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

Percentage Accurate: 95.9% → 99.0%

Time: 10.0s

Alternatives: 7

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{0 - z}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 10^{+158}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) (- 0.0 z))))
   (if (<= (* z t) -1e+301)
     t_1
     (if (<= (* z t) 1e+158) (/ x (- y (* z t))) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (0.0 - z);
	double tmp;
	if ((z * t) <= -1e+301) {
		tmp = t_1;
	} else if ((z * t) <= 1e+158) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / (0.0d0 - z)
    if ((z * t) <= (-1d+301)) then
        tmp = t_1
    else if ((z * t) <= 1d+158) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    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 t_1 = (x / t) / (0.0 - z);
	double tmp;
	if ((z * t) <= -1e+301) {
		tmp = t_1;
	} else if ((z * t) <= 1e+158) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / (0.0 - z)
	tmp = 0
	if (z * t) <= -1e+301:
		tmp = t_1
	elif (z * t) <= 1e+158:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(0.0 - z))
	tmp = 0.0
	if (Float64(z * t) <= -1e+301)
		tmp = t_1;
	elseif (Float64(z * t) <= 1e+158)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / (0.0 - z);
	tmp = 0.0;
	if ((z * t) <= -1e+301)
		tmp = t_1;
	elseif ((z * t) <= 1e+158)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / N[(0.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+301], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1e+158], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000005e301 or 9.99999999999999953e157 < (*.f64 z t)

   1. Initial program 83.5%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y + z \cdot t}{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{y + z \cdot t}}\right), x\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y - z \cdot t}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(y - z \cdot t\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), x\right) \]

      10. *-lowering-*.f64 83.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), x\right) \]

   4. Applied egg-rr 83.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{t \cdot z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(t \cdot z\right)\right), x\right) \]

      2. *-lowering-*.f64 83.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(t, z\right)\right), x\right) \]

   7. Simplified 83.6%

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

      1. associate-*l/ N/A

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

      2. neg-mul-1 N/A

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

      3. associate-/r* N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(x\right)}{t}\right), \color{blue}{z}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(0 - x\right), t\right), z\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, x\right), t\right), z\right) \]

   9. Applied egg-rr 99.8%

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

       1. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

       2. neg-lowering-neg.f64 99.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{neg.f64}\left(x\right), t\right), z\right) \]

   11. Applied egg-rr 99.8%

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

   if -1.00000000000000005e301 < (*.f64 z t) < 9.99999999999999953e157

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \mathbf{elif}\;z \cdot t \leq 10^{+158}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-86}:\\ \;\;\;\;\frac{0 - \frac{x}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \end{array} \end{array} \]

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) -1e-86)
   (/ (- 0.0 (/ x z)) t)
   (if (<= (* z t) 2e-12) (/ x y) (/ (/ x t) (- 0.0 z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e-86) {
		tmp = (0.0 - (x / z)) / t;
	} else if ((z * t) <= 2e-12) {
		tmp = x / y;
	} else {
		tmp = (x / t) / (0.0 - 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) <= (-1d-86)) then
        tmp = (0.0d0 - (x / z)) / t
    else if ((z * t) <= 2d-12) then
        tmp = x / y
    else
        tmp = (x / t) / (0.0d0 - 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) <= -1e-86) {
		tmp = (0.0 - (x / z)) / t;
	} else if ((z * t) <= 2e-12) {
		tmp = x / y;
	} else {
		tmp = (x / t) / (0.0 - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e-86:
		tmp = (0.0 - (x / z)) / t
	elif (z * t) <= 2e-12:
		tmp = x / y
	else:
		tmp = (x / t) / (0.0 - 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) <= -1e-86)
		tmp = Float64(Float64(0.0 - Float64(x / z)) / t);
	elseif (Float64(z * t) <= 2e-12)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / t) / Float64(0.0 - 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) <= -1e-86)
		tmp = (0.0 - (x / z)) / t;
	elseif ((z * t) <= 2e-12)
		tmp = x / y;
	else
		tmp = (x / t) / (0.0 - 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], -1e-86], N[(N[(0.0 - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-12], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(0.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000008e-86

   1. Initial program 94.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y + z \cdot t}{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{y + z \cdot t}}\right), x\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y - z \cdot t}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(y - z \cdot t\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), x\right) \]

      10. *-lowering-*.f64 94.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), x\right) \]

   4. Applied egg-rr 94.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{t \cdot z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(t \cdot z\right)\right), x\right) \]

