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

Percentage Accurate: 85.2% → 90.5%

Time: 8.2s

Alternatives: 9

Speedup: 0.7×

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: 85.2% 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: 90.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -7.4e+158)
     t_1
     (if (<= z 1.2e+96) (/ (- x (* y z)) (- t (* a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -7.4e+158) {
		tmp = t_1;
	} else if (z <= 1.2e+96) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-7.4d+158)) then
        tmp = t_1
    else if (z <= 1.2d+96) then
        tmp = (x - (y * z)) / (t - (a * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -7.4e+158) {
		tmp = t_1;
	} else if (z <= 1.2e+96) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -7.4e+158:
		tmp = t_1
	elif z <= 1.2e+96:
		tmp = (x - (y * z)) / (t - (a * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -7.4e+158)
		tmp = t_1;
	elseif (z <= 1.2e+96)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -7.4e+158)
		tmp = t_1;
	elseif (z <= 1.2e+96)
		tmp = (x - (y * z)) / (t - (a * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -7.4e+158], t$95$1, If[LessEqual[z, 1.2e+96], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.40000000000000021e158 or 1.19999999999999996e96 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

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

      11. *-rgt-identity N/A

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

      12. remove-double-neg N/A

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

      13. remove-double-neg N/A

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

      14. neg-mul-1 N/A

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

      15. remove-double-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -7.40000000000000021e158 < z < 1.19999999999999996e96

   1. Initial program 98.2%

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

Alternative 2: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\mathsf{fma}\left(a, z, -t\right)} \cdot y\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z (fma a z (- t))) y)))
   (if (<= z -5.8e+169)
     (/ y a)
     (if (<= z -1.25e-34)
       t_1
       (if (<= z 3.35e-248)
         (/ (- x (* y z)) t)
         (if (<= z 4.3e-30)
           (/ x (fma (- z) a t))
           (if (<= z 2.55e+181) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / fma(a, z, -t)) * y;
	double tmp;
	if (z <= -5.8e+169) {
		tmp = y / a;
	} else if (z <= -1.25e-34) {
		tmp = t_1;
	} else if (z <= 3.35e-248) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 4.3e-30) {
		tmp = x / fma(-z, a, t);
	} else if (z <= 2.55e+181) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / fma(a, z, Float64(-t))) * y)
	tmp = 0.0
	if (z <= -5.8e+169)
		tmp = Float64(y / a);
	elseif (z <= -1.25e-34)
		tmp = t_1;
	elseif (z <= 3.35e-248)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 4.3e-30)
		tmp = Float64(x / fma(Float64(-z), a, t));
	elseif (z <= 2.55e+181)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(a * z + (-t)), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -5.8e+169], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.25e-34], t$95$1, If[LessEqual[z, 3.35e-248], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.3e-30], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e+181], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8000000000000001e169 or 2.55e181 < z

   1. Initial program 50.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -5.8000000000000001e169 < z < -1.2500000000000001e-34 or 4.29999999999999966e-30 < z < 2.55e181

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. associate-*r* N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

      16. mul-1-neg N/A

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

      17. lower-neg.f64 59.9

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

   5. Applied rewrites 59.9%

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

   7. Applied rewrites 69.3%

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

   if -1.2500000000000001e-34 < z < 3.35e-248

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   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 80.8

