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

Percentage Accurate: 95.5% → 99.5%

Time: 11.0s

Alternatives: 8

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: 95.5% 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: 99.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+197}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+265}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t} \cdot \frac{-1}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -2e+197)
   (- (/ (/ x t) z))
   (if (<= (* z t) 2e+265)
     (/ x (fma z (- t) y))
     (expm1 (log1p (* (/ x t) (/ -1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -2e+197) {
		tmp = -((x / t) / z);
	} else if ((z * t) <= 2e+265) {
		tmp = x / fma(z, -t, y);
	} else {
		tmp = expm1(log1p(((x / t) * (-1.0 / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -2e+197)
		tmp = Float64(-Float64(Float64(x / t) / z));
	elseif (Float64(z * t) <= 2e+265)
		tmp = Float64(x / fma(z, Float64(-t), y));
	else
		tmp = expm1(log1p(Float64(Float64(x / t) * Float64(-1.0 / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+197], (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[N[(z * t), $MachinePrecision], 2e+265], N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision], N[(Exp[N[Log[1 + N[(N[(x / t), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]]]

Derivation

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+197} \lor \neg \left(z \cdot t \leq 10^{+185}\right):\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -2e+197) (not (<= (* z t) 1e+185)))
   (- (/ (/ x t) z))
   (/ x (fma z (- t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -2e+197) || !((z * t) <= 1e+185)) {
		tmp = -((x / t) / z);
	} else {
		tmp = x / fma(z, -t, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+197) || !(Float64(z * t) <= 1e+185))
		tmp = Float64(-Float64(Float64(x / t) / z));
	else
		tmp = Float64(x / fma(z, Float64(-t), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e+197], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+185]], $MachinePrecision]], (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 1000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 10^{+74}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -4e+133)
   (/ (/ x z) (- t))
   (if (<= (* z t) 1000.0)
     (/ x y)
     (if (<= (* z t) 1e+74)
       (/ (- x) (* z t))
       (if (<= (* z t) 5e+100) (/ x y) (- (/ (/ x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -4e+133) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 1000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+74) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 5e+100) {
		tmp = x / y;
	} else {
		tmp = -((x / t) / z);
	}
	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) :: tmp
    if ((z * t) <= (-4d+133)) then
        tmp = (x / z) / -t
    else if ((z * t) <= 1000.0d0) then
        tmp = x / y
    else if ((z * t) <= 1d+74) then
        tmp = -x / (z * t)
    else if ((z * t) <= 5d+100) then
        tmp = x / y
    else
        tmp = -((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -4e+133) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 1000.0) {
		tmp = x / y;
	} else if ((z * t) <= 1e+74) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 5e+100) {
		tmp = x / y;
	} else {
		tmp = -((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -4e+133:
		tmp = (x / z) / -t
	elif (z * t) <= 1000.0:
		tmp = x / y
	elif (z * t) <= 1e+74:
		tmp = -x / (z * t)
	elif (z * t) <= 5e+100:
		tmp = x / y
	else:
		tmp = -((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -4e+133)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (Float64(z * t) <= 1000.0)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 1e+74)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 5e+100)
		tmp = Float64(x / y);
	else
		tmp = Float64(-Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -4e+133)
		tmp = (x / z) / -t;
	elseif ((z * t) <= 1000.0)
		tmp = x / y;
	elseif ((z * t) <= 1e+74)
		tmp = -x / (z * t);
	elseif ((z * t) <= 5e+100)
		tmp = x / y;
	else
		tmp = -((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e+133], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+74], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+100], N[(x / y), $MachinePrecision], (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision])]]]]

