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

Percentage Accurate: 85.6% → 96.4%

Time: 15.5s

Alternatives: 11

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: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - z \cdot a\\ t_3 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-306}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{z}{y \cdot z - x} + \frac{t}{t\_1 \cdot a}\right)}\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+285}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{x}{y \cdot t\_2} - \frac{z}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (- t (* z a))) (t_3 (/ t_1 t_2)))
   (if (<= t_3 -4e-306)
     t_3
     (if (<= t_3 0.0)
       (/ 1.0 (* a (+ (/ z (- (* y z) x)) (/ t (* t_1 a)))))
       (if (<= t_3 4e+285)
         t_3
         (if (<= t_3 INFINITY)
           (* y (- (/ x (* y t_2)) (/ z t_2)))
           (/ 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 <= -4e-306) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = 1.0 / (a * ((z / ((y * z) - x)) + (t / (t_1 * a))));
	} else if (t_3 <= 4e+285) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = y * ((x / (y * t_2)) - (z / t_2));
	} 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 <= -4e-306) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = 1.0 / (a * ((z / ((y * z) - x)) + (t / (t_1 * a))));
	} else if (t_3 <= 4e+285) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = y * ((x / (y * t_2)) - (z / t_2));
	} 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 <= -4e-306:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = 1.0 / (a * ((z / ((y * z) - x)) + (t / (t_1 * a))))
	elif t_3 <= 4e+285:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = y * ((x / (y * t_2)) - (z / t_2))
	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 <= -4e-306)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(1.0 / Float64(a * Float64(Float64(z / Float64(Float64(y * z) - x)) + Float64(t / Float64(t_1 * a)))));
	elseif (t_3 <= 4e+285)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(y * Float64(Float64(x / Float64(y * t_2)) - Float64(z / t_2)));
	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 <= -4e-306)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = 1.0 / (a * ((z / ((y * z) - x)) + (t / (t_1 * a))));
	elseif (t_3 <= 4e+285)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = y * ((x / (y * t_2)) - (z / t_2));
	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, -4e-306], t$95$3, If[LessEqual[t$95$3, 0.0], N[(1.0 / N[(a * N[(N[(z / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(t / N[(t$95$1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+285], t$95$3, If[LessEqual[t$95$3, Infinity], N[(y * N[(N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.00000000000000011e-306 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 3.9999999999999999e285

   1. Initial program 97.6%

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

   if -4.00000000000000011e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

      1. clear-num 60.5%

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

      2. inv-pow 60.5%

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

      3. sub-neg 60.5%

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

      4. +-commutative 60.5%

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

      5. *-commutative 60.5%

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

      6. distribute-rgt-neg-in 60.5%

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

      7. fma-define 60.5%

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

   6. Applied egg-rr 60.5%

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

      1. unpow-1 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in a around inf 99.5%

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

   if 3.9999999999999999e285 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 41.3%

