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

Percentage Accurate: 95.6% → 99.7%

Time: 9.5s

Alternatives: 8

Speedup: 0.3×

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: 95.6% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+238}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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) (- INFINITY))
   (/ -1.0 (* t (/ z x)))
   (if (<= (* z t) 2e+238) (/ x (- y (* z t))) (/ (/ 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) <= -((double) INFINITY)) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 2e+238) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / t) / -z;
	}
	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 = -1.0 / (t * (z / x));
	} else if ((z * t) <= 2e+238) {
		tmp = x / (y - (z * t));
	} 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) <= -math.inf:
		tmp = -1.0 / (t * (z / x))
	elif (z * t) <= 2e+238:
		tmp = x / (y - (z * t))
	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) <= Float64(-Inf))
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (Float64(z * t) <= 2e+238)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / t) / Float64(-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) <= -Inf)
		tmp = -1.0 / (t * (z / x));
	elseif ((z * t) <= 2e+238)
		tmp = x / (y - (z * t));
	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], (-Infinity)], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+238], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 56.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 84.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

   4. Taylor expanded in z around inf 99.5%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{x}{z}}}{t} \]
   5. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto -1 \cdot \color{blue}{\frac{1}{\frac{t}{\frac{x}{z}}}} \]

      2. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{-1}{\frac{t}{\frac{x}{z}}}} \]

      3. div-inv 99.8%

         \[\leadsto \frac{-1}{\color{blue}{t \cdot \frac{1}{\frac{x}{z}}}} \]

      4. clear-num 99.9%

         \[\leadsto \frac{-1}{t \cdot \color{blue}{\frac{z}{x}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{-1}{t \cdot \frac{z}{x}}} \]

   if -inf.0 < (*.f64 z t) < 2.0000000000000001e238

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   if 2.0000000000000001e238 < (*.f64 z t)

   1. Initial program 65.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 65.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}} \]

      2. associate-/r/ 65.0%

         \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   4. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   5. Taylor expanded in y around 0 65.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 65.0%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 99.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-24} \lor \neg \left(t \leq 3.1 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= t -5.8e-24) (not (<= t 3.1e+60))) (/ (/ x t) (- z)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e-24) || !(t <= 3.1e+60)) {
		tmp = (x / t) / -z;
	} 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 ((t <= (-5.8d-24)) .or. (.not. (t <= 3.1d+60))) then
        tmp = (x / t) / -z
    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 ((t <= -5.8e-24) || !(t <= 3.1e+60)) {
		tmp = (x / t) / -z;
	} 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 (t <= -5.8e-24) or not (t <= 3.1e+60):
		tmp = (x / t) / -z
	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 ((t <= -5.8e-24) || !(t <= 3.1e+60))
		tmp = Float64(Float64(x / t) / Float64(-z));
	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 ((t <= -5.8e-24) || ~((t <= 3.1e+60)))
		tmp = (x / t) / -z;
	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[t, -5.8e-24], N[Not[LessEqual[t, 3.1e+60]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7999999999999997e-24 or 3.1000000000000001e60 < t

   1. Initial program 87.1%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 85.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}} \]

      2. associate-/r/ 87.0%

         \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   4. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   5. Taylor expanded in y around 0 59.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 72.0%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 72.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   if -5.7999999999999997e-24 < t < 3.1000000000000001e60

   1. Initial program 99.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.3%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-24} \lor \neg \left(t \leq 3.1 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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 -1e+64)
   (/ -1.0 (* t (/ z x)))
   (if (<= z 1.06e-128) (/ 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 <= -1e+64) {
		tmp = -1.0 / (t * (z / x));
	} else if (z <= 1.06e-128) {
		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 <= (-1d+64)) then
        tmp = (-1.0d0) / (t * (z / x))
    else if (z <= 1.06d-128) 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 <= -1e+64) {
		tmp = -1.0 / (t * (z / x));
	} else if (z <= 1.06e-128) {
		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 <= -1e+64:
		tmp = -1.0 / (t * (z / x))
	elif z <= 1.06e-128:
		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 (z <= -1e+64)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (z <= 1.06e-128)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / t) / Float64(-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 <= -1e+64)
		tmp = -1.0 / (t * (z / x));
	elseif (z <= 1.06e-128)
		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[z, -1e+64], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-128], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000002e64

   1. Initial program 87.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

   4. Taylor expanded in z around inf 74.4%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{x}{z}}}{t} \]
   5. Step-by-step derivation

      1. clear-num 74.5%

         \[\leadsto -1 \cdot \color{blue}{\frac{1}{\frac{t}{\frac{x}{z}}}} \]

      2. un-div-inv 74.5%

         \[\leadsto \color{blue}{\frac{-1}{\frac{t}{\frac{x}{z}}}} \]

      3. div-inv 76.1%

         \[\leadsto \frac{-1}{\color{blue}{t \cdot \frac{1}{\frac{x}{z}}}} \]

      4. clear-num 76.2%

         \[\leadsto \frac{-1}{t \cdot \color{blue}{\frac{z}{x}}} \]

   6. Applied egg-rr 76.2%

      \[\leadsto \color{blue}{\frac{-1}{t \cdot \frac{z}{x}}} \]

   if -1.00000000000000002e64 < z < 1.05999999999999995e-128

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.2%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 1.05999999999999995e-128 < z

   1. Initial program 91.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 90.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}} \]