      2. *-lowering-*.f64 72.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(t, z\right)\right), x\right) \]

   7. Simplified 72.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. neg-mul-1 N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(x\right)}{z}\right), \color{blue}{t}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), z\right), t\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(0 - x\right), z\right), t\right) \]

      8. --lowering--.f64 74.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, x\right), z\right), t\right) \]

   9. Applied egg-rr 74.4%

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

       1. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), z\right), t\right) \]

       2. neg-lowering-neg.f64 74.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{neg.f64}\left(x\right), z\right), t\right) \]

   11. Applied egg-rr 74.4%

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

   if -1.00000000000000008e-86 < (*.f64 z t) < 1.99999999999999996e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 84.9%

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

   if 1.99999999999999996e-12 < (*.f64 z t)

   1. Initial program 92.4%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y + z \cdot t}{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{y + z \cdot t}}\right), x\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y - z \cdot t}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(y - z \cdot t\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), x\right) \]

      10. *-lowering-*.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), x\right) \]

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{t \cdot z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(t \cdot z\right)\right), x\right) \]

      2. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(t, z\right)\right), x\right) \]

   7. Simplified 80.7%

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

      1. associate-*l/ N/A

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

      2. neg-mul-1 N/A

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

      3. associate-/r* N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(x\right)}{t}\right), \color{blue}{z}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(0 - x\right), t\right), z\right) \]

      7. --lowering--.f64 85.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, x\right), t\right), z\right) \]

   9. Applied egg-rr 85.2%

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

       1. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

       2. neg-lowering-neg.f64 85.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{neg.f64}\left(x\right), t\right), z\right) \]

   11. Applied egg-rr 85.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-86}:\\ \;\;\;\;\frac{0 - \frac{x}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{0 - z}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) (- 0.0 z))))
   (if (<= (* z t) -1e-9) t_1 (if (<= (* z t) 2e-12) (/ x y) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (0.0 - z);
	double tmp;
	if ((z * t) <= -1e-9) {
		tmp = t_1;
	} else if ((z * t) <= 2e-12) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / (0.0d0 - z)
    if ((z * t) <= (-1d-9)) then
        tmp = t_1
    else if ((z * t) <= 2d-12) then
        tmp = x / y
    else
        tmp = t_1
    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 t_1 = (x / t) / (0.0 - z);
	double tmp;
	if ((z * t) <= -1e-9) {
		tmp = t_1;
	} else if ((z * t) <= 2e-12) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / (0.0 - z)
	tmp = 0
	if (z * t) <= -1e-9:
		tmp = t_1
	elif (z * t) <= 2e-12:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(0.0 - z))
	tmp = 0.0
	if (Float64(z * t) <= -1e-9)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e-12)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / (0.0 - z);
	tmp = 0.0;
	if ((z * t) <= -1e-9)
		tmp = t_1;
	elseif ((z * t) <= 2e-12)
		tmp = x / y;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / N[(0.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e-9], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e-12], N[(x / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000006e-9 or 1.99999999999999996e-12 < (*.f64 z t)

   1. Initial program 92.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y + z \cdot t}{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right), \color{blue}{x}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{y \cdot y - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{y + z \cdot t}}\right), x\right) \]

      7. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y - z \cdot t}\right), x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(y - z \cdot t\right)\right), x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), x\right) \]

      10. *-lowering-*.f64 92.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), x\right) \]

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{t \cdot z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(t \cdot z\right)\right), x\right) \]

      2. *-lowering-*.f64 77.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(t, z\right)\right), x\right) \]

   7. Simplified 77.4%

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

      1. associate-*l/ N/A

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

      2. neg-mul-1 N/A

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

      3. associate-/r* N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(x\right)}{t}\right), \color{blue}{z}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(0 - x\right), t\right), z\right) \]

      7. --lowering--.f64 82.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, x\right), t\right), z\right) \]

   9. Applied egg-rr 82.6%

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

       1. sub0-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(x\right)\right), t\right), z\right) \]

       2. neg-lowering-neg.f64 82.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{neg.f64}\left(x\right), t\right), z\right) \]

