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

Percentage Accurate: 84.8% → 96.4%

Time: 15.8s

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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_1}\right)\\ t_3 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-311}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{\frac{t}{a} - z}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (* y (+ (/ z (- (* z a) t)) (/ x (* y t_1)))))
        (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -5e-311)
       t_3
       (if (<= t_3 0.0)
         (* (/ x a) (/ 1.0 (- (/ t a) z)))
         (if (<= t_3 2e+292) t_3 (if (<= t_3 INFINITY) t_2 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -5e-311) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (x / a) * (1.0 / ((t / a) - z));
	} else if (t_3 <= 2e+292) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = 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 = t - (z * a);
	double t_2 = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= -5e-311) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (x / a) * (1.0 / ((t / a) - z));
	} else if (t_3 <= 2e+292) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = y * ((z / ((z * a) - t)) + (x / (y * t_1)))
	t_3 = (x - (y * z)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= -5e-311:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (x / a) * (1.0 / ((t / a) - z))
	elif t_3 <= 2e+292:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_1))))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -5e-311)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(x / a) * Float64(1.0 / Float64(Float64(t / a) - z)));
	elseif (t_3 <= 2e+292)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	t_3 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= -5e-311)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (x / a) * (1.0 / ((t / a) - z));
	elseif (t_3 <= 2e+292)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -5e-311], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(x / a), $MachinePrecision] * N[(1.0 / N[(N[(t / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+292], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 2e292 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 52.0%

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

      1. *-commutative 52.0%

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

   3. Simplified 52.0%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-neg-frac2 99.7%

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

      3. cancel-sign-sub-inv 99.7%

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

      4. *-commutative 99.7%

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

      5. +-commutative 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-lft-neg-in 99.7%

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

      8. distribute-rgt-neg-in 99.7%

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

      9. fma-undefine 99.7%

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

      10. neg-sub0 99.7%

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

      11. fma-undefine 99.7%

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

      12. distribute-rgt-neg-in 99.7%

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

      13. distribute-lft-neg-in 99.7%

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

      14. *-commutative 99.7%

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

      15. associate--r+ 99.7%

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

      16. neg-sub0 99.7%

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

      17. distribute-rgt-neg-out 99.7%

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

      18. remove-double-neg 99.7%

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

   7. Simplified 99.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000000023e-311 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2e292

   1. Initial program 99.7%

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

   if -5.00000000000023e-311 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in a around inf 61.5%

