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

Percentage Accurate: 95.8% → 99.2%

Time: 7.9s

Alternatives: 6

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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 10^{+187}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

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 (* z (/ t x)))
   (if (<= (* z t) 1e+187) (/ 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 / (z * (t / x));
	} else if ((z * t) <= 1e+187) {
		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 / (z * (t / x));
	} else if ((z * t) <= 1e+187) {
		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 / (z * (t / x))
	elif (z * t) <= 1e+187:
		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(z * Float64(t / x)));
	elseif (Float64(z * t) <= 1e+187)
		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 / (z * (t / x));
	elseif ((z * t) <= 1e+187)
		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[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+187], 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 60.9%

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

      1. clear-num 60.9%

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

      2. associate-/r/ 60.9%

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

   4. Applied egg-rr 60.9%

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

   5. Taylor expanded in y around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-/r* 99.6%

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

      3. distribute-neg-frac2 99.6%

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

   7. Simplified 99.6%

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

      1. associate-/l/ 60.9%

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

      2. *-un-lft-identity 60.9%

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

      3. times-frac 99.8%

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

      4. add-sqr-sqrt 63.0%

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

      5. sqrt-unprod 70.1%

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

      6. sqr-neg 70.1%

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

      7. sqrt-prod 16.7%

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

      8. add-sqr-sqrt 60.3%

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

      9. frac-2neg 60.3%

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

      10. metadata-eval 60.3%

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

      11. add-sqr-sqrt 43.6%

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

      12. sqrt-unprod 70.4%

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

      13. sqr-neg 70.4%

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

      14. sqrt-prod 36.5%

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

      15. add-sqr-sqrt 99.8%

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

      16. times-frac 60.9%

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

      17. *-commutative 60.9%

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

      18. times-frac 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. *-commutative 99.7%

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

       2. clear-num 99.5%

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

       3. frac-times 99.7%

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

       4. metadata-eval 99.7%

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

       5. associate-/r/ 99.5%

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

       6. div-inv 99.5%

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

       7. clear-num 99.6%

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

   11. Applied egg-rr 99.6%

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

   if -inf.0 < (*.f64 z t) < 9.99999999999999907e186

   1. Initial program 99.9%

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

   if 9.99999999999999907e186 < (*.f64 z t)

   1. Initial program 77.0%

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

      1. clear-num 77.0%

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

      2. associate-/r/ 77.1%

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

   4. Applied egg-rr 77.1%

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

   5. Taylor expanded in y around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      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. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 10^{+187}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

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 -1.8e-15)
   (/ (/ x t) (- z))
   (if (<= t 1.2e+113) (/ x y) (/ -1.0 (* z (/ t x))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-15) {
		tmp = (x / t) / -z;
	} else if (t <= 1.2e+113) {
		tmp = x / y;
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	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 <= (-1.8d-15)) then
        tmp = (x / t) / -z
    else if (t <= 1.2d+113) then
        tmp = x / y
    else
        tmp = (-1.0d0) / (z * (t / x))
    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 <= -1.8e-15) {
		tmp = (x / t) / -z;
	} else if (t <= 1.2e+113) {
		tmp = x / y;
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-15:
		tmp = (x / t) / -z
	elif t <= 1.2e+113:
		tmp = x / y
	else:
		tmp = -1.0 / (z * (t / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-15)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (t <= 1.2e+113)
		tmp = Float64(x / y);
	else
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	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 <= -1.8e-15)
		tmp = (x / t) / -z;
	elseif (t <= 1.2e+113)
		tmp = x / y;
	else
		tmp = -1.0 / (z * (t / x));
	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, -1.8e-15], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[t, 1.2e+113], N[(x / y), $MachinePrecision], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e-15

   1. Initial program 89.6%

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

      1. clear-num 89.6%

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

      2. associate-/r/ 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in y around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-/r* 68.2%

