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

Percentage Accurate: 84.6% → 93.9%

Time: 7.2s

Alternatives: 9

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: 84.6% 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: 93.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - a \cdot z\\ t_3 := \frac{\frac{x}{y} - z}{t\_2} \cdot y\\ t_4 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (- t (* a z)))
        (t_3 (* (/ (- (/ x y) z) t_2) y))
        (t_4 (/ t_1 t_2)))
   (if (<= t_4 (- INFINITY))
     t_3
     (if (<= t_4 5e+275)
       (/ t_1 (fma (- z) a t))
       (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 - (a * z);
	double t_3 = (((x / y) - z) / t_2) * y;
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_4 <= 5e+275) {
		tmp = t_1 / fma(-z, a, t);
	} else if (t_4 <= ((double) INFINITY)) {
		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(a * z))
	t_3 = Float64(Float64(Float64(Float64(x / y) - z) / t_2) * y)
	t_4 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_4 <= 5e+275)
		tmp = Float64(t_1 / fma(Float64(-z), a, t));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y / a);
	end
	return 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[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x / y), $MachinePrecision] - z), $MachinePrecision] / t$95$2), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$3, If[LessEqual[t$95$4, 5e+275], N[(t$95$1 / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 5.0000000000000003e275 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 66.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. div-add-rev N/A

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

      7. metadata-eval N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. *-lft-identity N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.0000000000000003e275

   1. Initial program 94.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-neg-out N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 94.7

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

   4. Applied rewrites 94.7%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 2: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ \mathbf{if}\;\frac{t\_1}{t - a \cdot z} \leq \infty:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z))))
   (if (<= (/ t_1 (- t (* a z))) INFINITY) (/ t_1 (fma (- z) a t)) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double tmp;
	if ((t_1 / (t - (a * z))) <= ((double) INFINITY)) {
		tmp = t_1 / fma(-z, a, t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (Float64(t_1 / Float64(t - Float64(a * z))) <= Inf)
		tmp = Float64(t_1 / fma(Float64(-z), a, t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-neg-out N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 90.4

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

   4. Applied rewrites 90.4%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* a z)))))
   (if (<= t_1 INFINITY) t_1 (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (a * z));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} 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)) / (t - (a * z));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (a * z))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	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 - (a * z));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y / a;
	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[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.4%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{y \cdot z - x}{a \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+88)
   (/ y a)
   (if (<= z -3.5e-56)
     (/ (- (* y z) x) (* a z))
     (if (<= z 3.6e+50) (/ (- x (* z y)) t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+88) {
		tmp = y / a;
	} else if (z <= -3.5e-56) {
		tmp = ((y * z) - x) / (a * z);
	} else if (z <= 3.6e+50) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = y / 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 <= (-2.9d+88)) then
        tmp = y / a
    else if (z <= (-3.5d-56)) then
        tmp = ((y * z) - x) / (a * z)
    else if (z <= 3.6d+50) then
        tmp = (x - (z * y)) / t
    else
        tmp = y / 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 <= -2.9e+88) {
		tmp = y / a;
	} else if (z <= -3.5e-56) {
		tmp = ((y * z) - x) / (a * z);
	} else if (z <= 3.6e+50) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+88:
		tmp = y / a
	elif z <= -3.5e-56:
		tmp = ((y * z) - x) / (a * z)
	elif z <= 3.6e+50:
		tmp = (x - (z * y)) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+88)
		tmp = Float64(y / a);
	elseif (z <= -3.5e-56)
		tmp = Float64(Float64(Float64(y * z) - x) / Float64(a * z));
	elseif (z <= 3.6e+50)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+88)
		tmp = y / a;
	elseif (z <= -3.5e-56)
		tmp = ((y * z) - x) / (a * z);
	elseif (z <= 3.6e+50)
		tmp = (x - (z * y)) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+88], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.5e-56], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(a * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+50], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e88 or 3.59999999999999986e50 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 63.5