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

      1. *-commutative 41.3%

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

   3. Simplified 41.3%

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

   5. Taylor expanded in y around inf 99.8%

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

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

   1. 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 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-306}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{z}{y \cdot z - x} + \frac{t}{\left(x - y \cdot z\right) \cdot a}\right)}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 4 \cdot 10^{+285}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{x}{y \cdot \left(t - z \cdot a\right)} - \frac{z}{t - z \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-t}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- t)))))
   (if (<= z -3.9e-27)
     (/ y a)
     (if (<= z -9.2e-39)
       (/ x t)
       (if (<= z -2.3e-60)
         (/ x (* z (- a)))
         (if (<= z -2.25e-88)
           t_1
           (if (<= z 1.32e-28) (/ x t) (if (<= z 2.5e+40) t_1 (/ 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 <= -3.9e-27) {
		tmp = y / a;
	} else if (z <= -9.2e-39) {
		tmp = x / t;
	} else if (z <= -2.3e-60) {
		tmp = x / (z * -a);
	} else if (z <= -2.25e-88) {
		tmp = t_1;
	} else if (z <= 1.32e-28) {
		tmp = x / t;
	} else if (z <= 2.5e+40) {
		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) :: tmp
    t_1 = z * (y / -t)
    if (z <= (-3.9d-27)) then
        tmp = y / a
    else if (z <= (-9.2d-39)) then
        tmp = x / t
    else if (z <= (-2.3d-60)) then
        tmp = x / (z * -a)
    else if (z <= (-2.25d-88)) then
        tmp = t_1
    else if (z <= 1.32d-28) then
        tmp = x / t
    else if (z <= 2.5d+40) 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 = z * (y / -t);
	double tmp;
	if (z <= -3.9e-27) {
		tmp = y / a;
	} else if (z <= -9.2e-39) {
		tmp = x / t;
	} else if (z <= -2.3e-60) {
		tmp = x / (z * -a);
	} else if (z <= -2.25e-88) {
		tmp = t_1;
	} else if (z <= 1.32e-28) {
		tmp = x / t;
	} else if (z <= 2.5e+40) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -t)
	tmp = 0
	if z <= -3.9e-27:
		tmp = y / a
	elif z <= -9.2e-39:
		tmp = x / t
	elif z <= -2.3e-60:
		tmp = x / (z * -a)
	elif z <= -2.25e-88:
		tmp = t_1
	elif z <= 1.32e-28:
		tmp = x / t
	elif z <= 2.5e+40:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-t)))
	tmp = 0.0
	if (z <= -3.9e-27)
		tmp = Float64(y / a);
	elseif (z <= -9.2e-39)
		tmp = Float64(x / t);
	elseif (z <= -2.3e-60)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= -2.25e-88)
		tmp = t_1;
	elseif (z <= 1.32e-28)
		tmp = Float64(x / t);
	elseif (z <= 2.5e+40)
		tmp = t_1;
	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 <= -3.9e-27)
		tmp = y / a;
	elseif (z <= -9.2e-39)
		tmp = x / t;
	elseif (z <= -2.3e-60)
		tmp = x / (z * -a);
	elseif (z <= -2.25e-88)
		tmp = t_1;
	elseif (z <= 1.32e-28)
		tmp = x / t;
	elseif (z <= 2.5e+40)
		tmp = t_1;
	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, -3.9e-27], N[(y / a), $MachinePrecision], If[LessEqual[z, -9.2e-39], N[(x / t), $MachinePrecision], If[LessEqual[z, -2.3e-60], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-88], t$95$1, If[LessEqual[z, 1.32e-28], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.5e+40], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.89999999999999972e-27 or 2.50000000000000002e40 < z

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -3.89999999999999972e-27 < z < -9.20000000000000033e-39 or -2.24999999999999996e-88 < z < 1.32000000000000011e-28

   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 64.6%

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

   if -9.20000000000000033e-39 < z < -2.3000000000000001e-60

   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 75.5%

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

      1. *-commutative 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. mul-1-neg 75.5%

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

      3. *-commutative 75.5%

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

   10. Simplified 75.5%

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

   if -2.3000000000000001e-60 < z < -2.24999999999999996e-88 or 1.32000000000000011e-28 < z < 2.50000000000000002e40

