2.8e+72))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e-48) || ~((y <= 2.8e+72)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (1.0 + (a + (b * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e-48], N[Not[LessEqual[y, 2.8e+72]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 42.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -4.15 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.4e-102)
   (/ z b)
   (if (<= y -4.15e-271)
     (/ x a)
     (if (<= y 3.8e-295)
       x
       (if (<= y 8.2e-192) (/ x a) (if (<= y 6.5e-101) x (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e-102) {
		tmp = z / b;
	} else if (y <= -4.15e-271) {
		tmp = x / a;
	} else if (y <= 3.8e-295) {
		tmp = x;
	} else if (y <= 8.2e-192) {
		tmp = x / a;
	} else if (y <= 6.5e-101) {
		tmp = x;
	} 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 <= (-3.4d-102)) then
        tmp = z / b
    else if (y <= (-4.15d-271)) then
        tmp = x / a
    else if (y <= 3.8d-295) then
        tmp = x
    else if (y <= 8.2d-192) then
        tmp = x / a
    else if (y <= 6.5d-101) then
        tmp = x
    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 <= -3.4e-102) {
		tmp = z / b;
	} else if (y <= -4.15e-271) {
		tmp = x / a;
	} else if (y <= 3.8e-295) {
		tmp = x;
	} else if (y <= 8.2e-192) {
		tmp = x / a;
	} else if (y <= 6.5e-101) {
		tmp = x;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.4e-102:
		tmp = z / b
	elif y <= -4.15e-271:
		tmp = x / a
	elif y <= 3.8e-295:
		tmp = x
	elif y <= 8.2e-192:
		tmp = x / a
	elif y <= 6.5e-101:
		tmp = x
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.4e-102)
		tmp = Float64(z / b);
	elseif (y <= -4.15e-271)
		tmp = Float64(x / a);
	elseif (y <= 3.8e-295)
		tmp = x;
	elseif (y <= 8.2e-192)
		tmp = Float64(x / a);
	elseif (y <= 6.5e-101)
		tmp = x;
	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 <= -3.4e-102)
		tmp = z / b;
	elseif (y <= -4.15e-271)
		tmp = x / a;
	elseif (y <= 3.8e-295)
		tmp = x;
	elseif (y <= 8.2e-192)
		tmp = x / a;
	elseif (y <= 6.5e-101)
		tmp = x;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.4e-102], N[(z / b), $MachinePrecision], If[LessEqual[y, -4.15e-271], N[(x / a), $MachinePrecision], If[LessEqual[y, 3.8e-295], x, If[LessEqual[y, 8.2e-192], N[(x / a), $MachinePrecision], If[LessEqual[y, 6.5e-101], x, N[(z / b), $MachinePrecision]]]]]]

