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

Percentage Accurate: 96.1% → 99.7%

Time: 6.7s

Alternatives: 7

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: 96.1% 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

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 10^{+228}\right):\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (or (<= (* z t) (- INFINITY)) (not (<= (* z t) 1e+228)))
   (/ (/ x (- t)) z)
   (/ x (- y (* z 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)) || !((z * t) <= 1e+228)) {
		tmp = (x / -t) / z;
	} else {
		tmp = x / (y - (z * 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) || !((z * t) <= 1e+228)) {
		tmp = (x / -t) / z;
	} else {
		tmp = x / (y - (z * 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) or not ((z * t) <= 1e+228):
		tmp = (x / -t) / z
	else:
		tmp = x / (y - (z * 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)) || !(Float64(z * t) <= 1e+228))
		tmp = Float64(Float64(x / Float64(-t)) / z);
	else
		tmp = Float64(x / Float64(y - 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 * t) <= -Inf) || ~(((z * t) <= 1e+228)))
		tmp = (x / -t) / z;
	else
		tmp = x / (y - (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[Or[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+228]], $MachinePrecision]], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -inf.0 or 9.9999999999999992e227 < (*.f64 z t)

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. neg-mul-1 76.5%

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

   5. Simplified 76.5%

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

      1. neg-mul-1 76.5%

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

      2. times-frac 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.9%

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

      2. frac-2neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*l/ 99.9%

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

      5. *-un-lft-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 9.9999999999999992e227

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 10^{+228}\right):\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-9} \lor \neg \left(y \leq 230000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

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 (or (<= y -1.05e-9) (not (<= y 230000.0))) (/ 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 ((y <= -1.05e-9) || !(y <= 230000.0)) {
		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 ((y <= (-1.05d-9)) .or. (.not. (y <= 230000.0d0))) 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 ((y <= -1.05e-9) || !(y <= 230000.0)) {
		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 (y <= -1.05e-9) or not (y <= 230000.0):
		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 ((y <= -1.05e-9) || !(y <= 230000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(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 ((y <= -1.05e-9) || ~((y <= 230000.0)))
		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[Or[LessEqual[y, -1.05e-9], N[Not[LessEqual[y, 230000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e-9 or 2.3e5 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 73.2%

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

   if -1.0500000000000001e-9 < y < 2.3e5

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   5. Simplified 77.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-9} \lor \neg \left(y \leq 230000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-84} \lor \neg \left(t \leq 1.18 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -2.6e-84) (not (<= t 1.18e+106))) (/ (/ 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 <= -2.6e-84) || !(t <= 1.18e+106)) {
		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 <= (-2.6d-84)) .or. (.not. (t <= 1.18d+106))) 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 <= -2.6e-84) || !(t <= 1.18e+106)) {
		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 <= -2.6e-84) or not (t <= 1.18e+106):
		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 <= -2.6e-84) || !(t <= 1.18e+106))
		tmp = Float64(Float64(x / Float64(-t)) / 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 <= -2.6e-84) || ~((t <= 1.18e+106)))
		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, -2.6e-84], N[Not[LessEqual[t, 1.18e+106]], $MachinePrecision]], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e-84 or 1.17999999999999993e106 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. associate-*r/ 74.3%

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

      2. neg-mul-1 74.3%

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

   5. Simplified 74.3%

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

      1. neg-mul-1 74.3%

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

      2. times-frac 77.0%

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

   7. Applied egg-rr 77.0%

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

      1. associate-*r/ 80.4%

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

      2. frac-2neg 80.4%

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

      3. metadata-eval 80.4%

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

      4. associate-*l/ 80.5%

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

      5. *-un-lft-identity 80.5%

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

   9. Applied egg-rr 80.5%

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

   if -2.6e-84 < t < 1.17999999999999993e106

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-84} \lor \neg \left(t \leq 1.18 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

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 -6.9e-93)
   (/ (/ (- x) z) t)
   (if (<= t 3.5e+106) (/ 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 <= -6.9e-93) {
		tmp = (-x / z) / t;
	} else if (t <= 3.5e+106) {
		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 <= (-6.9d-93)) then
        tmp = (-x / z) / t
    else if (t <= 3.5d+106) 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 <= -6.9e-93) {
		tmp = (-x / z) / t;
	} else if (t <= 3.5e+106) {
		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 <= -6.9e-93:
		tmp = (-x / z) / t
	elif t <= 3.5e+106:
		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 <= -6.9e-93)
		tmp = Float64(Float64(Float64(-x) / z) / t);
	elseif (t <= 3.5e+106)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-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 <= -6.9e-93)
		tmp = (-x / z) / t;
	elseif (t <= 3.5e+106)
		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, -6.9e-93], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.5e+106], N[(x / y), $MachinePrecision], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.90000000000000031e-93

