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

Percentage Accurate: 84.8% → 97.6%

Time: 10.8s

Alternatives: 10

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-313}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* y (+ (/ z (- (* z a) t)) (/ x (* y t_1))))
     (if (<= t_2 -1e-313)
       t_2
       (if (<= t_2 0.0)
         (/ -1.0 (* z (/ (- (/ t z) a) (- (* y z) x))))
         (if (<= t_2 2e+297) t_2 (/ y (- a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -1e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -1e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (y * z)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)))
	elif t_2 <= -1e-313:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)))
	elif t_2 <= 2e+297:
		tmp = t_2
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_1))));
	elseif (t_2 <= -1e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(Float64(t / z) - a) / Float64(Float64(y * z) - x))));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	elseif (t_2 <= -1e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-313], t$95$2, If[LessEqual[t$95$2, 0.0], N[(-1.0 / N[(z * N[(N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+297], t$95$2, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000001e-313 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2e297

   1. Initial program 99.7%

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

   if -1.00000000001e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 53.8%

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

      1. *-commutative 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf 53.8%

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

      1. clear-num 53.8%

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

      2. inv-pow 53.8%

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

   7. Applied egg-rr 53.8%

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

      1. unpow-1 53.8%

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

      2. associate-/l* 99.1%

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

      3. *-commutative 99.1%

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

   9. Simplified 99.1%

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

   if 2e297 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 27.1%

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

      1. *-commutative 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in z around inf 27.1%

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

   6. Taylor expanded in x around 0 95.2%

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

      1. associate-*r/ 95.2%

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

      2. mul-1-neg 95.2%

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

   8. Simplified 95.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-313}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-313}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -1e-313)
     t_1
     (if (<= t_1 0.0)
       (/ -1.0 (* z (/ (- (/ t z) a) (- (* y z) x))))
       (if (<= t_1 2e+297) t_1 (/ y (- a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -1e-313) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= (-1d-313)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (-1.0d0) / (z * (((t / z) - a) / ((y * z) - x)))
    else if (t_1 <= 2d+297) then
        tmp = t_1
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -1e-313) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -1e-313:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)))
	elif t_1 <= 2e+297:
		tmp = t_1
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -1e-313)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(Float64(t / z) - a) / Float64(Float64(y * z) - x))));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -1e-313)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-313], t$95$1, If[LessEqual[t$95$1, 0.0], N[(-1.0 / N[(z * N[(N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$1, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000001e-313 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2e297

   1. Initial program 96.5%

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

   if -1.00000000001e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 53.8%

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

      1. *-commutative 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf 53.8%

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

      1. clear-num 53.8%

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

      2. inv-pow 53.8%

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

   7. Applied egg-rr 53.8%

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

      1. unpow-1 53.8%

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

      2. associate-/l* 99.1%

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

      3. *-commutative 99.1%

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

   9. Simplified 99.1%

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

   if 2e297 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 27.1%

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

      1. *-commutative 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in z around inf 27.1%

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

   6. Taylor expanded in x around 0 95.2%

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

      1. associate-*r/ 95.2%

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

      2. mul-1-neg 95.2%

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

   8. Simplified 95.2%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-313}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-313}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{t}{z} - a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -1e-313)
     t_1
     (if (<= t_1 0.0)
       (/ (/ x z) (- (/ t z) a))
       (if (<= t_1 2e+297) t_1 (/ y (- a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -1e-313) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x / z) / ((t / z) - a);
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= (-1d-313)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (x / z) / ((t / z) - a)
    else if (t_1 <= 2d+297) then
        tmp = t_1
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -1e-313) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x / z) / ((t / z) - a);
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -1e-313:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (x / z) / ((t / z) - a)
	elif t_1 <= 2e+297:
		tmp = t_1
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -1e-313)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x / z) / Float64(Float64(t / z) - a));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -1e-313)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (x / z) / ((t / z) - a);
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-313], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(x / z), $MachinePrecision] / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$1, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000001e-313 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2e297

   1. Initial program 96.5%

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

   if -1.00000000001e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 53.8%

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

      1. *-commutative 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf 53.8%

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

   6. Taylor expanded in x around inf 53.8%

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

      1. associate-/r* 85.3%

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

   8. Simplified 85.3%

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

   if 2e297 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 27.1%

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

      1. *-commutative 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in z around inf 27.1%