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

   6. Taylor expanded in x around inf 61.5%

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

      1. associate-/r* 88.7%

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

      2. div-inv 88.8%

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

   8. Applied egg-rr 88.8%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{\frac{t}{a} - z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))))
   (if (<= z -7.5e+116)
     (/ y a)
     (if (<= z -2.4e+19)
       (* z (/ (- y) t))
       (if (<= z -2.35e-26)
         t_1
         (if (<= z -1.36e-52)
           (* y (/ z (- t)))
           (if (<= z -1.26e-141)
             (/ y a)
             (if (<= z 1.2e-94)
               (/ x t)
               (if (<= z 2.25e-72)
                 t_1
                 (if (<= z 1.7e+35) (/ x t) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double tmp;
	if (z <= -7.5e+116) {
		tmp = y / a;
	} else if (z <= -2.4e+19) {
		tmp = z * (-y / t);
	} else if (z <= -2.35e-26) {
		tmp = t_1;
	} else if (z <= -1.36e-52) {
		tmp = y * (z / -t);
	} else if (z <= -1.26e-141) {
		tmp = y / a;
	} else if (z <= 1.2e-94) {
		tmp = x / t;
	} else if (z <= 2.25e-72) {
		tmp = t_1;
	} else if (z <= 1.7e+35) {
		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 = x / (z * -a)
    if (z <= (-7.5d+116)) then
        tmp = y / a
    else if (z <= (-2.4d+19)) then
        tmp = z * (-y / t)
    else if (z <= (-2.35d-26)) then
        tmp = t_1
    else if (z <= (-1.36d-52)) then
        tmp = y * (z / -t)
    else if (z <= (-1.26d-141)) then
        tmp = y / a
    else if (z <= 1.2d-94) then
        tmp = x / t
    else if (z <= 2.25d-72) then
        tmp = t_1
    else if (z <= 1.7d+35) 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 = x / (z * -a);
	double tmp;
	if (z <= -7.5e+116) {
		tmp = y / a;
	} else if (z <= -2.4e+19) {
		tmp = z * (-y / t);
	} else if (z <= -2.35e-26) {
		tmp = t_1;
	} else if (z <= -1.36e-52) {
		tmp = y * (z / -t);
	} else if (z <= -1.26e-141) {
		tmp = y / a;
	} else if (z <= 1.2e-94) {
		tmp = x / t;
	} else if (z <= 2.25e-72) {
		tmp = t_1;
	} else if (z <= 1.7e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	tmp = 0
	if z <= -7.5e+116:
		tmp = y / a
	elif z <= -2.4e+19:
		tmp = z * (-y / t)
	elif z <= -2.35e-26:
		tmp = t_1
	elif z <= -1.36e-52:
		tmp = y * (z / -t)
	elif z <= -1.26e-141:
		tmp = y / a
	elif z <= 1.2e-94:
		tmp = x / t
	elif z <= 2.25e-72:
		tmp = t_1
	elif z <= 1.7e+35:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	tmp = 0.0
	if (z <= -7.5e+116)
		tmp = Float64(y / a);
	elseif (z <= -2.4e+19)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= -2.35e-26)
		tmp = t_1;
	elseif (z <= -1.36e-52)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -1.26e-141)
		tmp = Float64(y / a);
	elseif (z <= 1.2e-94)
		tmp = Float64(x / t);
	elseif (z <= 2.25e-72)
		tmp = t_1;
	elseif (z <= 1.7e+35)
		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 = x / (z * -a);
	tmp = 0.0;
	if (z <= -7.5e+116)
		tmp = y / a;
	elseif (z <= -2.4e+19)
		tmp = z * (-y / t);
	elseif (z <= -2.35e-26)
		tmp = t_1;
	elseif (z <= -1.36e-52)
		tmp = y * (z / -t);
	elseif (z <= -1.26e-141)
		tmp = y / a;
	elseif (z <= 1.2e-94)
		tmp = x / t;
	elseif (z <= 2.25e-72)
		tmp = t_1;
	elseif (z <= 1.7e+35)
		tmp = x / t;
	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]}, If[LessEqual[z, -7.5e+116], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.4e+19], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-26], t$95$1, If[LessEqual[z, -1.36e-52], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.26e-141], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.2e-94], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.25e-72], t$95$1, If[LessEqual[z, 1.7e+35], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.5e116 or -1.36e-52 < z < -1.26e-141 or 1.7000000000000001e35 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 56.3%

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

   if -7.5e116 < z < -2.4e19

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-neg-frac2 76.1%

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

      3. cancel-sign-sub-inv 76.1%

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

      4. *-commutative 76.1%

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

      5. +-commutative 76.1%

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

      6. *-commutative 76.1%

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

      7. distribute-lft-neg-in 76.1%

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

      8. distribute-rgt-neg-in 76.1%

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

      9. fma-undefine 76.1%

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

      10. neg-sub0 76.1%

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

      11. fma-undefine 76.1%

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

      12. distribute-rgt-neg-in 76.1%

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

      13. distribute-lft-neg-in 76.1%

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

      14. *-commutative 76.1%

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

      15. associate--r+ 76.1%

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

      16. neg-sub0 76.1%

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

      17. distribute-rgt-neg-out 76.1%

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

      18. remove-double-neg 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in t around inf 62.9%

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

   9. Taylor expanded in z around inf 62.8%

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

       1. +-commutative 62.8%

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

       2. mul-1-neg 62.8%

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

       3. unsub-neg 62.8%

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

   11. Simplified 62.8%

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

   12. Taylor expanded in x around 0 52.5%

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

       1. associate-*r/ 52.5%

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

       2. mul-1-neg 52.5%

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

   14. Simplified 52.5%

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

   if -2.4e19 < z < -2.34999999999999995e-26 or 1.2e-94 < z < 2.25e-72

   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 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. neg-mul-1 68.5%

