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

Percentage Accurate: 74.8% → 90.6%

Time: 18.5s

Alternatives: 18

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: 74.8% 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: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{\mathsf{fma}\left(b, \frac{y}{t}, a + 1\right)}\\ \mathbf{elif}\;t_1 \leq 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (fma y (/ b t) a))))
     (if (<= t_1 -4e-146)
       t_1
       (if (<= t_1 0.0)
         (/ (fma y (/ z t) x) (fma b (/ y t) (+ a 1.0)))
         (if (<= t_1 1e+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 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + fma(y, (b / t), a)));
	} else if (t_1 <= -4e-146) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(y, (z / t), x) / fma(b, (y / t), (a + 1.0));
	} else if (t_1 <= 1e+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 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + fma(y, Float64(b / t), a))));
	elseif (t_1 <= -4e-146)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(y, Float64(z / t), x) / fma(b, Float64(y / t), Float64(a + 1.0)));
	elseif (t_1 <= 1e+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, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-146], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / N[(b * N[(y / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+295], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 88.0% accurate, 0.1× speedup

Math

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

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 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (fma y (/ b t) a))))
     (if (<= t_1 1e+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 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + fma(y, (b / t), a)));
	} else if (t_1 <= 1e+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 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + fma(y, Float64(b / t), a))));
	elseif (t_1 <= 1e+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, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+295], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

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

Alternative 3: 85.2% accurate, 0.5× speedup

Math

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

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+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+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+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+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+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+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+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+295], t$95$1, N[(z / b), $MachinePrecision]]]

Derivation

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

Alternative 4: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ t b) (+ (/ z t) (/ x y))))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 a)))
   (if (<= a -1e+76)
     t_3
     (if (<= a -2.15e-10)
       t_1
       (if (<= a -5.5e-301)
         t_2
         (if (<= a 1.05e-264)
           t_1
           (if (<= a 5.3e-195)
             t_2
             (if (<= a 1.75e-43)
               t_1
               (if (<= a 2.8e-21) t_2 (if (<= a 1.15e+17) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / b) * ((z / t) + (x / y));
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -1e+76) {
		tmp = t_3;
	} else if (a <= -2.15e-10) {
		tmp = t_1;
	} else if (a <= -5.5e-301) {
		tmp = t_2;
	} else if (a <= 1.05e-264) {
		tmp = t_1;
	} else if (a <= 5.3e-195) {
		tmp = t_2;
	} else if (a <= 1.75e-43) {
		tmp = t_1;
	} else if (a <= 2.8e-21) {
		tmp = t_2;
	} else if (a <= 1.15e+17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (t / b) * ((z / t) + (x / y))
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / a
    if (a <= (-1d+76)) then
        tmp = t_3
    else if (a <= (-2.15d-10)) then
        tmp = t_1
    else if (a <= (-5.5d-301)) then
        tmp = t_2
    else if (a <= 1.05d-264) then
        tmp = t_1
    else if (a <= 5.3d-195) then
        tmp = t_2
    else if (a <= 1.75d-43) then
        tmp = t_1
    else if (a <= 2.8d-21) then
        tmp = t_2
    else if (a <= 1.15d+17) then
        tmp = t_1
    else
        tmp = t_3
    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 = (t / b) * ((z / t) + (x / y));
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -1e+76) {
		tmp = t_3;
	} else if (a <= -2.15e-10) {
		tmp = t_1;
	} else if (a <= -5.5e-301) {
		tmp = t_2;
	} else if (a <= 1.05e-264) {
		tmp = t_1;
	} else if (a <= 5.3e-195) {
		tmp = t_2;
	} else if (a <= 1.75e-43) {
		tmp = t_1;
	} else if (a <= 2.8e-21) {
		tmp = t_2;
	} else if (a <= 1.15e+17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t / b) * ((z / t) + (x / y))
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / a
	tmp = 0
	if a <= -1e+76:
		tmp = t_3
	elif a <= -2.15e-10:
		tmp = t_1
	elif a <= -5.5e-301:
		tmp = t_2
	elif a <= 1.05e-264:
		tmp = t_1
	elif a <= 5.3e-195:
		tmp = t_2
	elif a <= 1.75e-43:
		tmp = t_1
	elif a <= 2.8e-21:
		tmp = t_2
	elif a <= 1.15e+17:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / a)
	tmp = 0.0
	if (a <= -1e+76)
		tmp = t_3;
	elseif (a <= -2.15e-10)
		tmp = t_1;
	elseif (a <= -5.5e-301)
		tmp = t_2;
	elseif (a <= 1.05e-264)
		tmp = t_1;
	elseif (a <= 5.3e-195)
		tmp = t_2;
	elseif (a <= 1.75e-43)
		tmp = t_1;
	elseif (a <= 2.8e-21)
		tmp = t_2;
	elseif (a <= 1.15e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t / b) * ((z / t) + (x / y));
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / a;
	tmp = 0.0;
	if (a <= -1e+76)
		tmp = t_3;
	elseif (a <= -2.15e-10)
		tmp = t_1;
	elseif (a <= -5.5e-301)
		tmp = t_2;
	elseif (a <= 1.05e-264)
		tmp = t_1;
	elseif (a <= 5.3e-195)
		tmp = t_2;
	elseif (a <= 1.75e-43)
		tmp = t_1;
	elseif (a <= 2.8e-21)
		tmp = t_2;
	elseif (a <= 1.15e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / a), $MachinePrecision]}, If[LessEqual[a, -1e+76], t$95$3, If[LessEqual[a, -2.15e-10], t$95$1, If[LessEqual[a, -5.5e-301], t$95$2, If[LessEqual[a, 1.05e-264], t$95$1, If[LessEqual[a, 5.3e-195], t$95$2, If[LessEqual[a, 1.75e-43], t$95$1, If[LessEqual[a, 2.8e-21], t$95$2, If[LessEqual[a, 1.15e+17], t$95$1, t$95$3]]]]]]]]]]]

