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

Percentage Accurate: 84.4% → 97.0%

Time: 12.5s

Alternatives: 10

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% 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: 97.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - z \cdot a\\ t_3 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\frac{t\_1}{z}}{\frac{t}{z} - a}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (- t (* z a))) (t_3 (/ t_1 t_2)))
   (if (<= t_3 (- INFINITY))
     (* y (+ (/ z (- (* z a) t)) (/ x (* y t_2))))
     (if (<= t_3 -5e-324)
       t_3
       (if (<= t_3 0.0)
         (/ (/ t_1 z) (- (/ t z) a))
         (if (<= t_3 INFINITY) t_3 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = t_1 / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	} else if (t_3 <= -5e-324) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t_1 / z) / ((t / z) - a);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = t_1 / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	} else if (t_3 <= -5e-324) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t_1 / z) / ((t / z) - a);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * z)
	t_2 = t - (z * a)
	t_3 = t_1 / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_2)))
	elif t_3 <= -5e-324:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (t_1 / z) / ((t / z) - a)
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_2))));
	elseif (t_3 <= -5e-324)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(t_1 / z) / Float64(Float64(t / z) - a));
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * z);
	t_2 = t - (z * a);
	t_3 = t_1 / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	elseif (t_3 <= -5e-324)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (t_1 / z) / ((t / z) - a);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y * N[(N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-324], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(t$95$1 / z), $MachinePrecision] / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 62.4%

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

      1. *-commutative 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 99.9%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.94066e-324 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 98.2%

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

   if -4.94066e-324 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 62.6%

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

      1. *-commutative 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in z around inf 62.6%

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

      1. div-sub 62.6%

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

   7. Applied egg-rr 62.6%

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

      1. div-sub 62.6%

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

      2. associate-/r* 100.0%

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

   9. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{z}}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{a \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+150)
   (/ y a)
   (if (<= z -3.45e+28)
     (* y (/ (- z) t))
     (if (<= z 4.1e-141)
       (/ x t)
       (if (<= z 1.35e-46) (/ x (* a (- z))) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+150) {
		tmp = y / a;
	} else if (z <= -3.45e+28) {
		tmp = y * (-z / t);
	} else if (z <= 4.1e-141) {
		tmp = x / t;
	} else if (z <= 1.35e-46) {
		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 <= (-1.9d+150)) then
        tmp = y / a
    else if (z <= (-3.45d+28)) then
        tmp = y * (-z / t)
    else if (z <= 4.1d-141) then
        tmp = x / t
    else if (z <= 1.35d-46) 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 <= -1.9e+150) {
		tmp = y / a;
	} else if (z <= -3.45e+28) {
		tmp = y * (-z / t);
	} else if (z <= 4.1e-141) {
		tmp = x / t;
	} else if (z <= 1.35e-46) {
		tmp = x / (a * -z);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+150:
		tmp = y / a
	elif z <= -3.45e+28:
		tmp = y * (-z / t)
	elif z <= 4.1e-141:
		tmp = x / t
	elif z <= 1.35e-46:
		tmp = x / (a * -z)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+150)
		tmp = Float64(y / a);
	elseif (z <= -3.45e+28)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 4.1e-141)
		tmp = Float64(x / t);
	elseif (z <= 1.35e-46)
		tmp = Float64(x / Float64(a * Float64(-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 <= -1.9e+150)
		tmp = y / a;
	elseif (z <= -3.45e+28)
		tmp = y * (-z / t);
	elseif (z <= 4.1e-141)
		tmp = x / t;
	elseif (z <= 1.35e-46)
		tmp = x / (a * -z);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+150], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.45e+28], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-141], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.35e-46], N[(x / N[(a * (-z)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.89999999999999995e150 or 1.35e-46 < z

   1. Initial program 71.0%

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

      1. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 60.4%

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

   if -1.89999999999999995e150 < z < -3.45e28

   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 t around inf 61.9%

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

      1. *-commutative 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in x around -inf 57.0%