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

      3. neg-sub0 68.5%

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

      4. sub-neg 68.5%

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

      5. distribute-rgt-neg-out 68.5%

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

      6. +-commutative 68.5%

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

      7. associate--r+ 68.5%

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

      8. neg-sub0 68.5%

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

      9. distribute-rgt-neg-out 68.5%

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

      10. remove-double-neg 68.5%

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

      11. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around 0 55.2%

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

      1. neg-mul-1 55.2%

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

   10. Simplified 55.2%

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

   if -2.34999999999999995e-26 < z < -1.36e-52

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-/l* 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

      4. distribute-neg-frac2 80.7%

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

      5. cancel-sign-sub-inv 80.7%

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

      6. *-commutative 80.7%

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

      7. +-commutative 80.7%

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

      8. *-commutative 80.7%

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

      9. distribute-lft-neg-in 80.7%

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

      10. distribute-rgt-neg-in 80.7%

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

      11. fma-undefine 80.7%

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

      12. neg-sub0 80.7%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 80.7%

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

      14. distribute-rgt-neg-in 80.7%

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

      15. distribute-lft-neg-in 80.7%

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

      16. *-commutative 80.7%

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

      17. associate--r+ 80.7%

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

      18. neg-sub0 80.7%

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

      19. distribute-rgt-neg-out 80.7%

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

      20. remove-double-neg 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in z around 0 61.2%

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

      1. associate-*r/ 61.2%

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

      2. mul-1-neg 61.2%

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

   10. Simplified 61.2%

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

   if -1.26e-141 < z < 1.2e-94 or 2.25e-72 < z < 1.7000000000000001e35

   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 66.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ t_2 := \frac{y \cdot z}{-t}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))) (t_2 (/ (* y z) (- t))))
   (if (<= z -8.5e+116)
     (/ y a)
     (if (<= z -2.55e+19)
       t_2
       (if (<= z -2.4e-26)
         t_1
         (if (<= z -5.1e-52)
           t_2
           (if (<= z -2.5e-141)
             (/ y a)
             (if (<= z 7e-95)
               (/ x t)
               (if (<= z 2.1e-74)
                 t_1
                 (if (<= z 1.9e+35) (/ x t) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double t_2 = (y * z) / -t;
	double tmp;
	if (z <= -8.5e+116) {
		tmp = y / a;
	} else if (z <= -2.55e+19) {
		tmp = t_2;
	} else if (z <= -2.4e-26) {
		tmp = t_1;
	} else if (z <= -5.1e-52) {
		tmp = t_2;
	} else if (z <= -2.5e-141) {
		tmp = y / a;
	} else if (z <= 7e-95) {
		tmp = x / t;
	} else if (z <= 2.1e-74) {
		tmp = t_1;
	} else if (z <= 1.9e+35) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x / (z * -a)
    t_2 = (y * z) / -t
    if (z <= (-8.5d+116)) then
        tmp = y / a
    else if (z <= (-2.55d+19)) then
        tmp = t_2
    else if (z <= (-2.4d-26)) then
        tmp = t_1
    else if (z <= (-5.1d-52)) then
        tmp = t_2
    else if (z <= (-2.5d-141)) then
        tmp = y / a
    else if (z <= 7d-95) then
        tmp = x / t
    else if (z <= 2.1d-74) then
        tmp = t_1
    else if (z <= 1.9d+35) 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 = x / (z * -a);
	double t_2 = (y * z) / -t;
	double tmp;
	if (z <= -8.5e+116) {
		tmp = y / a;
	} else if (z <= -2.55e+19) {
		tmp = t_2;
	} else if (z <= -2.4e-26) {
		tmp = t_1;
	} else if (z <= -5.1e-52) {
		tmp = t_2;
	} else if (z <= -2.5e-141) {
		tmp = y / a;
	} else if (z <= 7e-95) {
		tmp = x / t;
	} else if (z <= 2.1e-74) {
		tmp = t_1;
	} else if (z <= 1.9e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	t_2 = (y * z) / -t
	tmp = 0
	if z <= -8.5e+116:
		tmp = y / a
	elif z <= -2.55e+19:
		tmp = t_2
	elif z <= -2.4e-26:
		tmp = t_1
	elif z <= -5.1e-52:
		tmp = t_2
	elif z <= -2.5e-141:
		tmp = y / a
	elif z <= 7e-95:
		tmp = x / t
	elif z <= 2.1e-74:
		tmp = t_1
	elif z <= 1.9e+35:
		tmp = x / t
	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(Float64(y * z) / Float64(-t))
	tmp = 0.0
	if (z <= -8.5e+116)
		tmp = Float64(y / a);
	elseif (z <= -2.55e+19)
		tmp = t_2;
	elseif (z <= -2.4e-26)
		tmp = t_1;
	elseif (z <= -5.1e-52)
		tmp = t_2;
	elseif (z <= -2.5e-141)
		tmp = Float64(y / a);
	elseif (z <= 7e-95)
		tmp = Float64(x / t);
	elseif (z <= 2.1e-74)
		tmp = t_1;
	elseif (z <= 1.9e+35)
		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 = x / (z * -a);
	t_2 = (y * z) / -t;
	tmp = 0.0;
	if (z <= -8.5e+116)
		tmp = y / a;
	elseif (z <= -2.55e+19)
		tmp = t_2;
	elseif (z <= -2.4e-26)
		tmp = t_1;
	elseif (z <= -5.1e-52)
		tmp = t_2;
	elseif (z <= -2.5e-141)
		tmp = y / a;
	elseif (z <= 7e-95)
		tmp = x / t;
	elseif (z <= 2.1e-74)
		tmp = t_1;
	elseif (z <= 1.9e+35)
		tmp = x / t;
	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[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision]}, If[LessEqual[z, -8.5e+116], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.55e+19], t$95$2, If[LessEqual[z, -2.4e-26], t$95$1, If[LessEqual[z, -5.1e-52], t$95$2, If[LessEqual[z, -2.5e-141], N[(y / a), $MachinePrecision], If[LessEqual[z, 7e-95], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.1e-74], t$95$1, If[LessEqual[z, 1.9e+35], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5000000000000002e116 or -5.09999999999999989e-52 < z < -2.5e-141 or 1.9e35 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 56.3%