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 59.5%

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

   6. Taylor expanded in x around 0 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-*r* 56.7%

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

      3. neg-mul-1 56.7%

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

   8. Simplified 56.7%

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

      1. associate-/l* 56.8%

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

      2. neg-mul-1 56.8%

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

      3. associate-*l* 56.8%

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

      4. add-sqr-sqrt 19.6%

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

      5. sqrt-unprod 24.0%

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

      6. sqr-neg 24.0%

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

      7. sqrt-unprod 7.9%

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

      8. add-sqr-sqrt 17.1%

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

      9. associate-/l* 17.1%

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

      10. *-commutative 17.1%

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

      11. add-sqr-sqrt 7.9%

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

      12. sqrt-unprod 24.0%

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

      13. sqr-neg 24.0%

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

      14. sqrt-unprod 19.7%

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

      15. add-sqr-sqrt 56.7%

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

   10. Applied egg-rr 56.7%

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

       1. neg-mul-1 56.7%

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

       2. associate-*r/ 58.5%

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

   12. Simplified 58.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.58 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 52000000 \lor \neg \left(z \leq 1.75 \cdot 10^{+38}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.58e-27)
     t_1
     (if (<= z 7e-267)
       (/ x (- t (* z a)))
       (if (<= z 6e-27)
         (/ (- x (* y z)) t)
         (if (or (<= z 52000000.0) (not (<= z 1.75e+38)))
           t_1
           (* z (/ y (- t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.58e-27) {
		tmp = t_1;
	} else if (z <= 7e-267) {
		tmp = x / (t - (z * a));
	} else if (z <= 6e-27) {
		tmp = (x - (y * z)) / t;
	} else if ((z <= 52000000.0) || !(z <= 1.75e+38)) {
		tmp = t_1;
	} else {
		tmp = z * (y / -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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.58d-27)) then
        tmp = t_1
    else if (z <= 7d-267) then
        tmp = x / (t - (z * a))
    else if (z <= 6d-27) then
        tmp = (x - (y * z)) / t
    else if ((z <= 52000000.0d0) .or. (.not. (z <= 1.75d+38))) then
        tmp = t_1
    else
        tmp = z * (y / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.58e-27) {
		tmp = t_1;
	} else if (z <= 7e-267) {
		tmp = x / (t - (z * a));
	} else if (z <= 6e-27) {
		tmp = (x - (y * z)) / t;
	} else if ((z <= 52000000.0) || !(z <= 1.75e+38)) {
		tmp = t_1;
	} else {
		tmp = z * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.58e-27:
		tmp = t_1
	elif z <= 7e-267:
		tmp = x / (t - (z * a))
	elif z <= 6e-27:
		tmp = (x - (y * z)) / t
	elif (z <= 52000000.0) or not (z <= 1.75e+38):
		tmp = t_1
	else:
		tmp = z * (y / -t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.58e-27)
		tmp = t_1;
	elseif (z <= 7e-267)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 6e-27)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif ((z <= 52000000.0) || !(z <= 1.75e+38))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.58e-27)
		tmp = t_1;
	elseif (z <= 7e-267)
		tmp = x / (t - (z * a));
	elseif (z <= 6e-27)
		tmp = (x - (y * z)) / t;
	elseif ((z <= 52000000.0) || ~((z <= 1.75e+38)))
		tmp = t_1;
	else
		tmp = z * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.58e-27], t$95$1, If[LessEqual[z, 7e-267], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-27], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 52000000.0], N[Not[LessEqual[z, 1.75e+38]], $MachinePrecision]], t$95$1, N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.58e-27 or 6.0000000000000002e-27 < z < 5.2e7 or 1.75000000000000001e38 < z

   1. Initial program 69.2%

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

      1. *-commutative 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in y around inf 73.8%

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

   6. Taylor expanded in a around inf 75.7%

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

      1. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   8. Simplified 75.7%

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

   9. Taylor expanded in y around 0 76.5%

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

       1. mul-1-neg 76.5%

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

       2. unsub-neg 76.5%

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

   11. Simplified 76.5%

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

   if -1.58e-27 < z < 6.9999999999999999e-267

   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 84.1%

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

      1. *-commutative 84.1%

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

   7. Simplified 84.1%

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

   if 6.9999999999999999e-267 < z < 6.0000000000000002e-27

   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 t around inf 83.7%

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

   if 5.2e7 < z < 1.75000000000000001e38

   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 t around inf 80.1%

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

   6. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

   8. Simplified 80.2%

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

      1. associate-/l* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. associate-*l* 80.2%