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

   6. Taylor expanded in x around 0 95.2%

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

      1. associate-*r/ 95.2%

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

      2. mul-1-neg 95.2%

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

   8. Simplified 95.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-313}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.32e+61)
   (/ y a)
   (if (<= z 6.2e-115)
     (/ x t)
     (if (<= z 1.34e+101) (/ (/ (- x) a) z) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.32e+61) {
		tmp = y / a;
	} else if (z <= 6.2e-115) {
		tmp = x / t;
	} else if (z <= 1.34e+101) {
		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 <= (-2.32d+61)) then
        tmp = y / a
    else if (z <= 6.2d-115) then
        tmp = x / t
    else if (z <= 1.34d+101) 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 <= -2.32e+61) {
		tmp = y / a;
	} else if (z <= 6.2e-115) {
		tmp = x / t;
	} else if (z <= 1.34e+101) {
		tmp = (-x / a) / z;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.32e+61:
		tmp = y / a
	elif z <= 6.2e-115:
		tmp = x / t
	elif z <= 1.34e+101:
		tmp = (-x / a) / z
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.32e+61)
		tmp = Float64(y / a);
	elseif (z <= 6.2e-115)
		tmp = Float64(x / t);
	elseif (z <= 1.34e+101)
		tmp = Float64(Float64(Float64(-x) / 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 <= -2.32e+61)
		tmp = y / a;
	elseif (z <= 6.2e-115)
		tmp = x / t;
	elseif (z <= 1.34e+101)
		tmp = (-x / a) / z;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.32e+61], N[(y / a), $MachinePrecision], If[LessEqual[z, 6.2e-115], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.34e+101], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.32e61 or 1.3399999999999999e101 < z

   1. Initial program 58.2%

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

      1. *-commutative 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in z around inf 55.2%

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

   if -2.32e61 < z < 6.20000000000000013e-115

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

   if 6.20000000000000013e-115 < z < 1.3399999999999999e101

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around -inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. *-commutative 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in a around -inf 56.0%

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

      1. associate-/l* 51.9%

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

   10. Simplified 51.9%

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

   11. Taylor expanded in y around 0 36.0%

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

       1. associate-/r* 37.1%

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

   13. Simplified 37.1%

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

       1. associate-*r/ 41.1%

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

       2. frac-2neg 41.1%

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

       3. metadata-eval 41.1%

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

       4. un-div-inv 41.2%

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

   15. Applied egg-rr 41.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+61)
   (/ y a)
   (if (<= z 1.1e-115)
     (/ x t)
     (if (<= z 2.15e+135) (/ x (* z (- a))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+61) {
		tmp = y / a;
	} else if (z <= 1.1e-115) {
		tmp = x / t;
	} else if (z <= 2.15e+135) {
		tmp = x / (z * -a);
	} 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 <= (-2.7d+61)) then
        tmp = y / a
    else if (z <= 1.1d-115) then
        tmp = x / t
    else if (z <= 2.15d+135) then
        tmp = x / (z * -a)
    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 <= -2.7e+61) {
		tmp = y / a;
	} else if (z <= 1.1e-115) {
		tmp = x / t;
	} else if (z <= 2.15e+135) {
		tmp = x / (z * -a);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+61:
		tmp = y / a
	elif z <= 1.1e-115:
		tmp = x / t
	elif z <= 2.15e+135:
		tmp = x / (z * -a)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+61)
		tmp = Float64(y / a);
	elseif (z <= 1.1e-115)
		tmp = Float64(x / t);
	elseif (z <= 2.15e+135)
		tmp = Float64(x / Float64(z * Float64(-a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+61)
		tmp = y / a;
	elseif (z <= 1.1e-115)
		tmp = x / t;
	elseif (z <= 2.15e+135)
		tmp = x / (z * -a);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+61], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.1e-115], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.15e+135], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000002e61 or 2.14999999999999986e135 < z

   1. Initial program 57.5%

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

      1. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in z around inf 56.7%

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

   if -2.7000000000000002e61 < z < 1.1e-115

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

   if 1.1e-115 < z < 2.14999999999999986e135

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in a around -inf 58.7%

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

      1. associate-/l* 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in x around inf 37.5%