   11. Applied egg-rr 82.6%

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

   if -1.00000000000000006e-9 < (*.f64 z t) < 1.99999999999999996e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 81.4%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 81.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-9}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{0 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 0 - \frac{x}{z \cdot t}\\ \mathbf{if}\;z \cdot t \leq -1.02 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 1.65:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 0.0 (/ x (* z t)))))
   (if (<= (* z t) -1.02e-86) t_1 (if (<= (* z t) 1.65) (/ x y) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 0.0 - (x / (z * t));
	double tmp;
	if ((z * t) <= -1.02e-86) {
		tmp = t_1;
	} else if ((z * t) <= 1.65) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 0.0d0 - (x / (z * t))
    if ((z * t) <= (-1.02d-86)) then
        tmp = t_1
    else if ((z * t) <= 1.65d0) then
        tmp = x / y
    else
        tmp = t_1
    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 t_1 = 0.0 - (x / (z * t));
	double tmp;
	if ((z * t) <= -1.02e-86) {
		tmp = t_1;
	} else if ((z * t) <= 1.65) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 0.0 - (x / (z * t))
	tmp = 0
	if (z * t) <= -1.02e-86:
		tmp = t_1
	elif (z * t) <= 1.65:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(0.0 - Float64(x / Float64(z * t)))
	tmp = 0.0
	if (Float64(z * t) <= -1.02e-86)
		tmp = t_1;
	elseif (Float64(z * t) <= 1.65)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 0.0 - (x / (z * t));
	tmp = 0.0;
	if ((z * t) <= -1.02e-86)
		tmp = t_1;
	elseif ((z * t) <= 1.65)
		tmp = x / y;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(0.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1.02e-86], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1.65], N[(x / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.02000000000000005e-86 or 1.6499999999999999 < (*.f64 z t)

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z} + -1 \cdot \frac{x \cdot y}{{t}^{2} \cdot {z}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -1 \cdot \frac{x}{t \cdot z} + \left(\mathsf{neg}\left(\frac{x \cdot y}{{t}^{2} \cdot {z}^{2}}\right)\right) \]

      2. unsub-neg N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. associate-/r* N/A

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

      8. associate-/l* N/A

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

      9. unpow2 N/A

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

      10. times-frac N/A

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

      11. associate-/r* N/A

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

      12. distribute-lft-out-- N/A

          \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(\frac{-1}{t} - \frac{y}{{t}^{2} \cdot z}\right)} \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{-1}{t} - \frac{y}{{t}^{2} \cdot z}\right)}\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\color{blue}{\frac{-1}{t}} - \frac{y}{{t}^{2} \cdot z}\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\left(\frac{-1}{t}\right), \color{blue}{\left(\frac{y}{{t}^{2} \cdot z}\right)}\right)\right) \]

      16. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \left(\frac{\color{blue}{y}}{{t}^{2} \cdot z}\right)\right)\right) \]

      17. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(y, \color{blue}{\left({t}^{2} \cdot z\right)}\right)\right)\right) \]

      18. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(y, \left(\left(t \cdot t\right) \cdot z\right)\right)\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(y, \left(t \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot z\right)}\right)\right)\right)\right) \]

      21. *-lowering-*.f64 77.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right)\right) \]

   5. Simplified 77.2%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{t} - \frac{y}{t \cdot \left(t \cdot z\right)}\right), \color{blue}{\left(\frac{z}{x}\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{t} - \frac{y}{\left(t \cdot z\right) \cdot t}\right), \left(\frac{z}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{t} - \frac{y}{\left(z \cdot t\right) \cdot t}\right), \left(\frac{z}{x}\right)\right) \]

      7. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{t} - \frac{\frac{y}{z \cdot t}}{t}\right), \left(\frac{z}{x}\right)\right) \]

      8. sub-div N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1 - \frac{y}{z \cdot t}}{t}\right), \left(\frac{\color{blue}{z}}{x}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(-1 - \frac{y}{z \cdot t}\right), t\right), \left(\frac{\color{blue}{z}}{x}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \left(\frac{y}{z \cdot t}\right)\right), t\right), \left(\frac{z}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(y, \left(z \cdot t\right)\right)\right), t\right), \left(\frac{z}{x}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), t\right), \left(\frac{z}{x}\right)\right) \]

      13. /-lowering-/.f64 77.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), t\right), \mathsf{/.f64}\left(z, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 77.0%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{t}\right)}, \mathsf{/.f64}\left(z, x\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(-1, t\right), \mathsf{/.f64}\left(\color{blue}{z}, x\right)\right) \]

   10. Simplified 78.5%

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

       1. associate-/r/ N/A

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

       2. *-commutative N/A

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

       3. div-inv N/A

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

       4. mul-1-neg N/A

          \[\leadsto x \cdot \frac{\mathsf{neg}\left(\frac{1}{t}\right)}{z} \]