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

   5. Applied rewrites 80.8%

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

   if 3.35e-248 < z < 4.29999999999999966e-30

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 88.7

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

   5. Applied rewrites 88.7%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(-z, a, t\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(a, z, -t\right)} \cdot y\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+181}:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(a, z, -t\right)} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(a, z, -t\right)} \cdot z\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (fma a z (- t))) z)))
   (if (<= z -5.8e+169)
     (/ y a)
     (if (<= z -1.35e-34)
       t_1
       (if (<= z 3.35e-248)
         (/ (- x (* y z)) t)
         (if (<= z 4.3e-30)
           (/ x (fma (- z) a t))
           (if (<= z 1.46e+181) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / fma(a, z, -t)) * z;
	double tmp;
	if (z <= -5.8e+169) {
		tmp = y / a;
	} else if (z <= -1.35e-34) {
		tmp = t_1;
	} else if (z <= 3.35e-248) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 4.3e-30) {
		tmp = x / fma(-z, a, t);
	} else if (z <= 1.46e+181) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / fma(a, z, Float64(-t))) * z)
	tmp = 0.0
	if (z <= -5.8e+169)
		tmp = Float64(y / a);
	elseif (z <= -1.35e-34)
		tmp = t_1;
	elseif (z <= 3.35e-248)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 4.3e-30)
		tmp = Float64(x / fma(Float64(-z), a, t));
	elseif (z <= 1.46e+181)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a * z + (-t)), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.8e+169], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.35e-34], t$95$1, If[LessEqual[z, 3.35e-248], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.3e-30], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e+181], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8000000000000001e169 or 1.46000000000000008e181 < z

   1. Initial program 50.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -5.8000000000000001e169 < z < -1.35000000000000008e-34 or 4.29999999999999966e-30 < z < 1.46000000000000008e181

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. associate-*r* N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

      16. mul-1-neg N/A

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

      17. lower-neg.f64 59.9

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

   5. Applied rewrites 59.9%

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

   7. Applied rewrites 66.0%

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

   if -1.35000000000000008e-34 < z < 3.35e-248

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   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 80.8

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

   5. Applied rewrites 80.8%

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

   if 3.35e-248 < z < 4.29999999999999966e-30

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 88.7

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

   5. Applied rewrites 88.7%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(-z, a, t\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, z, -t\right)} \cdot z\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+181}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(a, z, -t\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;\frac{y \cdot z}{\mathsf{fma}\left(a, z, -t\right)}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4500000000:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -2.15e+63)
     t_1
     (if (<= z -1.25e-34)
       (/ (* y z) (fma a z (- t)))
       (if (<= z 3.35e-248)
         (/ (- x (* y z)) t)
         (if (<= z 4500000000.0) (/ x (fma (- z) a t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.15e+63) {
		tmp = t_1;
	} else if (z <= -1.25e-34) {
		tmp = (y * z) / fma(a, z, -t);
	} else if (z <= 3.35e-248) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 4500000000.0) {
		tmp = x / fma(-z, a, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -2.15e+63)
		tmp = t_1;
	elseif (z <= -1.25e-34)
		tmp = Float64(Float64(y * z) / fma(a, z, Float64(-t)));
	elseif (z <= 3.35e-248)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 4500000000.0)
		tmp = Float64(x / fma(Float64(-z), a, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.15e+63], t$95$1, If[LessEqual[z, -1.25e-34], N[(N[(y * z), $MachinePrecision] / N[(a * z + (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e-248], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4500000000.0], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15e63 or 4.5e9 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. div-sub N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. associate-/l* N/A

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

      10. *-inverses N/A

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

      11. *-rgt-identity N/A

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

      12. remove-double-neg N/A

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

      13. remove-double-neg N/A

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

      14. neg-mul-1 N/A

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

      15. remove-double-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

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

   if -2.15e63 < z < -1.2500000000000001e-34

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. associate-*r* N/A

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

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

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

      16. mul-1-neg N/A

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

      17. lower-neg.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.2500000000000001e-34 < z < 3.35e-248

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   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 80.8

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

   5. Applied rewrites 80.8%

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

   if 3.35e-248 < z < 4.5e9

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 81.3

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

   5. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(-z, a, t\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-34}:\\ \;\;\;\;\frac{y \cdot z}{\mathsf{fma}\left(a, z, -t\right)}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 4500000000:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+63)
   (/ y a)
   (if (<= z 3.35e-248)
     (/ (- x (* y z)) t)
     (if (<= z 2.1e+18) (/ x (fma (- z) a t)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+63) {
		tmp = y / a;
	} else if (z <= 3.35e-248) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.1e+18) {
		tmp = x / fma(-z, a, t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+63)
		tmp = Float64(y / a);
	elseif (z <= 3.35e-248)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 2.1e+18)
		tmp = Float64(x / fma(Float64(-z), a, t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+63], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.35e-248], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e+18], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999998e63 or 2.1e18 < z