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

      1. associate-*r* 57.0%

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

      2. neg-mul-1 57.0%

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

      3. associate-/l* 56.5%

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

      4. *-commutative 56.5%

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

   10. Simplified 56.5%

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

   11. Taylor expanded in x around 0 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-/l* 53.2%

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

       3. distribute-rgt-neg-in 53.2%

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

       4. distribute-neg-frac2 53.2%

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

   13. Simplified 53.2%

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

   if -3.45e28 < z < 4.10000000000000002e-141

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 57.7%

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

   if 4.10000000000000002e-141 < z < 1.35e-46

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 63.9%

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

   6. Taylor expanded in t around 0 46.3%

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

      1. associate-*r/ 46.3%

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

      2. mul-1-neg 46.3%

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

      3. *-commutative 46.3%

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

   8. Simplified 46.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{a \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z)))))
   (if (<= z -3.1e+60)
     t_1
     (if (<= z -2.2e-122)
       (/ (- x (* y z)) t)
       (if (<= z 2.2e-54) (/ x (- t (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double tmp;
	if (z <= -3.1e+60) {
		tmp = t_1;
	} else if (z <= -2.2e-122) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.2e-54) {
		tmp = x / (t - (z * a));
	} 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 / (a - (t / z))
    if (z <= (-3.1d+60)) then
        tmp = t_1
    else if (z <= (-2.2d-122)) then
        tmp = (x - (y * z)) / t
    else if (z <= 2.2d-54) then
        tmp = x / (t - (z * a))
    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 / (a - (t / z));
	double tmp;
	if (z <= -3.1e+60) {
		tmp = t_1;
	} else if (z <= -2.2e-122) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.2e-54) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - (t / z))
	tmp = 0
	if z <= -3.1e+60:
		tmp = t_1
	elif z <= -2.2e-122:
		tmp = (x - (y * z)) / t
	elif z <= 2.2e-54:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -3.1e+60)
		tmp = t_1;
	elseif (z <= -2.2e-122)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 2.2e-54)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -3.1e+60)
		tmp = t_1;
	elseif (z <= -2.2e-122)
		tmp = (x - (y * z)) / t;
	elseif (z <= 2.2e-54)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+60], t$95$1, If[LessEqual[z, -2.2e-122], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.2e-54], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000001e60 or 2.2e-54 < z

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 73.1%

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

   6. Taylor expanded in x around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   8. Simplified 78.7%

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

   if -3.1000000000000001e60 < z < -2.2e-122

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 79.0%

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

      1. *-commutative 79.0%

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

   7. Simplified 79.0%

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

   if -2.2e-122 < z < 2.2e-54

   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 x around inf 76.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+176}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+114}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+176)
   (/ (- y (/ x z)) a)
   (if (<= z 3.9e+114) (/ (- x (* y z)) (- t (* z a))) (/ y (- a (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+176) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 3.9e+114) {
		tmp = (x - (y * z)) / (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 (z <= (-7d+176)) then
        tmp = (y - (x / z)) / a
    else if (z <= 3.9d+114) then
        tmp = (x - (y * z)) / (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 (z <= -7e+176) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 3.9e+114) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+176:
		tmp = (y - (x / z)) / a
	elif z <= 3.9e+114:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+176)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (z <= 3.9e+114)
		tmp = Float64(Float64(x - Float64(y * z)) / 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 (z <= -7e+176)
		tmp = (y - (x / z)) / a;
	elseif (z <= 3.9e+114)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+176], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 3.9e+114], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000005e176

   1. Initial program 44.3%

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

      1. *-commutative 44.3%

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

   3. Simplified 44.3%

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

   5. Taylor expanded in z around inf 44.3%

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

      1. div-sub 44.3%

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

   7. Applied egg-rr 44.3%

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

      1. div-sub 44.3%

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

      2. associate-/r* 72.5%

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

   9. Simplified 72.5%

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

   10. Taylor expanded in t around 0 42.9%

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

       1. mul-1-neg 42.9%

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

       2. sub-neg 42.9%

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

       3. remove-double-neg 42.9%

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

       4. distribute-neg-in 42.9%

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

       5. +-commutative 42.9%

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

       6. sub-neg 42.9%

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

       7. *-commutative 42.9%

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

       8. distribute-frac-neg 42.9%

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

       9. remove-double-neg 42.9%

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

       10. associate-/r* 71.0%

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

       11. div-sub 71.0%

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

       12. associate-/l* 98.6%

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

       13. *-inverses 98.6%

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

       14. *-rgt-identity 98.6%

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

   12. Simplified 98.6%

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

   if -7.00000000000000005e176 < z < 3.9000000000000001e114

   1. Initial program 97.8%

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

   if 3.9000000000000001e114 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 61.4%

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

   6. Taylor expanded in x around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. neg-mul-1 80.0%

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

   8. Simplified 80.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+176}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+114}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+150)
   (/ y a)
   (if (<= z -3.3e+29)
     (* y (/ (- z) t))
     (if (<= z 4.1e-141) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+150) {
		tmp = y / a;
	} else if (z <= -3.3e+29) {
		tmp = y * (-z / t);
	} else if (z <= 4.1e-141) {
		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 <= (-1.9d+150)) then
        tmp = y / a
    else if (z <= (-3.3d+29)) then
        tmp = y * (-z / t)
    else if (z <= 4.1d-141) 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 <= -1.9e+150) {
		tmp = y / a;
	} else if (z <= -3.3e+29) {
		tmp = y * (-z / t);
	} else if (z <= 4.1e-141) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+150:
		tmp = y / a
	elif z <= -3.3e+29:
		tmp = y * (-z / t)
	elif z <= 4.1e-141:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+150)
		tmp = Float64(y / a);
	elseif (z <= -3.3e+29)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 4.1e-141)
		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 <= -1.9e+150)
		tmp = y / a;
	elseif (z <= -3.3e+29)
		tmp = y * (-z / t);
	elseif (z <= 4.1e-141)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+150], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.3e+29], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-141], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999995e150 or 4.10000000000000002e-141 < z