       5. remove-double-neg N/A

          \[\leadsto x \cdot \frac{\mathsf{neg}\left(\frac{1}{t}\right)}{\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)} \]

       6. frac-2neg N/A

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

       7. associate-*r/ N/A

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

       8. div-inv N/A

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

       9. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{neg}\left(\frac{\frac{x}{t}}{z}\right) \]

       10. neg-lowering-neg.f64 N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(\frac{\frac{x}{t}}{z}\right)\right) \]

       11. associate-/r* N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(\frac{x}{t \cdot z}\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(\frac{x}{z \cdot t}\right)\right) \]

       13. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(x, \left(z \cdot t\right)\right)\right) \]

       14. *-lowering-*.f64 75.8%

           \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, t\right)\right)\right) \]

   12. Applied egg-rr 75.8%

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

   if -1.02000000000000005e-86 < (*.f64 z t) < 1.6499999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 84.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.02 \cdot 10^{-86}:\\ \;\;\;\;0 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 1.65:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{y}{z} - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -1.2e+135) (/ 1.0 (* z (/ (- (/ y z) t) x))) (/ 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 <= -1.2e+135) {
		tmp = 1.0 / (z * (((y / z) - t) / x));
	} else {
		tmp = x / (y - (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 <= (-1.2d+135)) then
        tmp = 1.0d0 / (z * (((y / z) - t) / x))
    else
        tmp = x / (y - (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 <= -1.2e+135) {
		tmp = 1.0 / (z * (((y / z) - t) / x));
	} 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 <= -1.2e+135:
		tmp = 1.0 / (z * (((y / z) - t) / x))
	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 (z <= -1.2e+135)
		tmp = Float64(1.0 / Float64(z * Float64(Float64(Float64(y / z) - t) / x)));
	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 <= -1.2e+135)
		tmp = 1.0 / (z * (((y / z) - t) / x));
	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[LessEqual[z, -1.2e+135], N[(1.0 / N[(z * N[(N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999999e135

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{y}{z} - t\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{z} - t\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{y}{z}\right), \color{blue}{t}\right)\right)\right) \]

      3. /-lowering-/.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), t\right)\right)\right) \]

   5. Simplified 78.2%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{\frac{y}{z} - t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z} - t\right)\right), z\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{z}\right), t\right)\right), z\right) \]

      6. /-lowering-/.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), t\right)\right), z\right) \]

   7. Applied egg-rr 96.5%

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

      1. div-inv N/A

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

      2. clear-num N/A

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

      3. frac-times N/A

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

      4. metadata-eval N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{y}{z} - t}{x} \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{\frac{y}{z} - t}{x}\right), \color{blue}{z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{y}{z} - t\right), x\right), z\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{y}{z}\right), t\right), x\right), z\right)\right) \]

      9. /-lowering-/.f64 96.2%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), t\right), x\right), z\right)\right) \]

   9. Applied egg-rr 96.2%

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

   if -1.19999999999999999e135 < z

   1. Initial program 98.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{y}{z} - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+222}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{z} - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -5.1e+222) (/ (/ x (- (/ y z) 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 <= -5.1e+222) {
		tmp = (x / ((y / z) - t)) / z;
	} else {
		tmp = x / (y - (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 <= (-5.1d+222)) then
        tmp = (x / ((y / z) - t)) / z
    else
        tmp = x / (y - (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 <= -5.1e+222) {
		tmp = (x / ((y / z) - 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 <= -5.1e+222:
		tmp = (x / ((y / z) - 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 (z <= -5.1e+222)
		tmp = Float64(Float64(x / Float64(Float64(y / z) - 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 <= -5.1e+222)
		tmp = (x / ((y / z) - 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[LessEqual[z, -5.1e+222], N[(N[(x / N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0999999999999999e222

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{y}{z} - t\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{z} - t\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{y}{z}\right), \color{blue}{t}\right)\right)\right) \]

      3. /-lowering-/.f64 71.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), t\right)\right)\right) \]

   5. Simplified 71.1%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{\frac{y}{z} - t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z} - t\right)\right), z\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{y}{z}\right), t\right)\right), z\right) \]

      6. /-lowering-/.f64 93.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), t\right)\right), z\right) \]

   7. Applied egg-rr 93.8%

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

   if -5.0999999999999999e222 < z

   1. Initial program 97.9%

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

Alternative 7: 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 96.2%

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

3. Taylor expanded in y around inf

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

   1. /-lowering-/.f64 54.0%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

5. Simplified 54.0%

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

Developer Target 1: 96.8% 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 2024138 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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