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

Percentage Accurate: 84.4% → 89.9%

Time: 15.4s

Alternatives: 12

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: 89.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 6.5 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1} - \frac{z \cdot y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))))
   (if (or (<= z -3.6e+121) (not (<= z 6.5e+202)))
     (/ (- y (/ x z)) a)
     (- (/ x t_1) (/ (* z y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double tmp;
	if ((z <= -3.6e+121) || !(z <= 6.5e+202)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t_1) - ((z * y) / 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 = t - (z * a)
    if ((z <= (-3.6d+121)) .or. (.not. (z <= 6.5d+202))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t_1) - ((z * y) / 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 = t - (z * a);
	double tmp;
	if ((z <= -3.6e+121) || !(z <= 6.5e+202)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t_1) - ((z * y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	tmp = 0
	if (z <= -3.6e+121) or not (z <= 6.5e+202):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t_1) - ((z * y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	tmp = 0.0
	if ((z <= -3.6e+121) || !(z <= 6.5e+202))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t_1) - Float64(Float64(z * y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	tmp = 0.0;
	if ((z <= -3.6e+121) || ~((z <= 6.5e+202)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t_1) - ((z * y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.6e+121], N[Not[LessEqual[z, 6.5e+202]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999981e121 or 6.4999999999999996e202 < z

   1. Initial program 56.5%

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

      1. *-commutative 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in x around 0 56.5%

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

   6. Taylor expanded in a around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. unsub-neg 84.3%

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

   8. Simplified 84.3%

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

   if -3.59999999999999981e121 < z < 6.4999999999999996e202

   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 0 96.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z} + \frac{x}{t - a \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 6.5 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ t_2 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 0.0118:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))) (t_2 (* z (/ (- y) t))))
   (if (<= z -2.6e+65)
     (/ y a)
     (if (<= z -3.2e+34)
       t_2
       (if (<= z -1.02e-8)
         (/ y a)
         (if (<= z -5.2e-30)
           t_1
           (if (<= z -7.2e-72)
             t_2
             (if (<= z 1.4e-76)
               (/ x t)
               (if (<= z 0.0118) t_2 (if (<= z 1.7e+33) t_1 (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -2.6e+65) {
		tmp = y / a;
	} else if (z <= -3.2e+34) {
		tmp = t_2;
	} else if (z <= -1.02e-8) {
		tmp = y / a;
	} else if (z <= -5.2e-30) {
		tmp = t_1;
	} else if (z <= -7.2e-72) {
		tmp = t_2;
	} else if (z <= 1.4e-76) {
		tmp = x / t;
	} else if (z <= 0.0118) {
		tmp = t_2;
	} else if (z <= 1.7e+33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * -a)
    t_2 = z * (-y / t)
    if (z <= (-2.6d+65)) then
        tmp = y / a
    else if (z <= (-3.2d+34)) then
        tmp = t_2
    else if (z <= (-1.02d-8)) then
        tmp = y / a
    else if (z <= (-5.2d-30)) then
        tmp = t_1
    else if (z <= (-7.2d-72)) then
        tmp = t_2
    else if (z <= 1.4d-76) then
        tmp = x / t
    else if (z <= 0.0118d0) then
        tmp = t_2
    else if (z <= 1.7d+33) then
        tmp = t_1
    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 t_1 = x / (z * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -2.6e+65) {
		tmp = y / a;
	} else if (z <= -3.2e+34) {
		tmp = t_2;
	} else if (z <= -1.02e-8) {
		tmp = y / a;
	} else if (z <= -5.2e-30) {
		tmp = t_1;
	} else if (z <= -7.2e-72) {
		tmp = t_2;
	} else if (z <= 1.4e-76) {
		tmp = x / t;
	} else if (z <= 0.0118) {
		tmp = t_2;
	} else if (z <= 1.7e+33) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	t_2 = z * (-y / t)
	tmp = 0
	if z <= -2.6e+65:
		tmp = y / a
	elif z <= -3.2e+34:
		tmp = t_2
	elif z <= -1.02e-8:
		tmp = y / a
	elif z <= -5.2e-30:
		tmp = t_1
	elif z <= -7.2e-72:
		tmp = t_2
	elif z <= 1.4e-76:
		tmp = x / t
	elif z <= 0.0118:
		tmp = t_2
	elif z <= 1.7e+33:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	t_2 = Float64(z * Float64(Float64(-y) / t))
	tmp = 0.0
	if (z <= -2.6e+65)
		tmp = Float64(y / a);
	elseif (z <= -3.2e+34)
		tmp = t_2;
	elseif (z <= -1.02e-8)
		tmp = Float64(y / a);
	elseif (z <= -5.2e-30)
		tmp = t_1;
	elseif (z <= -7.2e-72)
		tmp = t_2;
	elseif (z <= 1.4e-76)
		tmp = Float64(x / t);
	elseif (z <= 0.0118)
		tmp = t_2;
	elseif (z <= 1.7e+33)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z * -a);
	t_2 = z * (-y / t);
	tmp = 0.0;
	if (z <= -2.6e+65)
		tmp = y / a;
	elseif (z <= -3.2e+34)
		tmp = t_2;
	elseif (z <= -1.02e-8)
		tmp = y / a;
	elseif (z <= -5.2e-30)
		tmp = t_1;
	elseif (z <= -7.2e-72)
		tmp = t_2;
	elseif (z <= 1.4e-76)
		tmp = x / t;
	elseif (z <= 0.0118)
		tmp = t_2;
	elseif (z <= 1.7e+33)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+65], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.2e+34], t$95$2, If[LessEqual[z, -1.02e-8], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.2e-30], t$95$1, If[LessEqual[z, -7.2e-72], t$95$2, If[LessEqual[z, 1.4e-76], N[(x / t), $MachinePrecision], If[LessEqual[z, 0.0118], t$95$2, If[LessEqual[z, 1.7e+33], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.60000000000000003e65 or -3.1999999999999998e34 < z < -1.02000000000000003e-8 or 1.7e33 < z

