Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.8% → 93.8%

Time: 14.0s

Alternatives: 10

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{t_1} - \frac{y}{\frac{t_1}{z}}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 -2e-292)
     (- (/ x t_1) (/ y (/ t_1 z)))
     (if (<= t_2 0.0)
       (/ (- y) (- (/ t z) a))
       (if (<= t_2 2e+287) t_2 (/ (- y (/ x z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -2e-292) {
		tmp = (x / t_1) - (y / (t_1 / z));
	} else if (t_2 <= 0.0) {
		tmp = -y / ((t / z) - a);
	} else if (t_2 <= 2e+287) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (z * a)
    t_2 = (x - (y * z)) / t_1
    if (t_2 <= (-2d-292)) then
        tmp = (x / t_1) - (y / (t_1 / z))
    else if (t_2 <= 0.0d0) then
        tmp = -y / ((t / z) - a)
    else if (t_2 <= 2d+287) then
        tmp = t_2
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -2e-292) {
		tmp = (x / t_1) - (y / (t_1 / z));
	} else if (t_2 <= 0.0) {
		tmp = -y / ((t / z) - a);
	} else if (t_2 <= 2e+287) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (y * z)) / t_1
	tmp = 0
	if t_2 <= -2e-292:
		tmp = (x / t_1) - (y / (t_1 / z))
	elif t_2 <= 0.0:
		tmp = -y / ((t / z) - a)
	elif t_2 <= 2e+287:
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= -2e-292)
		tmp = Float64(Float64(x / t_1) - Float64(y / Float64(t_1 / z)));
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-y) / Float64(Float64(t / z) - a));
	elseif (t_2 <= 2e+287)
		tmp = t_2;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_2 <= -2e-292)
		tmp = (x / t_1) - (y / (t_1 / z));
	elseif (t_2 <= 0.0)
		tmp = -y / ((t / z) - a);
	elseif (t_2 <= 2e+287)
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-292], N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+287], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 52.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{a}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-42}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) a)))
   (if (<= z -5e+45)
     (/ y a)
     (if (<= z -2.15e-42)
       (* (- z) (/ y t))
       (if (<= z -4.4e-72)
         (/ y a)
         (if (<= z -2.2e-98)
           (/ x t)
           (if (<= z -1.55e-124)
             t_1
             (if (<= z 1.6e+17) (/ x t) (if (<= z 8e+170) t_1 (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-x / z) / a;
	double tmp;
	if (z <= -5e+45) {
		tmp = y / a;
	} else if (z <= -2.15e-42) {
		tmp = -z * (y / t);
	} else if (z <= -4.4e-72) {
		tmp = y / a;
	} else if (z <= -2.2e-98) {
		tmp = x / t;
	} else if (z <= -1.55e-124) {
		tmp = t_1;
	} else if (z <= 1.6e+17) {
		tmp = x / t;
	} else if (z <= 8e+170) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (-x / z) / a
    if (z <= (-5d+45)) then
        tmp = y / a
    else if (z <= (-2.15d-42)) then
        tmp = -z * (y / t)
    else if (z <= (-4.4d-72)) then
        tmp = y / a
    else if (z <= (-2.2d-98)) then
        tmp = x / t
    else if (z <= (-1.55d-124)) then
        tmp = t_1
    else if (z <= 1.6d+17) then
        tmp = x / t
    else if (z <= 8d+170) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-x / z) / a;
	double tmp;
	if (z <= -5e+45) {
		tmp = y / a;
	} else if (z <= -2.15e-42) {
		tmp = -z * (y / t);
	} else if (z <= -4.4e-72) {
		tmp = y / a;
	} else if (z <= -2.2e-98) {
		tmp = x / t;
	} else if (z <= -1.55e-124) {
		tmp = t_1;
	} else if (z <= 1.6e+17) {
		tmp = x / t;
	} else if (z <= 8e+170) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-x / z) / a
	tmp = 0
	if z <= -5e+45:
		tmp = y / a
	elif z <= -2.15e-42:
		tmp = -z * (y / t)
	elif z <= -4.4e-72:
		tmp = y / a
	elif z <= -2.2e-98:
		tmp = x / t
	elif z <= -1.55e-124:
		tmp = t_1
	elif z <= 1.6e+17:
		tmp = x / t
	elif z <= 8e+170:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-x) / z) / a)
	tmp = 0.0
	if (z <= -5e+45)
		tmp = Float64(y / a);
	elseif (z <= -2.15e-42)
		tmp = Float64(Float64(-z) * Float64(y / t));
	elseif (z <= -4.4e-72)
		tmp = Float64(y / a);
	elseif (z <= -2.2e-98)
		tmp = Float64(x / t);
	elseif (z <= -1.55e-124)
		tmp = t_1;
	elseif (z <= 1.6e+17)
		tmp = Float64(x / t);
	elseif (z <= 8e+170)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-x / z) / a;
	tmp = 0.0;
	if (z <= -5e+45)
		tmp = y / a;
	elseif (z <= -2.15e-42)
		tmp = -z * (y / t);
	elseif (z <= -4.4e-72)
		tmp = y / a;
	elseif (z <= -2.2e-98)
		tmp = x / t;
	elseif (z <= -1.55e-124)
		tmp = t_1;
	elseif (z <= 1.6e+17)
		tmp = x / t;
	elseif (z <= 8e+170)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5e+45], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.15e-42], N[((-z) * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-72], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.2e-98], N[(x / t), $MachinePrecision], If[LessEqual[z, -1.55e-124], t$95$1, If[LessEqual[z, 1.6e+17], N[(x / t), $MachinePrecision], If[LessEqual[z, 8e+170], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 3: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 10^{+35}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + \frac{x}{z} \cdot \frac{-1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+31)
