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

Percentage Accurate: 95.7% → 97.8%

Time: 6.3s

Alternatives: 8

Speedup: 0.6×

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: 95.7% 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: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \end{array} \]

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) 2e+244) (/ x (fma z (- t) y)) (/ (- (/ x t)) z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 2e+244) {
		tmp = x / fma(z, -t, y);
	} else {
		tmp = -(x / t) / z;
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 2e+244)
		tmp = Float64(x / fma(z, Float64(-t), y));
	else
		tmp = Float64(Float64(-Float64(x / t)) / z);
	end
	return 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], 2e+244], N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision], N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 2.00000000000000015e244

   1. Initial program 98.6%

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

      1. cancel-sign-sub-inv 98.6%

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

      2. +-commutative 98.6%

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

      3. distribute-lft-neg-out 98.6%

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

      4. distribute-rgt-neg-out 98.6%

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

      5. fma-def 98.7%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(z, -t, y\right)}} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(z, -t, y\right)}} \]

   if 2.00000000000000015e244 < (*.f64 z t)

   1. Initial program 76.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \]

Alternative 2: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \end{array} \]

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) 2e+244) (/ 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) <= 2e+244) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -(x / t) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= 2d+244) then
        tmp = x / (y - (z * t))
    else
        tmp = -(x / t) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 2e+244) {
		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) <= 2e+244:
		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) <= 2e+244)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(-Float64(x / t)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= 2e+244)
		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], 2e+244], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 2.00000000000000015e244

   1. Initial program 98.6%

      \[\frac{x}{y - z \cdot t} \]

   if 2.00000000000000015e244 < (*.f64 z t)

   1. Initial program 76.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \]

Alternative 3: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 12500000\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= t -1.65e-103) (not (<= t 12500000.0))) (/ (- 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 ((t <= -1.65e-103) || !(t <= 12500000.0)) {
		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 ((t <= (-1.65d-103)) .or. (.not. (t <= 12500000.0d0))) 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 ((t <= -1.65e-103) || !(t <= 12500000.0)) {
		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 (t <= -1.65e-103) or not (t <= 12500000.0):
		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 ((t <= -1.65e-103) || !(t <= 12500000.0))
		tmp = Float64(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 ((t <= -1.65e-103) || ~((t <= 12500000.0)))
		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[t, -1.65e-103], N[Not[LessEqual[t, 12500000.0]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999995e-103 or 1.25e7 < t

   1. Initial program 94.3%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 71.3%

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

      1. associate-*r/ 71.3%

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

      2. neg-mul-1 71.3%

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

   4. Simplified 71.3%

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

   if -1.64999999999999995e-103 < t < 1.25e7

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 81.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 12500000\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 1800000\right):\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -1.65e-103) (not (<= t 1800000.0))) (/ (- (/ 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 <= -1.65e-103) || !(t <= 1800000.0)) {
		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 <= (-1.65d-103)) .or. (.not. (t <= 1800000.0d0))) 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 <= -1.65e-103) || !(t <= 1800000.0)) {
		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 <= -1.65e-103) or not (t <= 1800000.0):
		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 <= -1.65e-103) || !(t <= 1800000.0))
		tmp = Float64(Float64(-Float64(x / 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 <= -1.65e-103) || ~((t <= 1800000.0)))
		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, -1.65e-103], N[Not[LessEqual[t, 1800000.0]], $MachinePrecision]], N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999995e-103 or 1.8e6 < t

   1. Initial program 94.3%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/r* 74.8%

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

      3. distribute-neg-frac 74.8%

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

   4. Simplified 74.8%

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

   if -1.64999999999999995e-103 < t < 1.8e6

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 81.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 1800000\right):\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 5: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;t \leq 10200000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \end{array} \]

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 -1.4e-103)
   (/ (/ x z) (- t))
   (if (<= t 10200000.0) (/ 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 <= -1.4e-103) {
		tmp = (x / z) / -t;
	} else if (t <= 10200000.0) {
		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 <= (-1.4d-103)) then
        tmp = (x / z) / -t
    else if (t <= 10200000.0d0) 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 <= -1.4e-103) {
		tmp = (x / z) / -t;
	} else if (t <= 10200000.0) {
		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 <= -1.4e-103:
		tmp = (x / z) / -t
	elif t <= 10200000.0:
		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 <= -1.4e-103)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (t <= 10200000.0)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-Float64(x / t)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-103)
		tmp = (x / z) / -t;
	elseif (t <= 10200000.0)
		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, -1.4e-103], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[t, 10200000.0], N[(x / y), $MachinePrecision], N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000011e-103