   1. Initial program 70.1%

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

      1. *-commutative 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in z around inf 67.2%

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

   if -2.60000000000000003e65 < z < -3.1999999999999998e34 or -5.19999999999999973e-30 < z < -7.2e-72 or 1.40000000000000005e-76 < z < 0.0117999999999999997

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 66.7%

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

   6. Taylor expanded in x around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. associate-*r* 55.4%

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

      3. *-rgt-identity 55.4%

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

      4. times-frac 53.5%

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

      5. associate-*r/ 53.5%

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

      6. mul-1-neg 53.5%

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

      7. /-rgt-identity 53.5%

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

   8. Simplified 53.5%

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

   if -1.02000000000000003e-8 < z < -5.19999999999999973e-30 or 0.0117999999999999997 < z < 1.7e33

   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 72.3%

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

      1. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

      3. *-commutative 42.9%

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

   10. Simplified 42.9%

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

   if -7.2e-72 < z < 1.40000000000000005e-76

   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 61.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 0.0118:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ t_2 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))) (t_2 (* z (/ (- y) t))))
   (if (<= z -3.5e+58)
     (/ y a)
     (if (<= z -1.4e+39)
       t_2
       (if (<= z -2.3e-10)
         (/ y a)
         (if (<= z -6.9e-28)
           t_1
           (if (<= z -6.3e-71)
             (/ (* z (- y)) t)
             (if (<= z 5.5e-77)
               (/ x t)
               (if (<= z 3.9e-5) t_2 (if (<= z 6.4e+35) t_1 (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -3.5e+58) {
		tmp = y / a;
	} else if (z <= -1.4e+39) {
		tmp = t_2;
	} else if (z <= -2.3e-10) {
		tmp = y / a;
	} else if (z <= -6.9e-28) {
		tmp = t_1;
	} else if (z <= -6.3e-71) {
		tmp = (z * -y) / t;
	} else if (z <= 5.5e-77) {
		tmp = x / t;
	} else if (z <= 3.9e-5) {
		tmp = t_2;
	} else if (z <= 6.4e+35) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * -a)
    t_2 = z * (-y / t)
    if (z <= (-3.5d+58)) then
        tmp = y / a
    else if (z <= (-1.4d+39)) then
        tmp = t_2
    else if (z <= (-2.3d-10)) then
        tmp = y / a
    else if (z <= (-6.9d-28)) then
        tmp = t_1
    else if (z <= (-6.3d-71)) then
        tmp = (z * -y) / t
    else if (z <= 5.5d-77) then
        tmp = x / t
    else if (z <= 3.9d-5) then
        tmp = t_2
    else if (z <= 6.4d+35) then
        tmp = t_1
    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 t_1 = x / (z * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -3.5e+58) {