   (/ (- y (/ x z)) a)
   (if (<= z -4.5e-81)
     (/ (- x (* y z)) t)
     (if (<= z 1e+35)
       (/ x (- t (* z a)))
       (+ (/ y a) (* (/ x z) (/ -1.0 a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+31) {
		tmp = (y - (x / z)) / a;
	} else if (z <= -4.5e-81) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1e+35) {
		tmp = x / (t - (z * a));
	} else {
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-3.2d+31)) then
        tmp = (y - (x / z)) / a
    else if (z <= (-4.5d-81)) then
        tmp = (x - (y * z)) / t
    else if (z <= 1d+35) then
        tmp = x / (t - (z * a))
    else
        tmp = (y / a) + ((x / z) * ((-1.0d0) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+31) {
		tmp = (y - (x / z)) / a;
	} else if (z <= -4.5e-81) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1e+35) {
		tmp = x / (t - (z * a));
	} else {
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+31:
		tmp = (y - (x / z)) / a
	elif z <= -4.5e-81:
		tmp = (x - (y * z)) / t
	elif z <= 1e+35:
		tmp = x / (t - (z * a))
	else:
		tmp = (y / a) + ((x / z) * (-1.0 / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+31)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (z <= -4.5e-81)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1e+35)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y / a) + Float64(Float64(x / z) * Float64(-1.0 / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+31)
		tmp = (y - (x / z)) / a;
	elseif (z <= -4.5e-81)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1e+35)
		tmp = x / (t - (z * a));
	else
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+31], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -4.5e-81], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1e+35], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+115}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + \frac{x}{z} \cdot \frac{-1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+115)
   (/ (- y (/ x z)) a)
   (if (<= z 5e+127)
     (/ (- x (* y z)) (- t (* z a)))
     (+ (/ y a) (* (/ x z) (/ -1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+115) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 5e+127) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-3.3d+115)) then
        tmp = (y - (x / z)) / a
    else if (z <= 5d+127) then
        tmp = (x - (y * z)) / (t - (z * a))
    else
        tmp = (y / a) + ((x / z) * ((-1.0d0) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+115) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 5e+127) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+115:
		tmp = (y - (x / z)) / a
	elif z <= 5e+127:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = (y / a) + ((x / z) * (-1.0 / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+115)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (z <= 5e+127)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y / a) + Float64(Float64(x / z) * Float64(-1.0 / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+115)
		tmp = (y - (x / z)) / a;
	elseif (z <= 5e+127)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = (y / a) + ((x / z) * (-1.0 / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+115], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 5e+127], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -3.6e+31)
     t_1
     (if (<= z -6.8e-81)
       (/ (- x (* y z)) t)
       (if (<= z 8.5e+34) (/ x (- t (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -3.6e+31) {
		tmp = t_1;
	} else if (z <= -6.8e-81) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 8.5e+34) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-3.6d+31)) then
        tmp = t_1
    else if (z <= (-6.8d-81)) then
        tmp = (x - (y * z)) / t
    else if (z <= 8.5d+34) then
        tmp = x / (t - (z * a))
    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 t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -3.6e+31) {
		tmp = t_1;
	} else if (z <= -6.8e-81) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 8.5e+34) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -3.6e+31:
		tmp = t_1
	elif z <= -6.8e-81:
		tmp = (x - (y * z)) / t
	elif z <= 8.5e+34:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -3.6e+31)
		tmp = t_1;
	elseif (z <= -6.8e-81)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 8.5e+34)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -3.6e+31)
		tmp = t_1;
	elseif (z <= -6.8e-81)
		tmp = (x - (y * z)) / t;
	elseif (z <= 8.5e+34)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -3.6e+31], t$95$1, If[LessEqual[z, -6.8e-81], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 8.5e+34], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