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -7.19999999999999998e63 < z < 3.35e-248

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
   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 76.6

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

   5. Applied rewrites 76.6%

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

   if 3.35e-248 < z < 2.1e18

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 80.2

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

   5. Applied rewrites 80.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-248}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\left(-a\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-34)
   (/ y a)
   (if (<= z 1.8e-202) (/ x t) (if (<= z 4.3e-30) (/ x (* (- a) z)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-34) {
		tmp = y / a;
	} else if (z <= 1.8e-202) {
		tmp = x / t;
	} else if (z <= 4.3e-30) {
		tmp = x / (-a * z);
	} 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 <= (-1.35d-34)) then
        tmp = y / a
    else if (z <= 1.8d-202) then
        tmp = x / t
    else if (z <= 4.3d-30) then
        tmp = x / (-a * z)
    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 <= -1.35e-34) {
		tmp = y / a;
	} else if (z <= 1.8e-202) {
		tmp = x / t;
	} else if (z <= 4.3e-30) {
		tmp = x / (-a * z);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-34:
		tmp = y / a
	elif z <= 1.8e-202:
		tmp = x / t
	elif z <= 4.3e-30:
		tmp = x / (-a * z)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-34)
		tmp = Float64(y / a);
	elseif (z <= 1.8e-202)
		tmp = Float64(x / t);
	elseif (z <= 4.3e-30)
		tmp = Float64(x / Float64(Float64(-a) * z));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-34)
		tmp = y / a;
	elseif (z <= 1.8e-202)
		tmp = x / t;
	elseif (z <= 4.3e-30)
		tmp = x / (-a * z);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-34], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.8e-202], N[(x / t), $MachinePrecision], If[LessEqual[z, 4.3e-30], N[(x / N[((-a) * z), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000008e-34 or 4.29999999999999966e-30 < z

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -1.35000000000000008e-34 < z < 1.8000000000000001e-202

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 59.0

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

   5. Applied rewrites 59.0%

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

   if 1.8000000000000001e-202 < z < 4.29999999999999966e-30

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 64.2%

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

Alternative 7: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e-14)
   (/ y a)
   (if (<= z 2.1e+18) (/ x (fma (- z) a t)) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e-14) {
		tmp = y / a;
	} else if (z <= 2.1e+18) {
		tmp = x / fma(-z, a, t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e-14)
		tmp = Float64(y / a);
	elseif (z <= 2.1e+18)
		tmp = Float64(x / fma(Float64(-z), a, t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e-14], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.1e+18], N[(x / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000001e-14 or 2.1e18 < z

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 63.2

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

   5. Applied rewrites 63.2%

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

   if -3.70000000000000001e-14 < z < 2.1e18

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 73.5

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

   5. Applied rewrites 73.5%

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

Alternative 8: 54.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-34) (/ y a) (if (<= z 2.15e-45) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-34) {
		tmp = y / a;
	} else if (z <= 2.15e-45) {
		tmp = x / 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 <= (-1.35d-34)) then
        tmp = y / a
    else if (z <= 2.15d-45) then
        tmp = x / 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 <= -1.35e-34) {
		tmp = y / a;
	} else if (z <= 2.15e-45) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-34:
		tmp = y / a
	elif z <= 2.15e-45:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-34)
		tmp = Float64(y / a);
	elseif (z <= 2.15e-45)
		tmp = Float64(x / 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 <= -1.35e-34)
		tmp = y / a;
	elseif (z <= 2.15e-45)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-34], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.15e-45], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000008e-34 or 2.1499999999999999e-45 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 58.9

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

   5. Applied rewrites 58.9%

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

   if -1.35000000000000008e-34 < z < 2.1499999999999999e-45

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 54.9

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

   5. Applied rewrites 54.9%

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

Alternative 9: 35.8% 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 86.0%

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

3. Taylor expanded in z around 0

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

   1. lower-/.f64 34.1

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

5. Applied rewrites 34.1%

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

Developer Target 1: 97.2% 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 2024276 
(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))))