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

      4. add-sqr-sqrt 38.5%

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

      5. sqrt-unprod 39.5%

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

      6. sqr-neg 39.5%

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

      7. sqrt-unprod 9.0%

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

      8. add-sqr-sqrt 30.7%

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

      9. associate-/l* 30.7%

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

      10. *-commutative 30.7%

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

      11. add-sqr-sqrt 9.0%

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

      12. sqrt-unprod 39.5%

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

      13. sqr-neg 39.5%

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

      14. sqrt-unprod 38.5%

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

      15. add-sqr-sqrt 80.2%

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

   10. Applied egg-rr 80.2%

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

       1. neg-mul-1 80.2%

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

       2. associate-*r/ 84.5%

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

   12. Simplified 84.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.58 \cdot 10^{-27}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 52000000 \lor \neg \left(z \leq 1.75 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.05e-26)
     t_1
     (if (<= z 2.9e-266)
       (/ x (- t (* z a)))
       (if (<= z 8e-27)
         (/ (- x (* y z)) t)
         (if (<= z 48000000.0)
           (/ (- (* y z) x) (* z a))
           (if (<= z 2.05e+38) (* z (/ y (- t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.05e-26) {
		tmp = t_1;
	} else if (z <= 2.9e-266) {
		tmp = x / (t - (z * a));
	} else if (z <= 8e-27) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 48000000.0) {
		tmp = ((y * z) - x) / (z * a);
	} else if (z <= 2.05e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.05d-26)) then
        tmp = t_1
    else if (z <= 2.9d-266) then
        tmp = x / (t - (z * a))
    else if (z <= 8d-27) then
        tmp = (x - (y * z)) / t
    else if (z <= 48000000.0d0) then
        tmp = ((y * z) - x) / (z * a)
    else if (z <= 2.05d+38) then
        tmp = z * (y / -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.05e-26) {
		tmp = t_1;
	} else if (z <= 2.9e-266) {
		tmp = x / (t - (z * a));
	} else if (z <= 8e-27) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 48000000.0) {
		tmp = ((y * z) - x) / (z * a);
	} else if (z <= 2.05e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.05e-26:
		tmp = t_1
	elif z <= 2.9e-266:
		tmp = x / (t - (z * a))
	elif z <= 8e-27:
		tmp = (x - (y * z)) / t
	elif z <= 48000000.0:
		tmp = ((y * z) - x) / (z * a)
	elif z <= 2.05e+38:
		tmp = z * (y / -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.05e-26)
		tmp = t_1;
	elseif (z <= 2.9e-266)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 8e-27)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 48000000.0)
		tmp = Float64(Float64(Float64(y * z) - x) / Float64(z * a));
	elseif (z <= 2.05e+38)
		tmp = Float64(z * Float64(y / Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.05e-26)
		tmp = t_1;
	elseif (z <= 2.9e-266)
		tmp = x / (t - (z * a));
	elseif (z <= 8e-27)
		tmp = (x - (y * z)) / t;
	elseif (z <= 48000000.0)
		tmp = ((y * z) - x) / (z * a);
	elseif (z <= 2.05e+38)
		tmp = z * (y / -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.05e-26], t$95$1, If[LessEqual[z, 2.9e-266], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-27], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 48000000.0], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+38], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.05000000000000004e-26 or 2.0500000000000002e38 < z

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around inf 73.0%

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

   6. Taylor expanded in a around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. neg-mul-1 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in y around 0 76.0%

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

       1. mul-1-neg 76.0%

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

       2. unsub-neg 76.0%

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

   11. Simplified 76.0%

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

   if -1.05000000000000004e-26 < z < 2.89999999999999996e-266

   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 84.1%

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

      1. *-commutative 84.1%

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

   7. Simplified 84.1%

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

   if 2.89999999999999996e-266 < z < 8.0000000000000003e-27

   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 t around inf 83.7%

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

   if 8.0000000000000003e-27 < z < 4.8e7

   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 t around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. neg-mul-1 82.0%

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

      3. neg-sub0 82.0%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y \cdot z\right)}}{a \cdot z} \]

      4. sub-neg 82.0%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y \cdot z\right)\right)}}{a \cdot z} \]

      5. distribute-rgt-neg-out 82.0%

         \[\leadsto \frac{0 - \left(x + \color{blue}{y \cdot \left(-z\right)}\right)}{a \cdot z} \]

      6. +-commutative 82.0%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      7. associate--r+ 82.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      8. neg-sub0 82.0%

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

      9. distribute-rgt-neg-out 82.0%

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

      10. remove-double-neg 82.0%

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

      11. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   if 4.8e7 < z < 2.0500000000000002e38

   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 t around inf 80.1%

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

   6. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

   8. Simplified 80.2%

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

      1. associate-/l* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. associate-*l* 80.2%