   1. Initial program 94.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. associate-/r* 71.5%

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

      3. distribute-neg-frac 71.5%

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

   4. Simplified 71.5%

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

      1. distribute-neg-frac 71.5%

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

      2. associate-/r* 67.1%

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

      3. neg-mul-1 67.1%

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

      4. times-frac 69.4%

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

   6. Applied egg-rr 69.4%

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

      1. *-commutative 69.4%

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

      2. frac-2neg 69.4%

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

      3. metadata-eval 69.4%

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

      4. un-div-inv 69.4%

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

   8. Applied egg-rr 69.4%

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

   if -1.40000000000000011e-103 < t < 1.02e7

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 81.7%

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

   if 1.02e7 < t

   1. Initial program 93.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/r* 79.7%

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

      3. distribute-neg-frac 79.7%

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

   4. Simplified 79.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;t \leq 10200000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \]

Alternative 6: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+263} \lor \neg \left(z \leq 0.00043\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -1.6e+263) (not (<= z 0.00043))) (/ 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 <= -1.6e+263) || !(z <= 0.00043)) {
		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 <= (-1.6d+263)) .or. (.not. (z <= 0.00043d0))) 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 <= -1.6e+263) || !(z <= 0.00043)) {
		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 <= -1.6e+263) or not (z <= 0.00043):
		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 <= -1.6e+263) || !(z <= 0.00043))
		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 <= -1.6e+263) || ~((z <= 0.00043)))
		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, -1.6e+263], N[Not[LessEqual[z, 0.00043]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e263 or 4.29999999999999989e-4 < z

   1. Initial program 93.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. associate-/r* 83.7%

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

      3. distribute-neg-frac 83.7%

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

   4. Simplified 83.7%

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

      1. distribute-neg-frac 83.7%

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

      2. associate-/r* 77.5%

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

      3. expm1-log1p-u 73.1%

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

      4. expm1-udef 57.4%

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

      5. add-sqr-sqrt 27.1%

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

      6. sqrt-unprod 50.9%

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

      7. sqr-neg 50.9%

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

      8. sqrt-unprod 26.6%

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

      9. add-sqr-sqrt 53.8%

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

   6. Applied egg-rr 53.8%

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

      1. expm1-def 48.1%

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

      2. expm1-log1p 48.2%

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

   8. Simplified 48.2%

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

   if -1.6e263 < z < 4.29999999999999989e-4

   1. Initial program 97.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 63.3%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+263} \lor \neg \left(z \leq 0.00043\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 0.00066:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 -2.2e+213) (/ (/ x z) t) (if (<= z 0.00066) (/ 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 <= -2.2e+213) {
		tmp = (x / z) / t;
	} else if (z <= 0.00066) {
		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 <= (-2.2d+213)) then
        tmp = (x / z) / t
    else if (z <= 0.00066d0) 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 <= -2.2e+213) {
		tmp = (x / z) / t;
	} else if (z <= 0.00066) {
		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 <= -2.2e+213:
		tmp = (x / z) / t
	elif z <= 0.00066:
		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 <= -2.2e+213)
		tmp = Float64(Float64(x / z) / t);
	elseif (z <= 0.00066)
		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 <= -2.2e+213)
		tmp = (x / z) / t;
	elseif (z <= 0.00066)
		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, -2.2e+213], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 0.00066], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1999999999999999e213

   1. Initial program 87.5%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/r* 93.7%

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

      3. distribute-neg-frac 93.7%

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

   4. Simplified 93.7%

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

      1. distribute-neg-frac 93.7%

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

      2. associate-/r* 81.4%

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

      3. neg-mul-1 81.4%

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

      4. times-frac 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. associate-*l/ 96.8%

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

      2. associate-*r/ 96.8%

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

      3. neg-mul-1 96.8%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 63.0%

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

      6. sqr-neg 63.0%

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

      7. sqrt-unprod 62.3%

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

      8. add-sqr-sqrt 62.3%

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

      9. frac-2neg 62.3%

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

   8. Applied egg-rr 62.3%

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

   if -2.1999999999999999e213 < z < 6.6e-4

   1. Initial program 98.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 64.6%

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

   if 6.6e-4 < z

   1. Initial program 94.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/r* 77.6%

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

      3. distribute-neg-frac 77.6%

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

   4. Simplified 77.6%

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

      1. distribute-neg-frac 77.6%

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

      2. associate-/r* 72.3%

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

      3. expm1-log1p-u 66.2%

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

      4. expm1-udef 53.1%

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

      5. add-sqr-sqrt 24.4%

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

      6. sqrt-unprod 46.0%

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

      7. sqr-neg 46.0%

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

      8. sqrt-unprod 23.6%

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

      9. add-sqr-sqrt 48.1%

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

   6. Applied egg-rr 48.1%

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

      1. expm1-def 40.4%

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

      2. expm1-log1p 40.5%

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

   8. Simplified 40.5%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 0.00066:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8: 54.1% 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 96.5%

   \[\frac{x}{y - z \cdot t} \]

2. Taylor expanded in y around inf 53.8%

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

3. Final simplification 53.8%

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

Developer target: 96.3% 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 2023322 
(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))))