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

       1. associate-*r/ 37.5%

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

       2. neg-mul-1 37.5%

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

       3. *-commutative 37.5%

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

   13. Simplified 37.5%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-45} \lor \neg \left(x \leq 9.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.5e-45) (not (<= x 9.8e+22)))
   (/ x (- t (* z a)))
   (/ y (- a (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.5e-45) || !(x <= 9.8e+22)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / (a - (t / 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 ((x <= (-1.5d-45)) .or. (.not. (x <= 9.8d+22))) then
        tmp = x / (t - (z * a))
    else
        tmp = y / (a - (t / 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 ((x <= -1.5e-45) || !(x <= 9.8e+22)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.5e-45) or not (x <= 9.8e+22):
		tmp = x / (t - (z * a))
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.5e-45) || !(x <= 9.8e+22))
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.5e-45) || ~((x <= 9.8e+22)))
		tmp = x / (t - (z * a));
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.5e-45], N[Not[LessEqual[x, 9.8e+22]], $MachinePrecision]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000005e-45 or 9.79999999999999958e22 < x

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around inf 75.5%

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

   if -1.50000000000000005e-45 < x < 9.79999999999999958e22

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 78.6%

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

   6. Taylor expanded in x around 0 76.4%

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

      1. associate-*r/ 76.4%

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

      2. mul-1-neg 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-45} \lor \neg \left(x \leq 9.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+83} \lor \neg \left(y \leq 6.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.1e+83) (not (<= y 6.2e-30)))
   (/ (- x (* y z)) t)
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+83) || !(y <= 6.2e-30)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.1d+83)) .or. (.not. (y <= 6.2d-30))) then
        tmp = (x - (y * z)) / t
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+83) || !(y <= 6.2e-30)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.1e+83) or not (y <= 6.2e-30):
		tmp = (x - (y * z)) / t
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.1e+83) || !(y <= 6.2e-30))
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.1e+83) || ~((y <= 6.2e-30)))
		tmp = (x - (y * z)) / t;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.1e+83], N[Not[LessEqual[y, 6.2e-30]], $MachinePrecision]], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1000000000000001e83 or 6.19999999999999982e-30 < y

   1. Initial program 77.1%

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

      1. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in t around inf 57.3%

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

      1. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   if -4.1000000000000001e83 < y < 6.19999999999999982e-30

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 76.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+83} \lor \neg \left(y \leq 6.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+78} \lor \neg \left(z \leq 3.2 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+78) (not (<= z 3.2e+136))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+78) || !(z <= 3.2e+136)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d+78)) .or. (.not. (z <= 3.2d+136))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+78) || !(z <= 3.2e+136)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+78) or not (z <= 3.2e+136):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+78) || !(z <= 3.2e+136))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+78) || ~((z <= 3.2e+136)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+78], N[Not[LessEqual[z, 3.2e+136]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000034e78 or 3.19999999999999988e136 < z

   1. Initial program 56.3%

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

      1. *-commutative 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in z around inf 58.1%

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

   if -5.80000000000000034e78 < z < 3.19999999999999988e136

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 66.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+78} \lor \neg \left(z \leq 3.2 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+62} \lor \neg \left(z \leq 6.9 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+62) (not (<= z 6.9e-115))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+62) || !(z <= 6.9e-115)) {
		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+62)) .or. (.not. (z <= 6.9d-115))) 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+62) || !(z <= 6.9e-115)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+62) or not (z <= 6.9e-115):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+62) || !(z <= 6.9e-115))
		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+62) || ~((z <= 6.9e-115)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+62], N[Not[LessEqual[z, 6.9e-115]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000014e62 or 6.89999999999999999e-115 < z

   1. Initial program 72.5%

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

      1. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in z around inf 43.4%

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

   if -4.00000000000000014e62 < z < 6.89999999999999999e-115

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+62} \lor \neg \left(z \leq 6.9 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.6%

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

   1. *-commutative 85.6%

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

3. Simplified 85.6%

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

5. Taylor expanded in z around 0 35.9%

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

Developer Target 1: 97.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(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))))