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

      4. add-sqr-sqrt 38.5%

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

      5. sqrt-unprod 39.5%

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

      6. sqr-neg 39.5%

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

      7. sqrt-unprod 9.0%

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

      8. add-sqr-sqrt 30.7%

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

      9. associate-/l* 30.7%

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

      10. *-commutative 30.7%

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

      11. add-sqr-sqrt 9.0%

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

      12. sqrt-unprod 39.5%

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

      13. sqr-neg 39.5%

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

      14. sqrt-unprod 38.5%

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

      15. add-sqr-sqrt 80.2%

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

   10. Applied egg-rr 80.2%

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

       1. neg-mul-1 80.2%

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

       2. associate-*r/ 84.5%

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

   12. Simplified 84.5%

       \[\leadsto \color{blue}{-z \cdot \frac{y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-26}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+53)
   (/ y a)
   (if (<= z 6.8e-268)
     (/ x (- t (* z a)))
     (if (<= z 5e-17)
       (/ (- x (* y z)) t)
       (if (<= z 38000000.0)
         (/ x (* z (- a)))
         (if (<= z 2.25e+39) (* z (/ y (- t))) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+53) {
		tmp = y / a;
	} else if (z <= 6.8e-268) {
		tmp = x / (t - (z * a));
	} else if (z <= 5e-17) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 38000000.0) {
		tmp = x / (z * -a);
	} else if (z <= 2.25e+39) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+53)) then
        tmp = y / a
    else if (z <= 6.8d-268) then
        tmp = x / (t - (z * a))
    else if (z <= 5d-17) then
        tmp = (x - (y * z)) / t
    else if (z <= 38000000.0d0) then
        tmp = x / (z * -a)
    else if (z <= 2.25d+39) then
        tmp = z * (y / -t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+53) {
		tmp = y / a;
	} else if (z <= 6.8e-268) {
		tmp = x / (t - (z * a));
	} else if (z <= 5e-17) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 38000000.0) {
		tmp = x / (z * -a);
	} else if (z <= 2.25e+39) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+53:
		tmp = y / a
	elif z <= 6.8e-268:
		tmp = x / (t - (z * a))
	elif z <= 5e-17:
		tmp = (x - (y * z)) / t
	elif z <= 38000000.0:
		tmp = x / (z * -a)
	elif z <= 2.25e+39:
		tmp = z * (y / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+53)
		tmp = Float64(y / a);
	elseif (z <= 6.8e-268)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 5e-17)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 38000000.0)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 2.25e+39)
		tmp = Float64(z * Float64(y / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+53)
		tmp = y / a;
	elseif (z <= 6.8e-268)
		tmp = x / (t - (z * a));
	elseif (z <= 5e-17)
		tmp = (x - (y * z)) / t;
	elseif (z <= 38000000.0)
		tmp = x / (z * -a);
	elseif (z <= 2.25e+39)
		tmp = z * (y / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+53], N[(y / a), $MachinePrecision], If[LessEqual[z, 6.8e-268], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-17], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 38000000.0], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+39], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.59999999999999998e53 or 2.24999999999999998e39 < z

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in z around inf 61.7%

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

   if -2.59999999999999998e53 < z < 6.8e-268

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. *-commutative 77.7%

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

   7. Simplified 77.7%

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

   if 6.8e-268 < z < 4.9999999999999999e-17

   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 t around inf 81.1%

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

   if 4.9999999999999999e-17 < z < 3.8e7

   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 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in t around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. *-commutative 72.1%

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

   10. Simplified 72.1%

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

   if 3.8e7 < z < 2.24999999999999998e39

   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 t around inf 80.1%

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

   6. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

   8. Simplified 80.2%

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

      1. associate-/l* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. associate-*l* 80.2%