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. neg-mul-1 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-/r* 75.3%

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

   5. Simplified 75.3%

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

   if -6.90000000000000031e-93 < t < 3.49999999999999981e106

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.6%

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

   if 3.49999999999999981e106 < t

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0 73.3%

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

      1. associate-*r/ 73.3%

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

      2. neg-mul-1 73.3%

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

   5. Simplified 73.3%

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

      1. neg-mul-1 73.3%

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

      2. times-frac 78.5%

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

   7. Applied egg-rr 78.5%

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

      1. associate-*r/ 80.2%

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

      2. frac-2neg 80.2%

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

      3. metadata-eval 80.2%

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

      4. associate-*l/ 80.4%

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

      5. *-un-lft-identity 80.4%

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

   9. Applied egg-rr 80.4%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+158} \lor \neg \left(z \leq 4.3 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -5.6e+158) (not (<= z 4.3e-59))) (/ 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 <= -5.6e+158) || !(z <= 4.3e-59)) {
		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 <= (-5.6d+158)) .or. (.not. (z <= 4.3d-59))) 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 <= -5.6e+158) || !(z <= 4.3e-59)) {
		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 <= -5.6e+158) or not (z <= 4.3e-59):
		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 ((z <= -5.6e+158) || !(z <= 4.3e-59))
		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 <= -5.6e+158) || ~((z <= 4.3e-59)))
		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[z, -5.6e+158], N[Not[LessEqual[z, 4.3e-59]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.60000000000000003e158 or 4.3000000000000003e-59 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. neg-mul-1 73.9%

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

   5. Simplified 73.9%

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

      1. associate-/l/ 76.2%

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

      2. expm1-log1p-u 72.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      3. expm1-udef 55.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      4. associate-/r* 55.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      5. add-sqr-sqrt 24.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      6. sqrt-unprod 48.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      7. sqr-neg 48.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      8. sqrt-unprod 28.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      9. add-sqr-sqrt 48.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   7. Applied egg-rr 48.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 45.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 45.4%

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

      3. associate-/r* 46.3%

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

   9. Simplified 46.3%

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

   10. Taylor expanded in x around 0 45.4%

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

   if -5.60000000000000003e158 < z < 4.3000000000000003e-59

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 60.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+158} \lor \neg \left(z \leq 4.3 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 -6.2e+159) (/ (/ x z) t) (if (<= z 4.3e-59) (/ 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 <= -6.2e+159) {
		tmp = (x / z) / t;
	} else if (z <= 4.3e-59) {
		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 <= (-6.2d+159)) then
        tmp = (x / z) / t
    else if (z <= 4.3d-59) 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 <= -6.2e+159) {
		tmp = (x / z) / t;
	} else if (z <= 4.3e-59) {
		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 <= -6.2e+159:
		tmp = (x / z) / t
	elif z <= 4.3e-59:
		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 <= -6.2e+159)
		tmp = Float64(Float64(x / z) / t);
	elseif (z <= 4.3e-59)
		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 <= -6.2e+159)
		tmp = (x / z) / t;
	elseif (z <= 4.3e-59)
		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, -6.2e+159], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.3e-59], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999996e159

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

      1. associate-/l/ 72.4%

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

      2. expm1-log1p-u 68.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      3. expm1-udef 49.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      4. associate-/r* 49.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      5. add-sqr-sqrt 19.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      6. sqrt-unprod 44.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      7. sqr-neg 44.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      8. sqrt-unprod 28.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      9. add-sqr-sqrt 45.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   7. Applied egg-rr 45.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 44.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 44.4%

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

      3. associate-/r* 44.7%

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

   9. Simplified 44.7%

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

   if -6.1999999999999996e159 < z < 4.3000000000000003e-59

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 60.2%

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

   if 4.3000000000000003e-59 < z

   1. Initial program 91.6%

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

   3. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

   5. Simplified 70.6%

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

      1. associate-/l/ 77.8%

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

      2. expm1-log1p-u 74.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)\right)} \]

      3. expm1-udef 57.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{t}\right)} - 1} \]

      4. associate-/r* 57.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot t}}\right)} - 1 \]

      5. add-sqr-sqrt 26.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      6. sqrt-unprod 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      7. sqr-neg 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      8. sqrt-unprod 28.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      9. add-sqr-sqrt 49.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   7. Applied egg-rr 49.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 45.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 45.9%

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

      3. associate-/r* 46.9%

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

   9. Simplified 46.9%

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

   10. Taylor expanded in x around 0 45.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.4% 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 94.7%

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

3. Taylor expanded in y around inf 45.7%

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

4. Final simplification 45.7%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 96.5% 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 2024021 
(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))))