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 53.9%

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

   if -1.89999999999999995e150 < z < -3.29999999999999984e29

   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 t around inf 61.9%

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

      1. *-commutative 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in x around -inf 57.0%

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

      1. associate-*r* 57.0%

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

      2. neg-mul-1 57.0%

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

      3. associate-/l* 56.5%

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

      4. *-commutative 56.5%

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

   10. Simplified 56.5%

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

   11. Taylor expanded in x around 0 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-/l* 53.2%

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

       3. distribute-rgt-neg-in 53.2%

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

       4. distribute-neg-frac2 53.2%

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

   13. Simplified 53.2%

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

   if -3.29999999999999984e29 < z < 4.10000000000000002e-141

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 57.7%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+19} \lor \neg \left(t \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+19) (not (<= t 5.2e+127)))
   (/ (- x (* y z)) t)
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+19) || !(t <= 5.2e+127)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / 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 ((t <= (-2.5d+19)) .or. (.not. (t <= 5.2d+127))) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y - (x / 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 ((t <= -2.5e+19) || !(t <= 5.2e+127)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+19) or not (t <= 5.2e+127):
		tmp = (x - (y * z)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+19) || !(t <= 5.2e+127))
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+19) || ~((t <= 5.2e+127)))
		tmp = (x - (y * z)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+19], N[Not[LessEqual[t, 5.2e+127]], $MachinePrecision]], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e19 or 5.2000000000000004e127 < t

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in t around inf 79.2%

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

      1. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   if -2.5e19 < t < 5.2000000000000004e127

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 87.5%

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

      1. div-sub 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. div-sub 87.5%

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

      2. associate-/r* 85.3%

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

   9. Simplified 85.3%

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

   10. Taylor expanded in t around 0 63.5%

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

       1. mul-1-neg 63.5%

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

       2. sub-neg 63.5%

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

       3. remove-double-neg 63.5%

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

       4. distribute-neg-in 63.5%

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

       5. +-commutative 63.5%

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

       6. sub-neg 63.5%

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

       7. *-commutative 63.5%

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

       8. distribute-frac-neg 63.5%

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

       9. remove-double-neg 63.5%

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

       10. associate-/r* 64.4%

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

       11. div-sub 64.4%

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

       12. associate-/l* 70.5%

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

       13. *-inverses 70.5%

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

       14. *-rgt-identity 70.5%

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

   12. Simplified 70.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+19} \lor \neg \left(t \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+118} \lor \neg \left(z \leq 5.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+118) (not (<= z 5.5e+67))) (/ y a) (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+118) || !(z <= 5.5e+67)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / 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 <= (-4.8d+118)) .or. (.not. (z <= 5.5d+67))) then
        tmp = y / a
    else
        tmp = (x - (y * z)) / 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 <= -4.8e+118) || !(z <= 5.5e+67)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+118) or not (z <= 5.5e+67):
		tmp = y / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+118) || !(z <= 5.5e+67))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+118) || ~((z <= 5.5e+67)))
		tmp = y / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+118], N[Not[LessEqual[z, 5.5e+67]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e118 or 5.49999999999999968e67 < z

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 65.6%

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

   if -4.8e118 < z < 5.49999999999999968e67

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 70.3%

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

      1. *-commutative 70.3%

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

   7. Simplified 70.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+118} \lor \neg \left(z \leq 5.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+69} \lor \neg \left(z \leq 4.8 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.72e+69) (not (<= z 4.8e-25))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.72e+69) || !(z <= 4.8e-25)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.72d+69)) .or. (.not. (z <= 4.8d-25))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.72e+69) || !(z <= 4.8e-25)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.72e+69) or not (z <= 4.8e-25):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.72e+69) || !(z <= 4.8e-25))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.72e+69) || ~((z <= 4.8e-25)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.72e+69], N[Not[LessEqual[z, 4.8e-25]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.72e69 or 4.80000000000000018e-25 < z

   1. Initial program 71.3%

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

      1. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in z around inf 58.9%

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

   if -1.72e69 < z < 4.80000000000000018e-25

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 67.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+69} \lor \neg \left(z \leq 4.8 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+27} \lor \neg \left(z \leq 4.1 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+27) (not (<= z 4.1e-141))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+27) || !(z <= 4.1e-141)) {
		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 <= (-5.5d+27)) .or. (.not. (z <= 4.1d-141))) 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 <= -5.5e+27) || !(z <= 4.1e-141)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+27) or not (z <= 4.1e-141):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+27) || !(z <= 4.1e-141))
		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 <= -5.5e+27) || ~((z <= 4.1e-141)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+27], N[Not[LessEqual[z, 4.1e-141]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999966e27 or 4.10000000000000002e-141 < z

   1. Initial program 78.2%

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

      1. *-commutative 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in z around inf 50.8%

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

   if -5.49999999999999966e27 < z < 4.10000000000000002e-141

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.2%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+27} \lor \neg \left(z \leq 4.1 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.2% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. *-commutative 87.0%

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

3. Simplified 87.0%

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

5. Taylor expanded in z around 0 33.4%

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

Developer Target 1: 97.2% 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 2024148 
(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))))