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

Percentage Accurate: 95.8% → 99.6%

Time: 8.2s

Alternatives: 6

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;-\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 10^{+230}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (- (/ (/ x z) t))
   (if (<= (* z t) 1e+230) (/ x (- y (* z t))) (* (/ x z) (/ -1.0 t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = -((x / z) / t);
	} else if ((z * t) <= 1e+230) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = -((x / z) / t);
	} else if ((z * t) <= 1e+230) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = -((x / z) / t)
	elif (z * t) <= 1e+230:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / z) * (-1.0 / t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(-Float64(Float64(x / z) / t));
	elseif (Float64(z * t) <= 1e+230)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = -((x / z) / t);
	elseif ((z * t) <= 1e+230)
		tmp = x / (y - (z * t));
	else
		tmp = (x / z) * (-1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], (-N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), If[LessEqual[N[(z * t), $MachinePrecision], 1e+230], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 2: 79.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ t_2 := \frac{\frac{-x}{t}}{z}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 100000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 10^{+125}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))) (t_2 (/ (/ (- x) t) z)))
   (if (<= (* z t) -5e+128)
     t_2
     (if (<= (* z t) -5e-10)
       t_1
       (if (<= (* z t) 100000.0)
         (/ x y)
         (if (<= (* z t) 1e+44) t_1 (if (<= (* z t) 1e+125) (/ x y) t_2)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = (-x / t) / z;
	double tmp;
	if ((z * t) <= -5e+128) {
		tmp = t_2;
	} else if ((z * t) <= -5e-10) {
		tmp = t_1;
	} else if ((z * t) <= 100000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+44) {
		tmp = t_1;
	} else if ((z * t) <= 1e+125) {
		tmp = x / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / (z * t)
    t_2 = (-x / t) / z
    if ((z * t) <= (-5d+128)) then
        tmp = t_2
    else if ((z * t) <= (-5d-10)) then
        tmp = t_1
    else if ((z * t) <= 100000.0d0) then
        tmp = x / y
    else if ((z * t) <= 1d+44) then
        tmp = t_1
    else if ((z * t) <= 1d+125) then
        tmp = x / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = (-x / t) / z;
	double tmp;
	if ((z * t) <= -5e+128) {
		tmp = t_2;
	} else if ((z * t) <= -5e-10) {
		tmp = t_1;
	} else if ((z * t) <= 100000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+44) {
		tmp = t_1;
	} else if ((z * t) <= 1e+125) {
		tmp = x / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	t_2 = (-x / t) / z
	tmp = 0
	if (z * t) <= -5e+128:
		tmp = t_2
	elif (z * t) <= -5e-10:
		tmp = t_1
	elif (z * t) <= 100000.0:
		tmp = x / y
	elif (z * t) <= 1e+44:
		tmp = t_1
	elif (z * t) <= 1e+125:
		tmp = x / y
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	t_2 = Float64(Float64(Float64(-x) / t) / z)
	tmp = 0.0
	if (Float64(z * t) <= -5e+128)
		tmp = t_2;
	elseif (Float64(z * t) <= -5e-10)
		tmp = t_1;
	elseif (Float64(z * t) <= 100000.0)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+44)
		tmp = t_1;
	elseif (Float64(z * t) <= 1e+125)
		tmp = Float64(x / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	t_2 = (-x / t) / z;
	tmp = 0.0;
	if ((z * t) <= -5e+128)
		tmp = t_2;
	elseif ((z * t) <= -5e-10)
		tmp = t_1;
	elseif ((z * t) <= 100000.0)
		tmp = x / y;
	elseif ((z * t) <= 1e+44)
		tmp = t_1;
	elseif ((z * t) <= 1e+125)
		tmp = x / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+128], t$95$2, If[LessEqual[N[(z * t), $MachinePrecision], -5e-10], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 100000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+44], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1e+125], N[(x / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

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

Alternative 3: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 100000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+44}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{+125}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e-10)
   (/ -1.0 (* t (/ z x)))
   (if (<= (* z t) 100000.0)
     (/ x y)
     (if (<= (* z t) 1e+44)
       (/ (- x) (* z t))
       (if (<= (* z t) 1e+125) (/ x y) (/ (/ (- x) t) z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-10) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 100000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+44) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 1e+125) {
		tmp = x / y;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-5d-10)) then
        tmp = (-1.0d0) / (t * (z / x))
    else if ((z * t) <= 100000.0d0) then
        tmp = x / y
    else if ((z * t) <= 1d+44) then
        tmp = -x / (z * t)
    else if ((z * t) <= 1d+125) then
        tmp = x / y
    else
        tmp = (-x / t) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-10) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 100000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+44) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 1e+125) {
		tmp = x / y;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e-10:
		tmp = -1.0 / (t * (z / x))
	elif (z * t) <= 100000.0:
		tmp = x / y
	elif (z * t) <= 1e+44:
		tmp = -x / (z * t)
	elif (z * t) <= 1e+125:
		tmp = x / y
	else:
		tmp = (-x / t) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e-10)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (Float64(z * t) <= 100000.0)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+44)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 1e+125)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(-x) / t) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e-10)
		tmp = -1.0 / (t * (z / x));
	elseif ((z * t) <= 100000.0)
		tmp = x / y;
	elseif ((z * t) <= 1e+44)
		tmp = -x / (z * t);
	elseif ((z * t) <= 1e+125)
		tmp = x / y;
	else
		tmp = (-x / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e-10], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 100000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+44], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+125], N[(x / y), $MachinePrecision], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

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

Alternative 4: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-10} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;-\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e-10) (not (<= (* z t) 2e+14)))
   (- (/ (/ x z) t))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e-10) || !((z * t) <= 2e+14)) {
		tmp = -((x / z) / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * t) <= (-5d-10)) .or. (.not. ((z * t) <= 2d+14))) then
        tmp = -((x / z) / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e-10) || !((z * t) <= 2e+14)) {
		tmp = -((x / z) / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e-10) or not ((z * t) <= 2e+14):
		tmp = -((x / z) / t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e-10) || !(Float64(z * t) <= 2e+14))
		tmp = Float64(-Float64(Float64(x / z) / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e-10) || ~(((z * t) <= 2e+14)))
		tmp = -((x / z) / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-10], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+14]], $MachinePrecision]], (-N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), N[(x / y), $MachinePrecision]]

Derivation

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

Alternative 5: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+194} \lor \neg \left(z \cdot t \leq 10^{+221}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+194) (not (<= (* z t) 1e+221)))
   (/ x (* z t))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+194) || !((z * t) <= 1e+221)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * t) <= (-5d+194)) .or. (.not. ((z * t) <= 1d+221))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+194) || !((z * t) <= 1e+221)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+194) or not ((z * t) <= 1e+221):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+194) || !(Float64(z * t) <= 1e+221))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+194) || ~(((z * t) <= 1e+221)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+194], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+221]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

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

Alternative 6: 54.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x y))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / y;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / y
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / y

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / y)
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / y;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

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

Developer target: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

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

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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