Derivation

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

Alternative 5: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+177}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))))
   (if (<= y -3.5e+177)
     (/ z b)
     (if (<= y -1.3e+116)
       t_1
       (if (<= y -4.5e+107)
         (/ z b)
         (if (<= y 5e+19)
           (/ (+ x (* z (/ y t))) (+ (* b (/ y t)) (+ a 1.0)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (y <= -3.5e+177) {
		tmp = z / b;
	} else if (y <= -1.3e+116) {
		tmp = t_1;
	} else if (y <= -4.5e+107) {
		tmp = z / b;
	} else if (y <= 5e+19) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	} 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 = (x + (y / (t / z))) / (a + (1.0d0 + (y / (t / b))))
    if (y <= (-3.5d+177)) then
        tmp = z / b
    else if (y <= (-1.3d+116)) then
        tmp = t_1
    else if (y <= (-4.5d+107)) then
        tmp = z / b
    else if (y <= 5d+19) then
        tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0d0))
    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 = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (y <= -3.5e+177) {
		tmp = z / b;
	} else if (y <= -1.3e+116) {
		tmp = t_1;
	} else if (y <= -4.5e+107) {
		tmp = z / b;
	} else if (y <= 5e+19) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))))
	tmp = 0
	if y <= -3.5e+177:
		tmp = z / b
	elif y <= -1.3e+116:
		tmp = t_1
	elif y <= -4.5e+107:
		tmp = z / b
	elif y <= 5e+19:
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))))
	tmp = 0.0
	if (y <= -3.5e+177)
		tmp = Float64(z / b);
	elseif (y <= -1.3e+116)
		tmp = t_1;
	elseif (y <= -4.5e+107)
		tmp = Float64(z / b);
	elseif (y <= 5e+19)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	tmp = 0.0;
	if (y <= -3.5e+177)
		tmp = z / b;
	elseif (y <= -1.3e+116)
		tmp = t_1;
	elseif (y <= -4.5e+107)
		tmp = z / b;
	elseif (y <= 5e+19)
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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[y, -3.5e+177], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.3e+116], t$95$1, If[LessEqual[y, -4.5e+107], N[(z / b), $MachinePrecision], If[LessEqual[y, 5e+19], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 6: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (* b (/ y t)) (+ a 1.0)))))
   (if (<= y -1.42e+147)
     (/ z b)
     (if (<= y -9.5e-74)
       t_1
       (if (<= y -5.8e-97)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= y 1.12e+55)
           t_1
           (if (<= y 5.6e+175) (/ z b) (* (/ t b) (+ (/ z t) (/ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (y <= -1.42e+147) {
		tmp = z / b;
	} else if (y <= -9.5e-74) {
		tmp = t_1;
	} else if (y <= -5.8e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.12e+55) {
		tmp = t_1;
	} else if (y <= 5.6e+175) {
		tmp = z / b;
	} 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 = x / ((b * (y / t)) + (a + 1.0d0))
    if (y <= (-1.42d+147)) then
        tmp = z / b
    else if (y <= (-9.5d-74)) then
        tmp = t_1
    else if (y <= (-5.8d-97)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 1.12d+55) then
        tmp = t_1
    else if (y <= 5.6d+175) then
        tmp = z / b
    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 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (y <= -1.42e+147) {
		tmp = z / b;
	} else if (y <= -9.5e-74) {
		tmp = t_1;
	} else if (y <= -5.8e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.12e+55) {
		tmp = t_1;
	} else if (y <= 5.6e+175) {
		tmp = z / b;
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((b * (y / t)) + (a + 1.0))
	tmp = 0
	if y <= -1.42e+147:
		tmp = z / b
	elif y <= -9.5e-74:
		tmp = t_1
	elif y <= -5.8e-97:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 1.12e+55:
		tmp = t_1
	elif y <= 5.6e+175:
		tmp = z / b
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (y <= -1.42e+147)
		tmp = Float64(z / b);
	elseif (y <= -9.5e-74)
		tmp = t_1;
	elseif (y <= -5.8e-97)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 1.12e+55)
		tmp = t_1;
	elseif (y <= 5.6e+175)
		tmp = Float64(z / b);
	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 = x / ((b * (y / t)) + (a + 1.0));
	tmp = 0.0;
	if (y <= -1.42e+147)
		tmp = z / b;
	elseif (y <= -9.5e-74)
		tmp = t_1;
	elseif (y <= -5.8e-97)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 1.12e+55)
		tmp = t_1;
	elseif (y <= 5.6e+175)
		tmp = z / b;
	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[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e+147], N[(z / b), $MachinePrecision], If[LessEqual[y, -9.5e-74], t$95$1, If[LessEqual[y, -5.8e-97], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+55], t$95$1, If[LessEqual[y, 5.6e+175], N[(z / b), $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 7: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq -2.26 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6e+168)