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

   5. Applied rewrites 63.5%

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

   if -2.9e88 < z < -3.4999999999999998e-56

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac N/A

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

      4. lower-/.f64 N/A

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

      5. distribute-frac-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. fp-cancel-sub-sign-inv N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. distribute-lft-neg-in N/A

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

      15. metadata-eval N/A

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

      16. *-lft-identity N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower-neg.f64 63.2

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

   5. Applied rewrites 63.2%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(z, y, -x\right)}{a}}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 63.3%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 63.3%

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

   if -3.4999999999999998e-56 < z < 3.59999999999999986e50

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

Alternative 5: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+21)
   (/ y a)
   (if (<= z 5e-94)
     (/ x (fma (- z) a t))
     (if (<= z 3.6e+50) (/ (- x (* z y)) t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+21) {
		tmp = y / a;
	} else if (z <= 5e-94) {
		tmp = x / fma(-z, a, t);
	} else if (z <= 3.6e+50) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+21)
		tmp = Float64(y / a);
	elseif (z <= 5e-94)
		tmp = Float64(x / fma(Float64(-z), a, t));
	elseif (z <= 3.6e+50)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+21], N[(y / a), $MachinePrecision], If[LessEqual[z, 5e-94], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+50], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4e21 or 3.59999999999999986e50 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if -4e21 < z < 4.9999999999999995e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 75.5

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

   5. Applied rewrites 75.5%

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

   7. Applied rewrites 75.5%

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

   if 4.9999999999999995e-94 < z < 3.59999999999999986e50

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

Alternative 6: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+21) (not (<= z 2.7e+50))) (/ y a) (/ x (fma (- z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+21) || !(z <= 2.7e+50)) {
		tmp = y / a;
	} else {
		tmp = x / fma(-z, a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+21) || !(z <= 2.7e+50))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / fma(Float64(-z), a, t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+21], N[Not[LessEqual[z, 2.7e+50]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e21 or 2.7e50 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if -4e21 < z < 2.7e50

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 70.2

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

   5. Applied rewrites 70.2%

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

   7. Applied rewrites 70.2%

      \[\leadsto \frac{x}{\mathsf{fma}\left(-z, \color{blue}{a}, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+21) (not (<= z 2.7e+50))) (/ y a) (/ x (- t (* a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+21) || !(z <= 2.7e+50)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (a * 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) :: tmp
    if ((z <= (-4d+21)) .or. (.not. (z <= 2.7d+50))) then
        tmp = y / a
    else
        tmp = x / (t - (a * z))
    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 <= -4e+21) || !(z <= 2.7e+50)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (a * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+21) or not (z <= 2.7e+50):
		tmp = y / a
	else:
		tmp = x / (t - (a * z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+21) || !(z <= 2.7e+50))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(a * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+21) || ~((z <= 2.7e+50)))
		tmp = y / a;
	else
		tmp = x / (t - (a * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+21], N[Not[LessEqual[z, 2.7e+50]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e21 or 2.7e50 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 62.0

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

   5. Applied rewrites 62.0%

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

   if -4e21 < z < 2.7e50

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 70.2

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

   5. Applied rewrites 70.2%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-21} \lor \neg \left(z \leq 1.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e-21) (not (<= z 1.5e+50))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e-21) || !(z <= 1.5e+50)) {
		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 <= (-4d-21)) .or. (.not. (z <= 1.5d+50))) 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 <= -4e-21) || !(z <= 1.5e+50)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e-21) or not (z <= 1.5e+50):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e-21) || !(z <= 1.5e+50))
		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 <= -4e-21) || ~((z <= 1.5e+50)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e-21], N[Not[LessEqual[z, 1.5e+50]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999963e-21 or 1.4999999999999999e50 < z

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if -3.99999999999999963e-21 < z < 1.4999999999999999e50

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 53.9

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

   5. Applied rewrites 53.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-21} \lor \neg \left(z \leq 1.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.5% accurate, 2.3× 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 85.8%

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

3. Taylor expanded in z around 0

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

   1. lower-/.f64 31.8

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

5. Applied rewrites 31.8%

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

Developer Target 1: 97.3% accurate, 0.5× 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 2024339 
(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))))