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

Alternative 6: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+82} \lor \neg \left(z \leq 4.5 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+82) (not (<= z 4.5e+96))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+82) || !(z <= 4.5e+96)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-2.8d+82)) .or. (.not. (z <= 4.5d+96))) then
        tmp = y / a
    else
        tmp = x / (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 tmp;
	if ((z <= -2.8e+82) || !(z <= 4.5e+96)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+82) or not (z <= 4.5e+96):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+82) || !(z <= 4.5e+96))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+82) || ~((z <= 4.5e+96)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+82], N[Not[LessEqual[z, 4.5e+96]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 54.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+46)
   (/ y a)
   (if (<= z -7.8e-81) (/ (- y) (/ t z)) (if (<= z 1.4e+35) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+46) {
		tmp = y / a;
	} else if (z <= -7.8e-81) {
		tmp = -y / (t / z);
	} else if (z <= 1.4e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-3.2d+46)) then
        tmp = y / a
    else if (z <= (-7.8d-81)) then
        tmp = -y / (t / z)
    else if (z <= 1.4d+35) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+46) {
		tmp = y / a;
	} else if (z <= -7.8e-81) {
		tmp = -y / (t / z);
	} else if (z <= 1.4e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+46:
		tmp = y / a
	elif z <= -7.8e-81:
		tmp = -y / (t / z)
	elif z <= 1.4e+35:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+46)
		tmp = Float64(y / a);
	elseif (z <= -7.8e-81)
		tmp = Float64(Float64(-y) / Float64(t / z));
	elseif (z <= 1.4e+35)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+46)
		tmp = y / a;
	elseif (z <= -7.8e-81)
		tmp = -y / (t / z);
	elseif (z <= 1.4e+35)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+46], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.8e-81], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+35], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

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

Alternative 8: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+48)
   (/ y a)
   (if (<= z -5.8e-81)
     (/ (* y (- z)) t)
     (if (<= z 1.05e+35) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+48) {
		tmp = y / a;
	} else if (z <= -5.8e-81) {
		tmp = (y * -z) / t;
	} else if (z <= 1.05e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-9.2d+48)) then
        tmp = y / a
    else if (z <= (-5.8d-81)) then
        tmp = (y * -z) / t
    else if (z <= 1.05d+35) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+48) {
		tmp = y / a;
	} else if (z <= -5.8e-81) {
		tmp = (y * -z) / t;
	} else if (z <= 1.05e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+48:
		tmp = y / a
	elif z <= -5.8e-81:
		tmp = (y * -z) / t
	elif z <= 1.05e+35:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+48)
		tmp = Float64(y / a);
	elseif (z <= -5.8e-81)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 1.05e+35)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+48)
		tmp = y / a;
	elseif (z <= -5.8e-81)
		tmp = (y * -z) / t;
	elseif (z <= 1.05e+35)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+48], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e-81], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.05e+35], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

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

Alternative 9: 55.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+35} \lor \neg \left(z \leq 1.65 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+35) (not (<= z 1.65e+35))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+35) || !(z <= 1.65e+35)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-1.9d+35)) .or. (.not. (z <= 1.65d+35))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+35) || !(z <= 1.65e+35)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+35) or not (z <= 1.65e+35):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+35) || !(z <= 1.65e+35))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+35) || ~((z <= 1.65e+35)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+35], N[Not[LessEqual[z, 1.65e+35]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

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

Alternative 10: 36.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = x / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    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 t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))