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

Percentage Accurate: 85.3% → 96.0%

Time: 10.2s

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: 85.3% 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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - z \cdot a\\ t_3 := y \cdot \left(\frac{\frac{x}{y}}{t\_2} + \frac{z}{z \cdot a - t}\right)\\ t_4 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_4 \leq -2 \cdot 10^{+233}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{a}{t\_1}}\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{+292}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (- t (* z a)))
        (t_3 (* y (+ (/ (/ x y) t_2) (/ z (- (* z a) t)))))
        (t_4 (/ t_1 t_2)))
   (if (<= t_4 -2e+233)
     t_3
     (if (<= t_4 -1e-320)
       t_4
       (if (<= t_4 0.0)
         (/ -1.0 (* z (/ a t_1)))
         (if (<= t_4 4e+292) t_4 (if (<= t_4 INFINITY) t_3 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = y * (((x / y) / t_2) + (z / ((z * a) - t)));
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -2e+233) {
		tmp = t_3;
	} else if (t_4 <= -1e-320) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = -1.0 / (z * (a / t_1));
	} else if (t_4 <= 4e+292) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = y * (((x / y) / t_2) + (z / ((z * a) - t)));
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -2e+233) {
		tmp = t_3;
	} else if (t_4 <= -1e-320) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = -1.0 / (z * (a / t_1));
	} else if (t_4 <= 4e+292) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * z)
	t_2 = t - (z * a)
	t_3 = y * (((x / y) / t_2) + (z / ((z * a) - t)))
	t_4 = t_1 / t_2
	tmp = 0
	if t_4 <= -2e+233:
		tmp = t_3
	elif t_4 <= -1e-320:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = -1.0 / (z * (a / t_1))
	elif t_4 <= 4e+292:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(y * Float64(Float64(Float64(x / y) / t_2) + Float64(z / Float64(Float64(z * a) - t))))
	t_4 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_4 <= -2e+233)
		tmp = t_3;
	elseif (t_4 <= -1e-320)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(a / t_1)));
	elseif (t_4 <= 4e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * z);
	t_2 = t - (z * a);
	t_3 = y * (((x / y) / t_2) + (z / ((z * a) - t)));
	t_4 = t_1 / t_2;
	tmp = 0.0;
	if (t_4 <= -2e+233)
		tmp = t_3;
	elseif (t_4 <= -1e-320)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = -1.0 / (z * (a / t_1));
	elseif (t_4 <= 4e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(N[(x / y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, -2e+233], t$95$3, If[LessEqual[t$95$4, -1e-320], t$95$4, If[LessEqual[t$95$4, 0.0], N[(-1.0 / N[(z * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 4e+292], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$3, N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.99999999999999995e233 or 4.0000000000000001e292 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 63.4%

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

      1. *-commutative 63.4%

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

   3. Simplified 63.4%

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

      1. div-inv 63.4%

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

      2. sub-neg 63.4%

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

      3. +-commutative 63.4%

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

      4. distribute-rgt-neg-in 63.4%

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

      5. fma-define 63.4%

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

      6. sub-neg 63.4%

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

      7. +-commutative 63.4%

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

      8. *-commutative 63.4%

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

      9. distribute-rgt-neg-in 63.4%

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

      10. fma-define 63.4%

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

   6. Applied egg-rr 63.4%

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

   7. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. associate-/r* 99.8%

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

      5. mul-1-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

   9. Simplified 99.8%

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

   if -1.99999999999999995e233 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.99989e-321 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.0000000000000001e292

   1. Initial program 99.7%

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

   if -9.99989e-321 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 56.9%

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

      1. *-commutative 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in t around 0 37.3%

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

      1. associate-*r/ 37.3%

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

      2. mul-1-neg 37.3%

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

      3. sub-neg 37.3%

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

      4. distribute-rgt-neg-out 37.3%

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

      5. +-commutative 37.3%

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

      6. fma-define 37.3%

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

      7. neg-sub0 37.3%

         \[\leadsto \frac{\color{blue}{0 - \mathsf{fma}\left(y, -z, x\right)}}{a \cdot z} \]

      8. fma-define 37.3%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      9. associate--r+ 37.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      10. neg-sub0 37.3%

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

      11. distribute-rgt-neg-out 37.3%

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

      12. remove-double-neg 37.3%

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

      13. *-commutative 37.3%

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

   7. Simplified 37.3%

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

      1. clear-num 37.7%

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

      2. inv-pow 37.7%

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

      3. *-commutative 37.7%

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

      4. *-commutative 37.7%

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

   9. Applied egg-rr 37.7%

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

       1. unpow-1 37.7%

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

       2. associate-/l* 87.0%

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

       3. *-commutative 87.0%

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

   11. Simplified 87.0%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(\frac{\frac{x}{y}}{t - z \cdot a} + \frac{z}{z \cdot a - t}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{a}{x - y \cdot z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 4 \cdot 10^{+292}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{\frac{x}{y}}{t - z \cdot a} + \frac{z}{z \cdot a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+168} \lor \neg \left(z \leq 3.3 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+168) (not (<= z 3.3e+137)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+168) || !(z <= 3.3e+137)) {
		tmp = (y - (x / z)) / a;
	} 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 <= (-1.45d+168)) .or. (.not. (z <= 3.3d+137))) then
        tmp = (y - (x / z)) / a
    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 <= -1.45e+168) || !(z <= 3.3e+137)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+168) or not (z <= 3.3e+137):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+168) || !(z <= 3.3e+137))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	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 <= -1.45e+168) || ~((z <= 3.3e+137)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+168], N[Not[LessEqual[z, 3.3e+137]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $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 < -1.45e168 or 3.30000000000000003e137 < z

