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

Percentage Accurate: 84.8% → 92.1%

Time: 11.6s

Alternatives: 6

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ t_2 := y \cdot z - x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+259}:\\ \;\;\;\;{\left(a \cdot \frac{z}{t\_2} - \frac{t}{t\_2}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{a} - \frac{x}{a \cdot \left(y \cdot z\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))) (t_2 (- (* y z) x)))
   (if (<= t_1 -1e-309)
     t_1
     (if (<= t_1 1e+259)
       (pow (- (* a (/ z t_2)) (/ t t_2)) -1.0)
       (* y (- (/ 1.0 a) (/ x (* a (* y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double t_2 = (y * z) - x;
	double tmp;
	if (t_1 <= -1e-309) {
		tmp = t_1;
	} else if (t_1 <= 1e+259) {
		tmp = pow(((a * (z / t_2)) - (t / t_2)), -1.0);
	} else {
		tmp = y * ((1.0 / a) - (x / (a * (y * z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    t_2 = (y * z) - x
    if (t_1 <= (-1d-309)) then
        tmp = t_1
    else if (t_1 <= 1d+259) then
        tmp = ((a * (z / t_2)) - (t / t_2)) ** (-1.0d0)
    else
        tmp = y * ((1.0d0 / a) - (x / (a * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double t_2 = (y * z) - x;
	double tmp;
	if (t_1 <= -1e-309) {
		tmp = t_1;
	} else if (t_1 <= 1e+259) {
		tmp = Math.pow(((a * (z / t_2)) - (t / t_2)), -1.0);
	} else {
		tmp = y * ((1.0 / a) - (x / (a * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	t_2 = (y * z) - x
	tmp = 0
	if t_1 <= -1e-309:
		tmp = t_1
	elif t_1 <= 1e+259:
		tmp = math.pow(((a * (z / t_2)) - (t / t_2)), -1.0)
	else:
		tmp = y * ((1.0 / a) - (x / (a * (y * z))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y * z) - x)
	tmp = 0.0
	if (t_1 <= -1e-309)
		tmp = t_1;
	elseif (t_1 <= 1e+259)
		tmp = Float64(Float64(a * Float64(z / t_2)) - Float64(t / t_2)) ^ -1.0;
	else
		tmp = Float64(y * Float64(Float64(1.0 / a) - Float64(x / Float64(a * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	t_2 = (y * z) - x;
	tmp = 0.0;
	if (t_1 <= -1e-309)
		tmp = t_1;
	elseif (t_1 <= 1e+259)
		tmp = ((a * (z / t_2)) - (t / t_2)) ^ -1.0;
	else
		tmp = y * ((1.0 / a) - (x / (a * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-309], t$95$1, If[LessEqual[t$95$1, 1e+259], N[Power[N[(N[(a * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(t / t$95$2), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(y * N[(N[(1.0 / a), $MachinePrecision] - N[(x / N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.000000000000002e-309

   1. Initial program 96.2%

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

   if -1.000000000000002e-309 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.999999999999999e258

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 83.0%

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

      2. inv-pow 83.0%

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

      3. sub-neg 83.0%

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

      4. +-commutative 83.0%

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

      5. *-commutative 83.0%

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

      6. distribute-rgt-neg-in 83.0%

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

      7. fma-define 83.0%

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

   6. Applied egg-rr 83.0%

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

   7. Taylor expanded in a around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. mul-1-neg 82.2%

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

      3. unsub-neg 82.2%

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

      4. associate-/l* 97.6%

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

   9. Simplified 97.6%

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

   if 9.999999999999999e258 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 45.7%

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

      1. *-commutative 45.7%

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

   3. Simplified 45.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 45.7%

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

   6. Taylor expanded in t around 0 35.4%

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

      1. associate-*r/ 35.4%

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

      2. associate-*r* 35.4%

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

      3. neg-mul-1 35.4%

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

      4. *-commutative 35.4%

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

   8. Simplified 35.4%

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

   9. Taylor expanded in y around inf 86.2%

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

       1. +-commutative 86.2%

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

       2. mul-1-neg 86.2%

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

       3. unsub-neg 86.2%

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

       4. *-commutative 86.2%

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

       5. *-commutative 86.2%

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

   11. Simplified 86.2%

       \[\leadsto \color{blue}{y \cdot \left(\frac{1}{a} - \frac{x}{\left(z \cdot y\right) \cdot a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-309}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+259}:\\ \;\;\;\;{\left(a \cdot \frac{z}{y \cdot z - x} - \frac{t}{y \cdot z - x}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{a} - \frac{x}{a \cdot \left(y \cdot z\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+140} \lor \neg \left(z \leq 7.8 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+140) (not (<= z 7.8e+175)))
   (/ y (- a (/ t z)))
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+140) || !(z <= 7.8e+175)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.15d+140)) .or. (.not. (z <= 7.8d+175))) then
        tmp = y / (a - (t / z))
    else
        tmp = (x - (y * z)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+140) || !(z <= 7.8e+175)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+140) or not (z <= 7.8e+175):
		tmp = y / (a - (t / z))
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+140) || !(z <= 7.8e+175))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+140) || ~((z <= 7.8e+175)))
		tmp = y / (a - (t / z));
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+140], N[Not[LessEqual[z, 7.8e+175]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999995e140 or 7.79999999999999944e175 < z