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

      4. add-sqr-sqrt 38.5%

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

      5. sqrt-unprod 39.5%

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

      6. sqr-neg 39.5%

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

      7. sqrt-unprod 9.0%

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

      8. add-sqr-sqrt 30.7%

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

      9. associate-/l* 30.7%

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

      10. *-commutative 30.7%

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

      11. add-sqr-sqrt 9.0%

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

      12. sqrt-unprod 39.5%

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

      13. sqr-neg 39.5%

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

      14. sqrt-unprod 38.5%

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

      15. add-sqr-sqrt 80.2%

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

   10. Applied egg-rr 80.2%

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

       1. neg-mul-1 80.2%

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

       2. associate-*r/ 84.5%

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

   12. Simplified 84.5%

       \[\leadsto \color{blue}{-z \cdot \frac{y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.6e-27)
     t_1
     (if (<= z 6.5e-267)
       (/ x (- t (* z a)))
       (if (<= z 1.4e-101)
         (/ (- x (* y z)) t)
         (if (<= z 8.5e+115) (* y (/ z (- (* z a) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.6e-27) {
		tmp = t_1;
	} else if (z <= 6.5e-267) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.4e-101) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 8.5e+115) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.6d-27)) then
        tmp = t_1
    else if (z <= 6.5d-267) then
        tmp = x / (t - (z * a))
    else if (z <= 1.4d-101) then
        tmp = (x - (y * z)) / t
    else if (z <= 8.5d+115) then
        tmp = y * (z / ((z * a) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.6e-27) {
		tmp = t_1;
	} else if (z <= 6.5e-267) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.4e-101) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 8.5e+115) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.6e-27:
		tmp = t_1
	elif z <= 6.5e-267:
		tmp = x / (t - (z * a))
	elif z <= 1.4e-101:
		tmp = (x - (y * z)) / t
	elif z <= 8.5e+115:
		tmp = y * (z / ((z * a) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.6e-27)
		tmp = t_1;
	elseif (z <= 6.5e-267)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.4e-101)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 8.5e+115)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.6e-27)
		tmp = t_1;
	elseif (z <= 6.5e-267)
		tmp = x / (t - (z * a));
	elseif (z <= 1.4e-101)
		tmp = (x - (y * z)) / t;
	elseif (z <= 8.5e+115)
		tmp = y * (z / ((z * a) - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.6e-27], t$95$1, If[LessEqual[z, 6.5e-267], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-101], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 8.5e+115], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.59999999999999995e-27 or 8.50000000000000057e115 < z

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in y around inf 69.8%

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

   6. Taylor expanded in a around inf 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in y around 0 78.0%

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

       1. mul-1-neg 78.0%

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

       2. unsub-neg 78.0%

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

   11. Simplified 78.0%

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

   if -1.59999999999999995e-27 < z < 6.4999999999999999e-267

   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 84.1%

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

      1. *-commutative 84.1%

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

   7. Simplified 84.1%

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

   if 6.4999999999999999e-267 < z < 1.39999999999999995e-101

   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 t around inf 92.0%

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

   if 1.39999999999999995e-101 < z < 8.50000000000000057e115

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 71.2%

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

      3. distribute-lft-neg-in 71.2%

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

      4. *-commutative 71.2%

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

   7. Simplified 71.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.6e-27)
   (/ y a)
   (if (<= z 1.18e-27) (/ x t) (if (<= z 4.5e+38) (* z (/ y (- t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.6e-27) {
		tmp = y / a;
	} else if (z <= 1.18e-27) {
		tmp = x / t;
	} else if (z <= 4.5e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.6d-27)) then
        tmp = y / a
    else if (z <= 1.18d-27) then
        tmp = x / t
    else if (z <= 4.5d+38) then
        tmp = z * (y / -t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.6e-27) {
		tmp = y / a;
	} else if (z <= 1.18e-27) {
		tmp = x / t;
	} else if (z <= 4.5e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.6e-27:
		tmp = y / a
	elif z <= 1.18e-27:
		tmp = x / t
	elif z <= 4.5e+38:
		tmp = z * (y / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.6e-27)
		tmp = Float64(y / a);
	elseif (z <= 1.18e-27)
		tmp = Float64(x / t);
	elseif (z <= 4.5e+38)
		tmp = Float64(z * Float64(y / Float64(-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 <= -9.6e-27)
		tmp = y / a;
	elseif (z <= 1.18e-27)
		tmp = x / t;
	elseif (z <= 4.5e+38)
		tmp = z * (y / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.6e-27], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.18e-27], N[(x / t), $MachinePrecision], If[LessEqual[z, 4.5e+38], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.60000000000000008e-27 or 4.4999999999999998e38 < z

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -9.60000000000000008e-27 < z < 1.18e-27