   1. Initial program 57.9%

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

      1. *-commutative 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in t around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. mul-1-neg 47.8%

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

      3. sub-neg 47.8%

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

      4. distribute-rgt-neg-out 47.8%

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

      5. +-commutative 47.8%

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

      6. fma-define 47.8%

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

      7. neg-sub0 47.8%

         \[\leadsto \frac{\color{blue}{0 - \mathsf{fma}\left(y, -z, x\right)}}{a \cdot z} \]

      8. fma-define 47.8%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      9. associate--r+ 47.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      10. neg-sub0 47.8%

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

      11. distribute-rgt-neg-out 47.8%

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

      12. remove-double-neg 47.8%

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

      13. *-commutative 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in z around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   10. Simplified 75.3%

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

   11. Taylor expanded in a around 0 82.5%

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

   if -1.45e168 < z < 3.30000000000000003e137

   1. Initial program 95.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+168} \lor \neg \left(z \leq 3.3 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+105} \lor \neg \left(z \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+105) (not (<= z 6e+29)))
   (/ (- y (/ x z)) a)
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+105) || !(z <= 6e+29)) {
		tmp = (y - (x / z)) / 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 <= (-6.5d+105)) .or. (.not. (z <= 6d+29))) then
        tmp = (y - (x / z)) / 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 <= -6.5e+105) || !(z <= 6e+29)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+105) or not (z <= 6e+29):
		tmp = (y - (x / z)) / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+105) || !(z <= 6e+29))
		tmp = Float64(Float64(y - Float64(x / z)) / 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 <= -6.5e+105) || ~((z <= 6e+29)))
		tmp = (y - (x / z)) / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+105], N[Not[LessEqual[z, 6e+29]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000049e105 or 5.9999999999999998e29 < z

   1. Initial program 64.5%

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

      1. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in t around 0 48.1%

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

      1. associate-*r/ 48.1%

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

      2. mul-1-neg 48.1%

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

      3. sub-neg 48.1%

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

      4. distribute-rgt-neg-out 48.1%

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

      5. +-commutative 48.1%

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

      6. fma-define 48.1%

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

      7. neg-sub0 48.1%

         \[\leadsto \frac{\color{blue}{0 - \mathsf{fma}\left(y, -z, x\right)}}{a \cdot z} \]

      8. fma-define 48.1%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      9. associate--r+ 48.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      10. neg-sub0 48.1%

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

      11. distribute-rgt-neg-out 48.1%

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

      12. remove-double-neg 48.1%

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

      13. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in z around inf 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. unsub-neg 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in a around 0 75.3%

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

   if -6.50000000000000049e105 < z < 5.9999999999999998e29

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+105} \lor \neg \left(z \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+105} \lor \neg \left(z \leq 2.12 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+105) (not (<= z 2.12e+123))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+105) || !(z <= 2.12e+123)) {
		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 <= (-7d+105)) .or. (.not. (z <= 2.12d+123))) 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 <= -7e+105) || !(z <= 2.12e+123)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+105) or not (z <= 2.12e+123):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+105) || !(z <= 2.12e+123))
		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 <= -7e+105) || ~((z <= 2.12e+123)))
		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, -7e+105], N[Not[LessEqual[z, 2.12e+123]], $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 < -6.99999999999999982e105 or 2.12e123 < 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. Taylor expanded in z around inf 67.8%

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

   if -6.99999999999999982e105 < z < 2.12e123

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 70.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+105} \lor \neg \left(z \leq 2.12 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+77} \lor \neg \left(z \leq 460000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+77) (not (<= z 460000000000.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+77) || !(z <= 460000000000.0)) {
		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 <= (-1.2d+77)) .or. (.not. (z <= 460000000000.0d0))) 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 <= -1.2e+77) || !(z <= 460000000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+77) or not (z <= 460000000000.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+77) || !(z <= 460000000000.0))
		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 <= -1.2e+77) || ~((z <= 460000000000.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+77], N[Not[LessEqual[z, 460000000000.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1999999999999999e77 or 4.6e11 < z

   1. Initial program 67.1%

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

      1. *-commutative 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in z around inf 60.0%

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

   if -1.1999999999999999e77 < z < 4.6e11

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 55.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+77} \lor \neg \left(z \leq 460000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.2% 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 84.0%

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

   1. *-commutative 84.0%

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

3. Simplified 84.0%

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

5. Taylor expanded in z around 0 36.0%

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

Developer Target 1: 97.4% 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 2024182 
(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))))