Derivation

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

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+197} \lor \neg \left(z \cdot t \leq 10^{+185}\right):\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -2e+197) (not (<= (* z t) 1e+185)))
   (- (/ (/ x t) z))
   (/ x (- y (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -2e+197) || !((z * t) <= 1e+185)) {
		tmp = -((x / t) / z);
	} else {
		tmp = x / (y - (z * t));
	}
	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) :: tmp
    if (((z * t) <= (-2d+197)) .or. (.not. ((z * t) <= 1d+185))) then
        tmp = -((x / t) / z)
    else
        tmp = x / (y - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -2e+197) || !((z * t) <= 1e+185)) {
		tmp = -((x / t) / z);
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -2e+197) or not ((z * t) <= 1e+185):
		tmp = -((x / t) / z)
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+197) || !(Float64(z * t) <= 1e+185))
		tmp = Float64(-Float64(Float64(x / t) / z));
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -2e+197) || ~(((z * t) <= 1e+185)))
		tmp = -((x / t) / z);
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e+197], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+185]], $MachinePrecision]], (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-77} \lor \neg \left(t \leq 290\right) \land \left(t \leq 3.4 \cdot 10^{+42} \lor \neg \left(t \leq 1.42 \cdot 10^{+86}\right)\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.2e-77)
         (and (not (<= t 290.0)) (or (<= t 3.4e+42) (not (<= t 1.42e+86)))))
   (/ (- x) (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.2e-77) || (!(t <= 290.0) && ((t <= 3.4e+42) || !(t <= 1.42e+86)))) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if ((t <= (-9.2d-77)) .or. (.not. (t <= 290.0d0)) .and. (t <= 3.4d+42) .or. (.not. (t <= 1.42d+86))) then
        tmp = -x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.2e-77) || (!(t <= 290.0) && ((t <= 3.4e+42) || !(t <= 1.42e+86)))) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.2e-77) or (not (t <= 290.0) and ((t <= 3.4e+42) or not (t <= 1.42e+86))):
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.2e-77) || (!(t <= 290.0) && ((t <= 3.4e+42) || !(t <= 1.42e+86))))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.2e-77) || (~((t <= 290.0)) && ((t <= 3.4e+42) || ~((t <= 1.42e+86)))))
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.2e-77], And[N[Not[LessEqual[t, 290.0]], $MachinePrecision], Or[LessEqual[t, 3.4e+42], N[Not[LessEqual[t, 1.42e+86]], $MachinePrecision]]]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

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

Alternative 6: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{\frac{x}{t}}{z}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ (/ x t) z))))
   (if (<= t -4.5e-76)
     t_1
     (if (<= t 3.5)
       (/ x y)
       (if (<= t 1.8e+42)
         (/ (- x) (* z t))
         (if (<= t 1.18e+86) (/ x y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -((x / t) / z);
	double tmp;
	if (t <= -4.5e-76) {
		tmp = t_1;
	} else if (t <= 3.5) {
		tmp = x / y;
	} else if (t <= 1.8e+42) {
		tmp = -x / (z * t);
	} else if (t <= 1.18e+86) {
		tmp = x / y;
	} 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 = -((x / t) / z)
    if (t <= (-4.5d-76)) then
        tmp = t_1
    else if (t <= 3.5d0) then
        tmp = x / y
    else if (t <= 1.8d+42) then
        tmp = -x / (z * t)
    else if (t <= 1.18d+86) then
        tmp = x / y
    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 = -((x / t) / z);
	double tmp;
	if (t <= -4.5e-76) {
		tmp = t_1;
	} else if (t <= 3.5) {
		tmp = x / y;
	} else if (t <= 1.8e+42) {
		tmp = -x / (z * t);
	} else if (t <= 1.18e+86) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -((x / t) / z)
	tmp = 0
	if t <= -4.5e-76:
		tmp = t_1
	elif t <= 3.5:
		tmp = x / y
	elif t <= 1.8e+42:
		tmp = -x / (z * t)
	elif t <= 1.18e+86:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(Float64(x / t) / z))
	tmp = 0.0
	if (t <= -4.5e-76)
		tmp = t_1;
	elseif (t <= 3.5)
		tmp = Float64(x / y);
	elseif (t <= 1.8e+42)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (t <= 1.18e+86)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -((x / t) / z);
	tmp = 0.0;
	if (t <= -4.5e-76)
		tmp = t_1;
	elseif (t <= 3.5)
		tmp = x / y;
	elseif (t <= 1.8e+42)
		tmp = -x / (z * t);
	elseif (t <= 1.18e+86)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision])}, If[LessEqual[t, -4.5e-76], t$95$1, If[LessEqual[t, 3.5], N[(x / y), $MachinePrecision], If[LessEqual[t, 1.8e+42], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+86], N[(x / y), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 7: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+181} \lor \neg \left(z \cdot t \leq 10^{+185}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -4e+181) (not (<= (* z t) 1e+185)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e+181) || !((z * t) <= 1e+185)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-4d+181)) .or. (.not. ((z * t) <= 1d+185))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e+181) || !((z * t) <= 1e+185)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -4e+181) or not ((z * t) <= 1e+185):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -4e+181) || !(Float64(z * t) <= 1e+185))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -4e+181) || ~(((z * t) <= 1e+185)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -4e+181], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+185]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

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

Alternative 8: 53.6% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 96.5% 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 2024008 
(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))))