		tmp = y / a;
	} else if (z <= -1.4e+39) {
		tmp = t_2;
	} else if (z <= -2.3e-10) {
		tmp = y / a;
	} else if (z <= -6.9e-28) {
		tmp = t_1;
	} else if (z <= -6.3e-71) {
		tmp = (z * -y) / t;
	} else if (z <= 5.5e-77) {
		tmp = x / t;
	} else if (z <= 3.9e-5) {
		tmp = t_2;
	} else if (z <= 6.4e+35) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	t_2 = z * (-y / t)
	tmp = 0
	if z <= -3.5e+58:
		tmp = y / a
	elif z <= -1.4e+39:
		tmp = t_2
	elif z <= -2.3e-10:
		tmp = y / a
	elif z <= -6.9e-28:
		tmp = t_1
	elif z <= -6.3e-71:
		tmp = (z * -y) / t
	elif z <= 5.5e-77:
		tmp = x / t
	elif z <= 3.9e-5:
		tmp = t_2
	elif z <= 6.4e+35:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	t_2 = Float64(z * Float64(Float64(-y) / t))
	tmp = 0.0
	if (z <= -3.5e+58)
		tmp = Float64(y / a);
	elseif (z <= -1.4e+39)
		tmp = t_2;
	elseif (z <= -2.3e-10)
		tmp = Float64(y / a);
	elseif (z <= -6.9e-28)
		tmp = t_1;
	elseif (z <= -6.3e-71)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= 5.5e-77)
		tmp = Float64(x / t);
	elseif (z <= 3.9e-5)
		tmp = t_2;
	elseif (z <= 6.4e+35)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z * -a);
	t_2 = z * (-y / t);
	tmp = 0.0;
	if (z <= -3.5e+58)
		tmp = y / a;
	elseif (z <= -1.4e+39)
		tmp = t_2;
	elseif (z <= -2.3e-10)
		tmp = y / a;
	elseif (z <= -6.9e-28)
		tmp = t_1;
	elseif (z <= -6.3e-71)
		tmp = (z * -y) / t;
	elseif (z <= 5.5e-77)
		tmp = x / t;
	elseif (z <= 3.9e-5)
		tmp = t_2;
	elseif (z <= 6.4e+35)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+58], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.4e+39], t$95$2, If[LessEqual[z, -2.3e-10], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.9e-28], t$95$1, If[LessEqual[z, -6.3e-71], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.5e-77], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.9e-5], t$95$2, If[LessEqual[z, 6.4e+35], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.4999999999999997e58 or -1.40000000000000001e39 < z < -2.30000000000000007e-10 or 6.39999999999999965e35 < z

   1. Initial program 70.1%

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

      1. *-commutative 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in z around inf 67.2%

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

   if -3.4999999999999997e58 < z < -1.40000000000000001e39 or 5.49999999999999998e-77 < z < 3.8999999999999999e-5

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 70.9%

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

   6. Taylor expanded in x around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*r* 58.7%

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

      3. *-rgt-identity 58.7%

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

      4. times-frac 58.7%

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

      5. associate-*r/ 58.7%

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

      6. mul-1-neg 58.7%

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

      7. /-rgt-identity 58.7%

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

   8. Simplified 58.7%

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

   if -2.30000000000000007e-10 < z < -6.90000000000000001e-28 or 3.8999999999999999e-5 < z < 6.39999999999999965e35