      2. associate-/r/ 91.3%

         \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   4. Applied egg-rr 91.3%

      \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   5. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.0%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 64.5%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 64.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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 -1e+64)
   (/ (/ x (- z)) t)
   (if (<= z 1.06e-128) (/ 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 <= -1e+64) {
		tmp = (x / -z) / t;
	} else if (z <= 1.06e-128) {
		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 <= (-1d+64)) then
        tmp = (x / -z) / t
    else if (z <= 1.06d-128) 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 <= -1e+64) {
		tmp = (x / -z) / t;
	} else if (z <= 1.06e-128) {
		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 <= -1e+64:
		tmp = (x / -z) / t
	elif z <= 1.06e-128:
		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 (z <= -1e+64)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= 1.06e-128)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / t) / Float64(-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 <= -1e+64)
		tmp = (x / -z) / t;
	elseif (z <= 1.06e-128)
		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[z, -1e+64], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.06e-128], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000002e64

   1. Initial program 87.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

   4. Taylor expanded in z around inf 74.4%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{x}{z}}}{t} \]
   5. Step-by-step derivation

      1. mul-1-neg 74.4%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{t}} \]

      2. distribute-neg-frac2 74.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{-t}} \]

   6. Applied egg-rr 74.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{-t}} \]

   if -1.00000000000000002e64 < z < 1.05999999999999995e-128

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.2%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 1.05999999999999995e-128 < z

   1. Initial program 91.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 90.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}} \]

      2. associate-/r/ 91.3%

         \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   4. Applied egg-rr 91.3%

      \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   5. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.0%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 64.5%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac2 64.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]

   7. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{-z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= y -4e+38)
   (/ 1.0 (/ y x))
   (if (<= y 3.5e-57) (/ x (* t (- z))) (/ x y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+38) {
		tmp = 1.0 / (y / x);
	} else if (y <= 3.5e-57) {
		tmp = x / (t * -z);
	} 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 (y <= (-4d+38)) then
        tmp = 1.0d0 / (y / x)
    else if (y <= 3.5d-57) then
        tmp = x / (t * -z)
    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 (y <= -4e+38) {
		tmp = 1.0 / (y / x);
	} else if (y <= 3.5e-57) {
		tmp = x / (t * -z);
	} 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 y <= -4e+38:
		tmp = 1.0 / (y / x)
	elif y <= 3.5e-57:
		tmp = x / (t * -z)
	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 (y <= -4e+38)
		tmp = Float64(1.0 / Float64(y / x));
	elseif (y <= 3.5e-57)
		tmp = Float64(x / Float64(t * Float64(-z)));
	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 (y <= -4e+38)
		tmp = 1.0 / (y / x);
	elseif (y <= 3.5e-57)
		tmp = x / (t * -z);
	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[LessEqual[y, -4e+38], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-57], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999991e38

   1. Initial program 95.6%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.4%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. clear-num 85.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. inv-pow 85.6%

         \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]

   5. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 85.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

   if -3.99999999999999991e38 < y < 3.49999999999999991e-57

   1. Initial program 93.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 71.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 71.6%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   5. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]

   if 3.49999999999999991e-57 < y

   1. Initial program 94.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.7%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

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 (<= t 1.9e+172) (/ 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 (t <= 1.9e+172) {
		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 (t <= 1.9d+172) 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 (t <= 1.9e+172) {
		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 t <= 1.9e+172:
		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 (t <= 1.9e+172)
		tmp = Float64(x / y);
	else
		tmp = 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 (t <= 1.9e+172)
		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[t, 1.9e+172], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.89999999999999985e172

   1. Initial program 94.8%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.3%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 1.89999999999999985e172 < t

   1. Initial program 86.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

   4. Taylor expanded in z around inf 77.0%

      \[\leadsto -1 \cdot \frac{\color{blue}{\frac{x}{z}}}{t} \]
   5. Step-by-step derivation

      1. associate-/l/ 68.0%

         \[\leadsto -1 \cdot \color{blue}{\frac{x}{t \cdot z}} \]

      2. associate-*r/ 68.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      3. neg-mul-1 68.0%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      4. add-sqr-sqrt 33.6%

         \[\leadsto \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      5. sqrt-unprod 58.6%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t \cdot z} \]

      6. sqr-neg 58.6%

         \[\leadsto \frac{\sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      7. sqrt-unprod 29.3%

         \[\leadsto \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      8. add-sqr-sqrt 49.3%

         \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]

      9. associate-/r* 49.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]

   6. Applied egg-rr 49.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 5e-45) (/ x y) (/ x (* z t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5e-45) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	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 <= 5d-45) then
        tmp = x / y
    else
        tmp = x / (z * t)
    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 <= 5e-45) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 5e-45:
		tmp = x / y
	else:
		tmp = x / (z * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5e-45)
		tmp = Float64(x / y);
	else
		tmp = Float64(x / Float64(z * 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 <= 5e-45)
		tmp = x / y;
	else
		tmp = x / (z * 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[z, 5e-45], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999976e-45

   1. Initial program 96.1%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 4.99999999999999976e-45 < z

   1. Initial program 89.7%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 63.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 63.5%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. neg-sub0 63.5%

         \[\leadsto \frac{\color{blue}{0 - x}}{t \cdot z} \]

      2. sub-neg 63.5%

         \[\leadsto \frac{\color{blue}{0 + \left(-x\right)}}{t \cdot z} \]

      3. add-sqr-sqrt 29.6%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      4. sqrt-unprod 46.8%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t \cdot z} \]

      5. sqr-neg 46.8%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      6. sqrt-unprod 16.4%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      7. add-sqr-sqrt 27.6%

         \[\leadsto \frac{0 + \color{blue}{x}}{t \cdot z} \]

   7. Applied egg-rr 27.6%

      \[\leadsto \frac{\color{blue}{0 + x}}{t \cdot z} \]
   8. Step-by-step derivation

      1. +-lft-identity 27.6%

         \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]

   9. Simplified 27.6%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.4% 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

1. Initial program 94.1%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 56.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Add Preprocessing

Developer Target 1: 96.4% accurate, 0.3× 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 2024144 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

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