   (/ z b)
   (if (<= y -6.8e-74)
     (/ x (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= y -2.26e-97)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (<= y 1.2e+55)
         (/ x (+ (* b (/ y t)) (+ a 1.0)))
         (if (<= y 4.4e+174) (/ z b) (* (/ t b) (+ (/ z t) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6e+168) {
		tmp = z / b;
	} else if (y <= -6.8e-74) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (y <= -2.26e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.2e+55) {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	} else if (y <= 4.4e+174) {
		tmp = z / b;
	} 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) :: tmp
    if (y <= (-6d+168)) then
        tmp = z / b
    else if (y <= (-6.8d-74)) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else if (y <= (-2.26d-97)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 1.2d+55) then
        tmp = x / ((b * (y / t)) + (a + 1.0d0))
    else if (y <= 4.4d+174) then
        tmp = z / b
    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 tmp;
	if (y <= -6e+168) {
		tmp = z / b;
	} else if (y <= -6.8e-74) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (y <= -2.26e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.2e+55) {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	} else if (y <= 4.4e+174) {
		tmp = z / b;
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6e+168:
		tmp = z / b
	elif y <= -6.8e-74:
		tmp = x / (((y * b) / t) + (a + 1.0))
	elif y <= -2.26e-97:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 1.2e+55:
		tmp = x / ((b * (y / t)) + (a + 1.0))
	elif y <= 4.4e+174:
		tmp = z / b
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6e+168)
		tmp = Float64(z / b);
	elseif (y <= -6.8e-74)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (y <= -2.26e-97)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 1.2e+55)
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (y <= 4.4e+174)
		tmp = Float64(z / b);
	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)
	tmp = 0.0;
	if (y <= -6e+168)
		tmp = z / b;
	elseif (y <= -6.8e-74)
		tmp = x / (((y * b) / t) + (a + 1.0));
	elseif (y <= -2.26e-97)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 1.2e+55)
		tmp = x / ((b * (y / t)) + (a + 1.0));
	elseif (y <= 4.4e+174)
		tmp = z / b;
	else
		tmp = (t / b) * ((z / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6e+168], N[(z / b), $MachinePrecision], If[LessEqual[y, -6.8e-74], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.26e-97], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+55], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+174], N[(z / b), $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 8: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.8e+168)
   (/ z b)
   (if (<= y -7.2e-13)
     (/ x (+ (/ (* y b) t) (+ a 1.0)))
     (if (<= y 3.5e+123)
       (/ (+ x (* z (/ y t))) (+ a 1.0))
       (if (<= y 3.05e+168)
         (/ z b)
         (if (<= y 2.5e+201)
           (/ x (+ (* b (/ y t)) (+ a 1.0)))
           (* (/ t b) (+ (/ z t) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+168) {
		tmp = z / b;
	} else if (y <= -7.2e-13) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (y <= 3.5e+123) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 3.05e+168) {
		tmp = z / b;
	} else if (y <= 2.5e+201) {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	} 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) :: tmp
    if (y <= (-6.8d+168)) then
        tmp = z / b
    else if (y <= (-7.2d-13)) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else if (y <= 3.5d+123) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (y <= 3.05d+168) then
        tmp = z / b
    else if (y <= 2.5d+201) then
        tmp = x / ((b * (y / t)) + (a + 1.0d0))
    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 tmp;
	if (y <= -6.8e+168) {
		tmp = z / b;
	} else if (y <= -7.2e-13) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (y <= 3.5e+123) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 3.05e+168) {
		tmp = z / b;
	} else if (y <= 2.5e+201) {
		tmp = x / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.8e+168:
		tmp = z / b
	elif y <= -7.2e-13:
		tmp = x / (((y * b) / t) + (a + 1.0))
	elif y <= 3.5e+123:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif y <= 3.05e+168:
		tmp = z / b
	elif y <= 2.5e+201:
		tmp = x / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.8e+168)
		tmp = Float64(z / b);