   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 60.9%

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

   if 1.18e-27 < z < 4.4999999999999998e38

   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 t around inf 53.5%

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

   6. Taylor expanded in x around 0 53.7%

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

      1. associate-*r/ 53.7%

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

      2. associate-*r* 53.7%

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

      3. neg-mul-1 53.7%

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

   8. Simplified 53.7%

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

      1. associate-/l* 53.7%

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

      2. neg-mul-1 53.7%

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

      3. associate-*l* 53.7%

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

      4. add-sqr-sqrt 23.8%

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

      5. sqrt-unprod 25.0%

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

      6. sqr-neg 25.0%

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

      7. sqrt-unprod 5.2%

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

      8. add-sqr-sqrt 16.6%

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

      9. associate-/l* 16.6%

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

      10. *-commutative 16.6%

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

      11. add-sqr-sqrt 5.2%

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

      12. sqrt-unprod 25.1%

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

      13. sqr-neg 25.1%

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

      14. sqrt-unprod 23.9%

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

      15. add-sqr-sqrt 53.7%

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

   10. Applied egg-rr 53.7%

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

       1. neg-mul-1 53.7%

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

       2. associate-*r/ 55.8%

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

   12. Simplified 55.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+51)
   (/ y a)
   (if (<= z 48000000.0)
     (/ x (- t (* z a)))
     (if (<= z 3.9e+38) (* z (/ y (- t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+51) {
		tmp = y / a;
	} else if (z <= 48000000.0) {
		tmp = x / (t - (z * a));
	} else if (z <= 3.9e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.35d+51)) then
        tmp = y / a
    else if (z <= 48000000.0d0) then
        tmp = x / (t - (z * a))
    else if (z <= 3.9d+38) then
        tmp = z * (y / -t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+51) {
		tmp = y / a;
	} else if (z <= 48000000.0) {
		tmp = x / (t - (z * a));
	} else if (z <= 3.9e+38) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+51:
		tmp = y / a
	elif z <= 48000000.0:
		tmp = x / (t - (z * a))
	elif z <= 3.9e+38:
		tmp = z * (y / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+51)
		tmp = Float64(y / a);
	elseif (z <= 48000000.0)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 3.9e+38)
		tmp = Float64(z * Float64(y / Float64(-t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+51)
		tmp = y / a;
	elseif (z <= 48000000.0)
		tmp = x / (t - (z * a));
	elseif (z <= 3.9e+38)
		tmp = z * (y / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+51], N[(y / a), $MachinePrecision], If[LessEqual[z, 48000000.0], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+38], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3500000000000001e51 or 3.90000000000000023e38 < z

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in z around inf 61.7%

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

   if -2.3500000000000001e51 < z < 4.8e7

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if 4.8e7 < z < 3.90000000000000023e38

   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 t around inf 80.1%

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

   6. Taylor expanded in x around 0 80.2%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

   8. Simplified 80.2%

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

      1. associate-/l* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. associate-*l* 80.2%

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

      4. add-sqr-sqrt 38.5%

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

      5. sqrt-unprod 39.5%

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

      6. sqr-neg 39.5%

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

      7. sqrt-unprod 9.0%

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

      8. add-sqr-sqrt 30.7%

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

      9. associate-/l* 30.7%

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

      10. *-commutative 30.7%

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

      11. add-sqr-sqrt 9.0%

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

      12. sqrt-unprod 39.5%

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

      13. sqr-neg 39.5%

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

      14. sqrt-unprod 38.5%

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

      15. add-sqr-sqrt 80.2%

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

   10. Applied egg-rr 80.2%

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

       1. neg-mul-1 80.2%

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

       2. associate-*r/ 84.5%

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

   12. Simplified 84.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 48000000:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+104} \lor \neg \left(z \leq 6.6 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+104) (not (<= z 6.6e+117)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+104) || !(z <= 6.6e+117)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (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 <= (-3.5d+104)) .or. (.not. (z <= 6.6d+117))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / (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 <= -3.5e+104) || !(z <= 6.6e+117)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+104) or not (z <= 6.6e+117):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+104) || !(z <= 6.6e+117))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+104) || ~((z <= 6.6e+117)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+104], N[Not[LessEqual[z, 6.6e+117]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e104 or 6.5999999999999996e117 < z

   1. Initial program 52.8%

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

      1. *-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 64.1%

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

   6. Taylor expanded in a around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in y around 0 83.8%

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

       1. mul-1-neg 83.8%

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

       2. unsub-neg 83.8%

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

   11. Simplified 83.8%

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

   if -3.5000000000000002e104 < z < 6.5999999999999996e117

   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 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+104} \lor \neg \left(z \leq 6.6 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.72 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-27) (not (<= z 1.72e-28))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-27) || !(z <= 1.72e-28)) {
		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 <= (-4.5d-27)) .or. (.not. (z <= 1.72d-28))) 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 <= -4.5e-27) || !(z <= 1.72e-28)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-27) or not (z <= 1.72e-28):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-27) || !(z <= 1.72e-28))
		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 <= -4.5e-27) || ~((z <= 1.72e-28)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-27], N[Not[LessEqual[z, 1.72e-28]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000002e-27 or 1.7199999999999999e-28 < z

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -4.5000000000000002e-27 < z < 1.7199999999999999e-28

   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 60.9%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.72 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.9% 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 84.3%

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

   1. *-commutative 84.3%

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

3. Simplified 84.3%

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

5. Taylor expanded in z around 0 33.3%

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

6. Final simplification 33.3%

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

Developer target: 97.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (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))))