   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 72.3%

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

      1. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

      3. *-commutative 42.9%

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

   10. Simplified 42.9%

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

   if -6.90000000000000001e-28 < z < -6.3000000000000003e-71

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around inf 56.3%

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

   6. Taylor expanded in x around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. associate-*r* 47.5%

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

      3. mul-1-neg 47.5%

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

   8. Simplified 47.5%

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

   if -6.3000000000000003e-71 < z < 5.49999999999999998e-77

   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 61.5%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 12600000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) t))))
   (if (<= z -4.1e+58)
     (/ y a)
     (if (<= z -3.6e-71)
       t_1
       (if (<= z 2.15e-82)
         (/ x t)
         (if (<= z 1.2e-27) t_1 (if (<= z 12600000.0) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / t);
	double tmp;
	if (z <= -4.1e+58) {
		tmp = y / a;
	} else if (z <= -3.6e-71) {
		tmp = t_1;
	} else if (z <= 2.15e-82) {
		tmp = x / t;
	} else if (z <= 1.2e-27) {
		tmp = t_1;
	} else if (z <= 12600000.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / t)
    if (z <= (-4.1d+58)) then
        tmp = y / a
    else if (z <= (-3.6d-71)) then
        tmp = t_1
    else if (z <= 2.15d-82) then
        tmp = x / t
    else if (z <= 1.2d-27) then
        tmp = t_1
    else if (z <= 12600000.0d0) 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 t_1 = z * (-y / t);
	double tmp;
	if (z <= -4.1e+58) {
		tmp = y / a;
	} else if (z <= -3.6e-71) {
		tmp = t_1;
	} else if (z <= 2.15e-82) {
		tmp = x / t;
	} else if (z <= 1.2e-27) {
		tmp = t_1;
	} else if (z <= 12600000.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / t)
	tmp = 0
	if z <= -4.1e+58:
		tmp = y / a
	elif z <= -3.6e-71:
		tmp = t_1
	elif z <= 2.15e-82:
		tmp = x / t
	elif z <= 1.2e-27:
		tmp = t_1
	elif z <= 12600000.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / t))
	tmp = 0.0
	if (z <= -4.1e+58)
		tmp = Float64(y / a);
	elseif (z <= -3.6e-71)
		tmp = t_1;
	elseif (z <= 2.15e-82)
		tmp = Float64(x / t);
	elseif (z <= 1.2e-27)
		tmp = t_1;
	elseif (z <= 12600000.0)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / t);
	tmp = 0.0;
	if (z <= -4.1e+58)
		tmp = y / a;
	elseif (z <= -3.6e-71)
		tmp = t_1;
	elseif (z <= 2.15e-82)
		tmp = x / t;
	elseif (z <= 1.2e-27)
		tmp = t_1;
	elseif (z <= 12600000.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+58], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.6e-71], t$95$1, If[LessEqual[z, 2.15e-82], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.2e-27], t$95$1, If[LessEqual[z, 12600000.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e58 or 1.26e7 < z

   1. Initial program 69.4%

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

      1. *-commutative 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around inf 65.4%

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

   if -4.1e58 < z < -3.6e-71 or 2.15000000000000009e-82 < z < 1.20000000000000001e-27

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 57.1%

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

   6. Taylor expanded in x around 0 47.7%

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

      1. associate-*r/ 47.7%

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

      2. associate-*r* 47.7%

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

      3. *-rgt-identity 47.7%

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

      4. times-frac 46.1%

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

      5. associate-*r/ 46.1%

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

      6. mul-1-neg 46.1%

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

      7. /-rgt-identity 46.1%

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

   8. Simplified 46.1%

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

   if -3.6e-71 < z < 2.15000000000000009e-82 or 1.20000000000000001e-27 < z < 1.26e7

   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 60.0%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 12600000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-12} \lor \neg \left(a \leq 5.8 \cdot 10^{+24}\right) \land a \leq 4.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e-24)
   (/ x (- t (* z a)))
   (if (or (<= a 1.35e-12) (and (not (<= a 5.8e+24)) (<= a 4.3e+72)))
     (/ (- x (* z y)) t)
     (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-24) {
		tmp = x / (t - (z * a));
	} else if ((a <= 1.35e-12) || (!(a <= 5.8e+24) && (a <= 4.3e+72))) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d-24)) then
        tmp = x / (t - (z * a))
    else if ((a <= 1.35d-12) .or. (.not. (a <= 5.8d+24)) .and. (a <= 4.3d+72)) then
        tmp = (x - (z * y)) / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-24) {
		tmp = x / (t - (z * a));
	} else if ((a <= 1.35e-12) || (!(a <= 5.8e+24) && (a <= 4.3e+72))) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e-24:
		tmp = x / (t - (z * a))
	elif (a <= 1.35e-12) or (not (a <= 5.8e+24) and (a <= 4.3e+72)):
		tmp = (x - (z * y)) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e-24)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif ((a <= 1.35e-12) || (!(a <= 5.8e+24) && (a <= 4.3e+72)))
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e-24)
		tmp = x / (t - (z * a));
	elseif ((a <= 1.35e-12) || (~((a <= 5.8e+24)) && (a <= 4.3e+72)))
		tmp = (x - (z * y)) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e-24], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.35e-12], And[N[Not[LessEqual[a, 5.8e+24]], $MachinePrecision], LessEqual[a, 4.3e+72]]], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8999999999999999e-24

   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 x around inf 63.9%

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

      1. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -2.8999999999999999e-24 < a < 1.3499999999999999e-12 or 5.79999999999999958e24 < a < 4.3000000000000001e72