	elseif (y <= -7.2e-13)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (y <= 3.5e+123)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (y <= 3.05e+168)
		tmp = Float64(z / b);
	elseif (y <= 2.5e+201)
		tmp = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	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)
	tmp = 0.0;
	if (y <= -6.8e+168)
		tmp = z / b;
	elseif (y <= -7.2e-13)
		tmp = x / (((y * b) / t) + (a + 1.0));
	elseif (y <= 3.5e+123)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (y <= 3.05e+168)
		tmp = z / b;
	elseif (y <= 2.5e+201)
		tmp = x / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (t / b) * ((z / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.8e+168], N[(z / b), $MachinePrecision], If[LessEqual[y, -7.2e-13], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+123], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e+168], N[(z / b), $MachinePrecision], If[LessEqual[y, 2.5e+201], N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $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 9: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;x \leq -3.55 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-272}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (* b (/ y t)) (+ a 1.0)))))
   (if (<= x -3.55e+34)
     t_1
     (if (<= x -2.55e-272)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (<= x 1.55e-27)
         (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
         (if (<= x 3.2e+94) (/ (+ x (* z (/ y t))) (+ a 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (x <= -3.55e+34) {
		tmp = t_1;
	} else if (x <= -2.55e-272) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (x <= 1.55e-27) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (x <= 3.2e+94) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} 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 = x / ((b * (y / t)) + (a + 1.0d0))
    if (x <= (-3.55d+34)) then
        tmp = t_1
    else if (x <= (-2.55d-272)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (x <= 1.55d-27) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (x <= 3.2d+94) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    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 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (x <= -3.55e+34) {
		tmp = t_1;
	} else if (x <= -2.55e-272) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (x <= 1.55e-27) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (x <= 3.2e+94) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((b * (y / t)) + (a + 1.0))
	tmp = 0
	if x <= -3.55e+34:
		tmp = t_1
	elif x <= -2.55e-272:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif x <= 1.55e-27:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif x <= 3.2e+94:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (x <= -3.55e+34)
		tmp = t_1;
	elseif (x <= -2.55e-272)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (x <= 1.55e-27)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (x <= 3.2e+94)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((b * (y / t)) + (a + 1.0));
	tmp = 0.0;
	if (x <= -3.55e+34)
		tmp = t_1;
	elseif (x <= -2.55e-272)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (x <= 1.55e-27)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (x <= 3.2e+94)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.55e+34], t$95$1, If[LessEqual[x, -2.55e-272], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-27], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+94], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 10: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-256} \lor \neg \left(t \leq 2.5 \cdot 10^{-221}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.02e-256) (not (<= t 2.5e-221)))
   (/ (+ x (* z (/ y t))) (+ 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 ((t <= -1.02e-256) || !(t <= 2.5e-221)) {
		tmp = (x + (z * (y / t))) / (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 ((t <= (-1.02d-256)) .or. (.not. (t <= 2.5d-221))) then
        tmp = (x + (z * (y / t))) / (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 ((t <= -1.02e-256) || !(t <= 2.5e-221)) {
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.02e-256) or not (t <= 2.5e-221):
		tmp = (x + (z * (y / t))) / (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 ((t <= -1.02e-256) || !(t <= 2.5e-221))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(1.0 + Float64(a + Float64(y * Float64(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 ((t <= -1.02e-256) || ~((t <= 2.5e-221)))
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.02e-256], N[Not[LessEqual[t, 2.5e-221]], $MachinePrecision]], 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], N[(z / b), $MachinePrecision]]