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

      3. distribute-neg-frac2 68.2%

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

   7. Simplified 68.2%

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

   if -1.8000000000000001e-15 < t < 1.19999999999999992e113

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 69.8%

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

   if 1.19999999999999992e113 < t

   1. Initial program 86.3%

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

      1. clear-num 86.2%

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

      2. associate-/r/ 86.3%

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

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/r* 80.5%

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

      3. distribute-neg-frac2 80.5%

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

   7. Simplified 80.5%

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

      1. associate-/l/ 69.9%

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

      2. *-un-lft-identity 69.9%

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

      3. times-frac 80.5%

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

      4. add-sqr-sqrt 46.9%

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

      5. sqrt-unprod 50.4%

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

      6. sqr-neg 50.4%

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

      7. sqrt-prod 11.4%

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

      8. add-sqr-sqrt 33.8%

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

      9. frac-2neg 33.8%

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

      10. metadata-eval 33.8%

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

      11. add-sqr-sqrt 22.4%

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

      12. sqrt-unprod 45.8%

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

      13. sqr-neg 45.8%

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

      14. sqrt-prod 33.4%

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

      15. add-sqr-sqrt 80.5%

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

      16. times-frac 69.9%

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

      17. *-commutative 69.9%

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

      18. times-frac 73.4%

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

   9. Applied egg-rr 73.4%

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

       1. *-commutative 73.4%

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

       2. clear-num 73.3%

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

       3. frac-times 75.1%

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

       4. metadata-eval 75.1%

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

       5. associate-/r/ 80.4%

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

       6. div-inv 80.5%

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

       7. clear-num 80.3%

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

   11. Applied egg-rr 80.3%

       \[\leadsto \color{blue}{\frac{-1}{z \cdot \frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-15} \lor \neg \left(t \leq 1.1 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -3.3e-15) (not (<= t 1.1e+113))) (/ (/ 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 <= -3.3e-15) || !(t <= 1.1e+113)) {
		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 <= (-3.3d-15)) .or. (.not. (t <= 1.1d+113))) 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 <= -3.3e-15) || !(t <= 1.1e+113)) {
		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 <= -3.3e-15) or not (t <= 1.1e+113):
		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 <= -3.3e-15) || !(t <= 1.1e+113))
		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 <= -3.3e-15) || ~((t <= 1.1e+113)))
		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, -3.3e-15], N[Not[LessEqual[t, 1.1e+113]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e-15 or 1.10000000000000005e113 < t

   1. Initial program 88.2%

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

      1. clear-num 88.1%

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

      2. associate-/r/ 88.1%

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-/r* 73.5%

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

      3. distribute-neg-frac2 73.5%

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

   7. Simplified 73.5%

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

   if -3.3e-15 < t < 1.10000000000000005e113

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 69.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-15} \lor \neg \left(t \leq 1.1 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 -9.5e-28)
   (/ 1.0 (/ y x))
   (if (<= y 9e-23) (/ 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 <= -9.5e-28) {
		tmp = 1.0 / (y / x);
	} else if (y <= 9e-23) {
		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 <= (-9.5d-28)) then
        tmp = 1.0d0 / (y / x)
    else if (y <= 9d-23) 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 <= -9.5e-28) {
		tmp = 1.0 / (y / x);
	} else if (y <= 9e-23) {
		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 <= -9.5e-28:
		tmp = 1.0 / (y / x)
	elif y <= 9e-23:
		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 <= -9.5e-28)
		tmp = Float64(1.0 / Float64(y / x));
	elseif (y <= 9e-23)
		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 <= -9.5e-28)
		tmp = 1.0 / (y / x);
	elseif (y <= 9e-23)
		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, -9.5e-28], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-23], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000001e-28

   1. Initial program 93.2%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. associate-*l/ 74.4%

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

      2. *-un-lft-identity 74.4%

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

      3. clear-num 74.4%

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

   7. Applied egg-rr 74.4%

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

   if -9.50000000000000001e-28 < y < 8.9999999999999995e-23

   1. Initial program 95.0%

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

   3. Taylor expanded in y around 0 75.2%

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

      1. associate-*r/ 75.2%

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

      2. neg-mul-1 75.2%

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

   5. Simplified 75.2%

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

   if 8.9999999999999995e-23 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 80.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (<= z -1.4e+187) (/ 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 <= -1.4e+187) {
		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 <= (-1.4d+187)) 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 <= -1.4e+187) {
		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 <= -1.4e+187:
		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 <= -1.4e+187)
		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 <= -1.4e+187)
		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[LessEqual[z, -1.4e+187], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999995e187

   1. Initial program 86.5%

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

      1. clear-num 86.4%

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

      2. associate-/r/ 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in y around 0 72.9%

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

      1. associate-*l/ 72.9%

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

      2. *-commutative 72.9%

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

      3. times-frac 86.1%

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

      4. metadata-eval 86.1%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-prod 54.7%

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

      7. sqr-neg 54.7%

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

      8. sqrt-unprod 54.3%

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

      9. add-sqr-sqrt 54.3%

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

      10. frac-2neg 54.3%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-prod 54.7%

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

      13. sqr-neg 54.7%

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

      14. sqrt-unprod 86.1%

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

      15. add-sqr-sqrt 86.1%

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

      16. times-frac 72.9%

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

      17. *-un-lft-identity 72.9%

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

      18. associate-/l/ 86.1%

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

      19. add-sqr-sqrt 86.1%

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

      20. sqrt-unprod 54.7%

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

      21. sqr-neg 54.7%

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

      22. sqrt-prod 0.0%

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

      23. add-sqr-sqrt 54.3%

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

   7. Applied egg-rr 54.3%

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

   8. Taylor expanded in x around 0 54.9%

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

   if -1.39999999999999995e187 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 58.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 94.4%

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

3. Taylor expanded in y around inf 55.1%

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

4. Final simplification 55.1%

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

Developer target: 96.6% 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 2024076 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))