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 72.7%

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

   if 1.3499999999999999e-12 < a < 5.79999999999999958e24 or 4.3000000000000001e72 < a

   1. Initial program 73.0%

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

      1. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in z around inf 63.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-12} \lor \neg \left(a \leq 5.8 \cdot 10^{+24}\right) \land a \leq 4.3 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.32e+70)
   (/ y a)
   (if (<= z -5.8e+35)
     (* z (/ (- y) t))
     (if (<= z 1.55e+33) (/ x (- t (* z a))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.32e+70) {
		tmp = y / a;
	} else if (z <= -5.8e+35) {
		tmp = z * (-y / t);
	} else if (z <= 1.55e+33) {
		tmp = x / (t - (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 <= (-1.32d+70)) then
        tmp = y / a
    else if (z <= (-5.8d+35)) then
        tmp = z * (-y / t)
    else if (z <= 1.55d+33) then
        tmp = x / (t - (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 <= -1.32e+70) {
		tmp = y / a;
	} else if (z <= -5.8e+35) {
		tmp = z * (-y / t);
	} else if (z <= 1.55e+33) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.32e+70:
		tmp = y / a
	elif z <= -5.8e+35:
		tmp = z * (-y / t)
	elif z <= 1.55e+33:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.32e+70)
		tmp = Float64(y / a);
	elseif (z <= -5.8e+35)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 1.55e+33)
		tmp = Float64(x / Float64(t - Float64(z * 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 <= -1.32e+70)
		tmp = y / a;
	elseif (z <= -5.8e+35)
		tmp = z * (-y / t);
	elseif (z <= 1.55e+33)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.32e+70], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e+35], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+33], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3199999999999999e70 or 1.55e33 < z

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 67.6%

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

   if -1.3199999999999999e70 < z < -5.79999999999999989e35

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 88.8%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. associate-*r* 83.9%

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

      3. *-rgt-identity 83.9%

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

      4. times-frac 83.9%

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

      5. associate-*r/ 83.9%

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

      6. mul-1-neg 83.9%

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

      7. /-rgt-identity 83.9%

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

   8. Simplified 83.9%

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

   if -5.79999999999999989e35 < z < 1.55e33

   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 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+121} \lor \neg \left(z \leq 6.8 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+121) (not (<= z 6.8e+202)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+121) || !(z <= 6.8e+202)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (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+121)) .or. (.not. (z <= 6.8d+202))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / (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+121) || !(z <= 6.8e+202)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+121) or not (z <= 6.8e+202):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+121) || !(z <= 6.8e+202))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / 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+121) || ~((z <= 6.8e+202)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+121], N[Not[LessEqual[z, 6.8e+202]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999998e121 or 6.8e202 < z

   1. Initial program 56.5%

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

      1. *-commutative 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in x around 0 56.5%

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

   6. Taylor expanded in a around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. unsub-neg 84.3%

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

   8. Simplified 84.3%

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

   if -5.7999999999999998e121 < z < 6.8e202

   1. Initial program 96.6%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+121} \lor \neg \left(z \leq 6.8 \cdot 10^{+202}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-56} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e-56) (not (<= t 8.2e+45)))
   (- (/ x t) (* y (/ z t)))
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-56) || !(t <= 8.2e+45)) {
		tmp = (x / t) - (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 <= (-4.6d-56)) .or. (.not. (t <= 8.2d+45))) then
        tmp = (x / t) - (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 <= -4.6e-56) || !(t <= 8.2e+45)) {
		tmp = (x / t) - (y * (z / t));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e-56) or not (t <= 8.2e+45):
		tmp = (x / t) - (y * (z / t))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e-56) || !(t <= 8.2e+45))
		tmp = Float64(Float64(x / t) - Float64(y * Float64(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 <= -4.6e-56) || ~((t <= 8.2e+45)))
		tmp = (x / t) - (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, -4.6e-56], N[Not[LessEqual[t, 8.2e+45]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.60000000000000005e-56 or 8.20000000000000025e45 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in x around 0 83.3%