Derivation

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

Alternative 11: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-257} \lor \neg \left(t \leq 2.85 \cdot 10^{-221}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6e-257) (not (<= t 2.85e-221)))
   (/ (+ x (* z (/ y t))) (+ (* b (/ y t)) (+ a 1.0)))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6e-257) || !(t <= 2.85e-221)) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (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 ((t <= (-6d-257)) .or. (.not. (t <= 2.85d-221))) then
        tmp = (x + (z * (y / t))) / ((b * (y / t)) + (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 ((t <= -6e-257) || !(t <= 2.85e-221)) {
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6e-257) or not (t <= 2.85e-221):
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6e-257) || !(t <= 2.85e-221))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(b * Float64(y / t)) + 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 ((t <= -6e-257) || ~((t <= 2.85e-221)))
		tmp = (x + (z * (y / t))) / ((b * (y / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6e-257], N[Not[LessEqual[t, 2.85e-221]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

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

Alternative 12: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.85 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.85e+174)
   (/ z b)
   (if (<= y 2e-29)
     (/ (+ x (/ (* y z) t)) (+ (* b (/ y t)) (+ a 1.0)))
     (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.85e+174) {
		tmp = z / b;
	} else if (y <= 2e-29) {
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / 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 <= (-3.85d+174)) then
        tmp = z / b
    else if (y <= 2d-29) then
        tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0d0))
    else
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (y / (t / 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 <= -3.85e+174) {
		tmp = z / b;
	} else if (y <= 2e-29) {
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.85e+174:
		tmp = z / b
	elif y <= 2e-29:
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.85e+174)
		tmp = Float64(z / b);
	elseif (y <= 2e-29)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.85e+174)
		tmp = z / b;
	elseif (y <= 2e-29)
		tmp = (x + ((y * z) / t)) / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.85e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, 2e-29], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]