   1. Initial program 50.1%

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

      1. *-commutative 50.1%

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

   3. Simplified 50.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 50.1%

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

      2. inv-pow 50.1%

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

      3. sub-neg 50.1%

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

      4. +-commutative 50.1%

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

      5. *-commutative 50.1%

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

      6. distribute-rgt-neg-in 50.1%

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

      7. fma-define 50.1%

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

   6. Applied egg-rr 50.1%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. associate-/l* 66.8%

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

   9. Simplified 66.8%

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

   10. Taylor expanded in y around -inf 89.0%

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

       1. associate-*r/ 89.0%

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

       2. mul-1-neg 89.0%

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

   12. Simplified 89.0%

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

       1. frac-2neg 89.0%

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

       2. div-inv 88.8%

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

       3. remove-double-neg 88.8%

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

       4. sub-neg 88.8%

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

       5. distribute-neg-in 88.8%

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

       6. remove-double-neg 88.8%

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

   14. Applied egg-rr 88.8%

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

       1. associate-*r/ 89.0%

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

       2. *-rgt-identity 89.0%

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

       3. distribute-frac-neg 89.0%

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

       4. +-commutative 89.0%

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

       5. distribute-frac-neg 89.0%

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

       6. unsub-neg 89.0%

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

   16. Simplified 89.0%

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

   if -1.14999999999999995e140 < z < 7.79999999999999944e175

   1. Initial program 94.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+140} \lor \neg \left(z \leq 7.8 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+79} \lor \neg \left(z \leq 1.55 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+79) (not (<= z 1.55e+27)))
   (/ y (- a (/ t z)))
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+79) || !(z <= 1.55e+27)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+79)) .or. (.not. (z <= 1.55d+27))) then
        tmp = y / (a - (t / z))
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+79) || !(z <= 1.55e+27)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+79) or not (z <= 1.55e+27):
		tmp = y / (a - (t / z))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+79) || !(z <= 1.55e+27))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+79) || ~((z <= 1.55e+27)))
		tmp = y / (a - (t / z));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+79], N[Not[LessEqual[z, 1.55e+27]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999994e79 or 1.54999999999999998e27 < z

   1. Initial program 62.6%

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

      1. *-commutative 62.6%

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

   3. Simplified 62.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 61.9%

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

      2. inv-pow 61.9%

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

      3. sub-neg 61.9%

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

      4. +-commutative 61.9%

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

      5. *-commutative 61.9%

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

      6. distribute-rgt-neg-in 61.9%

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

      7. fma-define 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around 0 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. associate-/l* 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in y around -inf 80.0%

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

       1. associate-*r/ 80.0%

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

       2. mul-1-neg 80.0%

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

   12. Simplified 80.0%

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

       1. frac-2neg 80.0%

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

       2. div-inv 79.8%

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

       3. remove-double-neg 79.8%

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

       4. sub-neg 79.8%

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

       5. distribute-neg-in 79.8%

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

       6. remove-double-neg 79.8%

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

   14. Applied egg-rr 79.8%

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

       1. associate-*r/ 80.0%

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

       2. *-rgt-identity 80.0%

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

       3. distribute-frac-neg 80.0%

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

       4. +-commutative 80.0%

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

       5. distribute-frac-neg 80.0%

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

       6. unsub-neg 80.0%

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

   16. Simplified 80.0%

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

   if -9.49999999999999994e79 < z < 1.54999999999999998e27

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.9%

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

      1. *-commutative 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+79} \lor \neg \left(z \leq 1.55 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+80} \lor \neg \left(z \leq 5.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+80) (not (<= z 5.5e+50))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+80) || !(z <= 5.5e+50)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d+80)) .or. (.not. (z <= 5.5d+50))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+80) || !(z <= 5.5e+50)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+80) or not (z <= 5.5e+50):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+80) || !(z <= 5.5e+50))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+80) || ~((z <= 5.5e+50)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+80], N[Not[LessEqual[z, 5.5e+50]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999991e80 or 5.4999999999999998e50 < z

   1. Initial program 60.7%

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

      1. *-commutative 60.7%

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

   3. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.3%

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

   if -1.34999999999999991e80 < z < 5.4999999999999998e50

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

   7. Simplified 77.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+80} \lor \neg \left(z \leq 5.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \lor \neg \left(z \leq 3.05 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2) (not (<= z 3.05e-19))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2) || !(z <= 3.05e-19)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.2d0)) .or. (.not. (z <= 3.05d-19))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2) || !(z <= 3.05e-19)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2) or not (z <= 3.05e-19):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2) || !(z <= 3.05e-19))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2) || ~((z <= 3.05e-19)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2], N[Not[LessEqual[z, 3.05e-19]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999993 or 3.0500000000000001e-19 < z

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 61.8%

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

   if -9.1999999999999993 < z < 3.0500000000000001e-19

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.7%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \lor \neg \left(z \leq 3.05 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ x t))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 84.9%

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

   1. *-commutative 84.9%

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

3. Simplified 84.9%

   \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 39.6%

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

Developer Target 1: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

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