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

   6. Taylor expanded in a around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. neg-mul-1 65.8%

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

      3. sub-neg 65.8%

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

      4. *-lft-identity 65.8%

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

      5. times-frac 67.6%

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

      6. /-rgt-identity 67.6%

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

   8. Simplified 67.6%

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

   if -4.60000000000000005e-56 < t < 8.20000000000000025e45

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around 0 88.2%

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

   6. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-56} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{t} + \frac{-1}{\frac{\frac{t}{z}}{y}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e-56)
   (+ (/ x t) (/ -1.0 (/ (/ t z) y)))
   (if (<= t 4.6e+45) (/ (- y (/ x z)) a) (- (/ x t) (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e-56) {
		tmp = (x / t) + (-1.0 / ((t / z) / y));
	} else if (t <= 4.6e+45) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (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 (t <= (-5.6d-56)) then
        tmp = (x / t) + ((-1.0d0) / ((t / z) / y))
    else if (t <= 4.6d+45) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t) - (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 (t <= -5.6e-56) {
		tmp = (x / t) + (-1.0 / ((t / z) / y));
	} else if (t <= 4.6e+45) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e-56:
		tmp = (x / t) + (-1.0 / ((t / z) / y))
	elif t <= 4.6e+45:
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t) - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e-56)
		tmp = Float64(Float64(x / t) + Float64(-1.0 / Float64(Float64(t / z) / y)));
	elseif (t <= 4.6e+45)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t) - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e-56)
		tmp = (x / t) + (-1.0 / ((t / z) / y));
	elseif (t <= 4.6e+45)
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t) - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e-56], N[(N[(x / t), $MachinePrecision] + N[(-1.0 / N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+45], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999986e-56

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in x around 0 86.3%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. neg-mul-1 69.0%

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

      3. sub-neg 69.0%

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

      4. associate-/l* 70.2%

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

   8. Simplified 70.2%

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

      1. clear-num 70.3%

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

      2. inv-pow 70.3%

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

      3. associate-/l/ 69.0%

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

      4. *-commutative 69.0%

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

   10. Applied egg-rr 69.0%

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

       1. unpow-1 69.0%

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

       2. associate-/r* 70.3%

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

   12. Simplified 70.3%

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

   if -5.59999999999999986e-56 < t < 4.60000000000000025e45

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around 0 88.2%

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

   6. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

   if 4.60000000000000025e45 < t

   1. Initial program 79.2%

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

      1. *-commutative 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in x around 0 79.2%

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

   6. Taylor expanded in a around 0 61.4%

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

      1. +-commutative 61.4%

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

      2. neg-mul-1 61.4%

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

      3. sub-neg 61.4%

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

      4. *-lft-identity 61.4%

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

      5. times-frac 64.0%

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

      6. /-rgt-identity 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{t} + \frac{-1}{\frac{\frac{t}{z}}{y}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-56} \lor \neg \left(t \leq 2 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e-56) (not (<= t 2e+47)))
   (/ (- x (* z y)) t)
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-56) || !(t <= 2e+47)) {
		tmp = (x - (z * y)) / 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 <= (-4d-56)) .or. (.not. (t <= 2d+47))) then
        tmp = (x - (z * y)) / 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 <= -4e-56) || !(t <= 2e+47)) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e-56) or not (t <= 2e+47):
		tmp = (x - (z * y)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e-56) || !(t <= 2e+47))
		tmp = Float64(Float64(x - Float64(z * y)) / 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 <= -4e-56) || ~((t <= 2e+47)))
		tmp = (x - (z * y)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e-56], N[Not[LessEqual[t, 2e+47]], $MachinePrecision]], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000002e-56 or 2.0000000000000001e47 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in t around inf 65.8%

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

   if -4.0000000000000002e-56 < t < 2.0000000000000001e47

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around 0 88.2%

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

   6. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-56} \lor \neg \left(t \leq 2 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-73} \lor \neg \left(z \leq 17500000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.55e-73) (not (<= z 17500000000000.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e-73) || !(z <= 17500000000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.55d-73)) .or. (.not. (z <= 17500000000000.0d0))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e-73) || !(z <= 17500000000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.55e-73) or not (z <= 17500000000000.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.55e-73) || !(z <= 17500000000000.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.55e-73) || ~((z <= 17500000000000.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.55e-73], N[Not[LessEqual[z, 17500000000000.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.55e-73 or 1.75e13 < z

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in z around inf 57.4%

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

   if -2.55e-73 < z < 1.75e13

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 55.0%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-73} \lor \neg \left(z \leq 17500000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.5% 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 85.8%

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

   1. *-commutative 85.8%

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

3. Simplified 85.8%

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

5. Taylor expanded in z around 0 28.5%

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

6. Final simplification 28.5%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.1% 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 2024019 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))