Derivation

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

Alternative 13: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -0.0006:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+40}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 a)))
   (if (<= a -0.0006)
     t_2
     (if (<= a -2.65e-306)
       t_1
       (if (<= a 5.8e-265)
         (/ (/ (* x t) b) y)
         (if (<= a 7e-21) t_1 (if (<= a 1.06e+40) (/ z b) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -0.0006) {
		tmp = t_2;
	} else if (a <= -2.65e-306) {
		tmp = t_1;
	} else if (a <= 5.8e-265) {
		tmp = ((x * t) / b) / y;
	} else if (a <= 7e-21) {
		tmp = t_1;
	} else if (a <= 1.06e+40) {
		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 + ((y * z) / t)
    t_2 = t_1 / a
    if (a <= (-0.0006d0)) then
        tmp = t_2
    else if (a <= (-2.65d-306)) then
        tmp = t_1
    else if (a <= 5.8d-265) then
        tmp = ((x * t) / b) / y
    else if (a <= 7d-21) then
        tmp = t_1
    else if (a <= 1.06d+40) 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 + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -0.0006) {
		tmp = t_2;
	} else if (a <= -2.65e-306) {
		tmp = t_1;
	} else if (a <= 5.8e-265) {
		tmp = ((x * t) / b) / y;
	} else if (a <= 7e-21) {
		tmp = t_1;
	} else if (a <= 1.06e+40) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / a
	tmp = 0
	if a <= -0.0006:
		tmp = t_2
	elif a <= -2.65e-306:
		tmp = t_1
	elif a <= 5.8e-265:
		tmp = ((x * t) / b) / y
	elif a <= 7e-21:
		tmp = t_1
	elif a <= 1.06e+40:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -0.0006)
		tmp = t_2;
	elseif (a <= -2.65e-306)
		tmp = t_1;
	elseif (a <= 5.8e-265)
		tmp = Float64(Float64(Float64(x * t) / b) / y);
	elseif (a <= 7e-21)
		tmp = t_1;
	elseif (a <= 1.06e+40)
		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 + ((y * z) / t);
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -0.0006)
		tmp = t_2;
	elseif (a <= -2.65e-306)
		tmp = t_1;
	elseif (a <= 5.8e-265)
		tmp = ((x * t) / b) / y;
	elseif (a <= 7e-21)
		tmp = t_1;
	elseif (a <= 1.06e+40)
		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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -0.0006], t$95$2, If[LessEqual[a, -2.65e-306], t$95$1, If[LessEqual[a, 5.8e-265], N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[a, 7e-21], t$95$1, If[LessEqual[a, 1.06e+40], N[(z / b), $MachinePrecision], t$95$2]]]]]]]