Derivation

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

Alternative 8: 55.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-48} \lor \neg \left(y \leq 3.1 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+102)
   (/ z b)
   (if (<= y -2.6e-48)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (or (<= y -1.2e-48) (not (<= y 3.1e+71))) (/ 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 <= -3e+102) {
		tmp = z / b;
	} else if (y <= -2.6e-48) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((y <= -1.2e-48) || !(y <= 3.1e+71)) {
		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 <= (-3d+102)) then
        tmp = z / b
    else if (y <= (-2.6d-48)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if ((y <= (-1.2d-48)) .or. (.not. (y <= 3.1d+71))) 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 <= -3e+102) {
		tmp = z / b;
	} else if (y <= -2.6e-48) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((y <= -1.2e-48) || !(y <= 3.1e+71)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e+102:
		tmp = z / b
	elif y <= -2.6e-48:
		tmp = (y / t) * (z / (a + 1.0))
	elif (y <= -1.2e-48) or not (y <= 3.1e+71):
		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 <= -3e+102)
		tmp = Float64(z / b);
	elseif (y <= -2.6e-48)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif ((y <= -1.2e-48) || !(y <= 3.1e+71))
		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 <= -3e+102)
		tmp = z / b;
	elseif (y <= -2.6e-48)
		tmp = (y / t) * (z / (a + 1.0));
	elseif ((y <= -1.2e-48) || ~((y <= 3.1e+71)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+102], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.6e-48], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.2e-48], N[Not[LessEqual[y, 3.1e+71]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 9: 55.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1950 \lor \neg \left(a \leq 7.2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1950.0) (not (<= a 7.2e-11)))
   (/ (+ x (/ y (/ t z))) a)
   (/ x (+ 1.0 (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1950.0) || !(a <= 7.2e-11)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (1.0 + (y * (b / 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 ((a <= (-1950.0d0)) .or. (.not. (a <= 7.2d-11))) then
        tmp = (x + (y / (t / z))) / a
    else
        tmp = x / (1.0d0 + (y * (b / 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 ((a <= -1950.0) || !(a <= 7.2e-11)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (1.0 + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1950.0) or not (a <= 7.2e-11):
		tmp = (x + (y / (t / z))) / a
	else:
		tmp = x / (1.0 + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1950.0) || !(a <= 7.2e-11))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	else
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1950.0) || ~((a <= 7.2e-11)))
		tmp = (x + (y / (t / z))) / a;
	else
		tmp = x / (1.0 + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1950.0], N[Not[LessEqual[a, 7.2e-11]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 58.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-49} \lor \neg \left(y \leq 1.4 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.2e-49) (not (<= y 1.4e-80)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.2e-49) || !(y <= 1.4e-80)) {
		tmp = (z + ((x * t) / y)) / 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 <= (-9.2d-49)) .or. (.not. (y <= 1.4d-80))) then
        tmp = (z + ((x * t) / y)) / 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 <= -9.2e-49) || !(y <= 1.4e-80)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.2e-49) or not (y <= 1.4e-80):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.2e-49) || !(y <= 1.4e-80))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / 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 <= -9.2e-49) || ~((y <= 1.4e-80)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.2e-49], N[Not[LessEqual[y, 1.4e-80]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 55.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -136000000000:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -136000000000.0)
   (/ (+ x (/ (* y z) t)) a)
   (if (<= a 7.2e-11) (/ x (+ 1.0 (* y (/ b t)))) (/ (+ x (/ y (/ t z))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -136000000000.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= 7.2e-11) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = (x + (y / (t / z))) / 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 <= (-136000000000.0d0)) then
        tmp = (x + ((y * z) / t)) / a
    else if (a <= 7.2d-11) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else
        tmp = (x + (y / (t / z))) / 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 <= -136000000000.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= 7.2e-11) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -136000000000.0:
		tmp = (x + ((y * z) / t)) / a
	elif a <= 7.2e-11:
		tmp = x / (1.0 + (y * (b / t)))
	else:
		tmp = (x + (y / (t / z))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -136000000000.0)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (a <= 7.2e-11)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -136000000000.0)
		tmp = (x + ((y * z) / t)) / a;
	elseif (a <= 7.2e-11)
		tmp = x / (1.0 + (y * (b / t)));
	else
		tmp = (x + (y / (t / z))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -136000000000.0], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 7.2e-11], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

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

Alternative 12: 55.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-48} \lor \neg \left(y \leq 3.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-48) (not (<= y 3.8e+71))) (/ 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 <= -1.25e-48) || !(y <= 3.8e+71)) {
		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 <= (-1.25d-48)) .or. (.not. (y <= 3.8d+71))) 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 <= -1.25e-48) || !(y <= 3.8e+71)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e-48) or not (y <= 3.8e+71):
		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 <= -1.25e-48) || !(y <= 3.8e+71))
		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 <= -1.25e-48) || ~((y <= 3.8e+71)))
		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, -1.25e-48], N[Not[LessEqual[y, 3.8e+71]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 41.6% 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 14: 19.7% 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: 79.1% 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 2023350 
(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))))