Derivation

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

Alternative 14: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+222}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+92} \lor \neg \left(b \leq 1.18 \cdot 10^{-63}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (* b (/ y t)) (+ a 1.0)))))
   (if (<= b -2.15e+249)
     t_1
     (if (<= b -4.5e+222)
       (/ z b)
       (if (or (<= b -3e+92) (not (<= b 1.18e-63)))
         t_1
         (/ (+ x (/ (* y z) t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (b <= -2.15e+249) {
		tmp = t_1;
	} else if (b <= -4.5e+222) {
		tmp = z / b;
	} else if ((b <= -3e+92) || !(b <= 1.18e-63)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((b * (y / t)) + (a + 1.0d0))
    if (b <= (-2.15d+249)) then
        tmp = t_1
    else if (b <= (-4.5d+222)) then
        tmp = z / b
    else if ((b <= (-3d+92)) .or. (.not. (b <= 1.18d-63))) then
        tmp = t_1
    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 t_1 = x / ((b * (y / t)) + (a + 1.0));
	double tmp;
	if (b <= -2.15e+249) {
		tmp = t_1;
	} else if (b <= -4.5e+222) {
		tmp = z / b;
	} else if ((b <= -3e+92) || !(b <= 1.18e-63)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((b * (y / t)) + (a + 1.0))
	tmp = 0
	if b <= -2.15e+249:
		tmp = t_1
	elif b <= -4.5e+222:
		tmp = z / b
	elif (b <= -3e+92) or not (b <= 1.18e-63):
		tmp = t_1
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (b <= -2.15e+249)
		tmp = t_1;
	elseif (b <= -4.5e+222)
		tmp = Float64(z / b);
	elseif ((b <= -3e+92) || !(b <= 1.18e-63))
		tmp = t_1;
	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)
	t_1 = x / ((b * (y / t)) + (a + 1.0));
	tmp = 0.0;
	if (b <= -2.15e+249)
		tmp = t_1;
	elseif (b <= -4.5e+222)
		tmp = z / b;
	elseif ((b <= -3e+92) || ~((b <= 1.18e-63)))
		tmp = t_1;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+249], t$95$1, If[LessEqual[b, -4.5e+222], N[(z / b), $MachinePrecision], If[Or[LessEqual[b, -3e+92], N[Not[LessEqual[b, 1.18e-63]], $MachinePrecision]], t$95$1, 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: 56.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -1.42e+94)
     (/ z b)
     (if (<= y -4.7e-73)
       t_1
       (if (<= y -5.2e-97)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= y 1.15e+55) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -1.42e+94) {
		tmp = z / b;
	} else if (y <= -4.7e-73) {
		tmp = t_1;
	} else if (y <= -5.2e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.15e+55) {
		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 / (a + 1.0d0)
    if (y <= (-1.42d+94)) then
        tmp = z / b
    else if (y <= (-4.7d-73)) then
        tmp = t_1
    else if (y <= (-5.2d-97)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 1.15d+55) 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 / (a + 1.0);
	double tmp;
	if (y <= -1.42e+94) {
		tmp = z / b;
	} else if (y <= -4.7e-73) {
		tmp = t_1;
	} else if (y <= -5.2e-97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 1.15e+55) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -1.42e+94:
		tmp = z / b
	elif y <= -4.7e-73:
		tmp = t_1
	elif y <= -5.2e-97:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 1.15e+55:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -1.42e+94)
		tmp = Float64(z / b);
	elseif (y <= -4.7e-73)
		tmp = t_1;
	elseif (y <= -5.2e-97)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 1.15e+55)
		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 / (a + 1.0);
	tmp = 0.0;
	if (y <= -1.42e+94)
		tmp = z / b;
	elseif (y <= -4.7e-73)
		tmp = t_1;
	elseif (y <= -5.2e-97)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 1.15e+55)
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e+94], N[(z / b), $MachinePrecision], If[LessEqual[y, -4.7e-73], t$95$1, If[LessEqual[y, -5.2e-97], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+55], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

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

Alternative 16: 56.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+97} \lor \neg \left(y \leq 1.22 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.2e+97) (not (<= y 1.22e+55))) (/ 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 <= -5.2e+97) || !(y <= 1.22e+55)) {
		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 <= (-5.2d+97)) .or. (.not. (y <= 1.22d+55))) 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 <= -5.2e+97) || !(y <= 1.22e+55)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.2e+97) or not (y <= 1.22e+55):
		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 <= -5.2e+97) || !(y <= 1.22e+55))
		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 <= -5.2e+97) || ~((y <= 1.22e+55)))
		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, -5.2e+97], N[Not[LessEqual[y, 1.22e+55]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 41.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+84} \lor \neg \left(y \leq 1.12 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+84) (not (<= y 1.12e+55))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+84) || !(y <= 1.12e+55)) {
		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 ((y <= (-2.7d+84)) .or. (.not. (y <= 1.12d+55))) 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 ((y <= -2.7e+84) || !(y <= 1.12e+55)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+84) or not (y <= 1.12e+55):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+84) || !(y <= 1.12e+55))
		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 ((y <= -2.7e+84) || ~((y <= 1.12e+55)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+84], N[Not[LessEqual[y, 1.12e+55]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

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

Alternative 18: 25.7% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

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 / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

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

Developer target: 79.2% 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 2024008 
(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))))