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

   if -8.5000000000000002e116 < z < -2.55e19 or -2.4000000000000001e-26 < z < -5.09999999999999989e-52

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. associate-/l* 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. distribute-neg-frac2 69.2%

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

      5. cancel-sign-sub-inv 69.2%

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

      6. *-commutative 69.2%

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

      7. +-commutative 69.2%

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

      8. *-commutative 69.2%

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

      9. distribute-lft-neg-in 69.2%

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

      10. distribute-rgt-neg-in 69.2%

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

      11. fma-undefine 69.2%

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

      12. neg-sub0 69.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 69.2%

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

      14. distribute-rgt-neg-in 69.2%

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

      15. distribute-lft-neg-in 69.2%

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

      16. *-commutative 69.2%

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

      17. associate--r+ 69.2%

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

      18. neg-sub0 69.2%

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

      19. distribute-rgt-neg-out 69.2%

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

      20. remove-double-neg 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in z around 0 54.6%

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

      1. associate-*r/ 54.6%

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

      2. associate-*r* 54.6%

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

      3. mul-1-neg 54.6%

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

   10. Simplified 54.6%

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

   if -2.55e19 < z < -2.4000000000000001e-26 or 6.9999999999999994e-95 < z < 2.1e-74

   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 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. neg-mul-1 68.5%

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

      3. neg-sub0 68.5%

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

      4. sub-neg 68.5%

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

      5. distribute-rgt-neg-out 68.5%

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

      6. +-commutative 68.5%

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

      7. associate--r+ 68.5%

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

      8. neg-sub0 68.5%

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

      9. distribute-rgt-neg-out 68.5%

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

      10. remove-double-neg 68.5%

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

      11. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around 0 55.2%

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

      1. neg-mul-1 55.2%

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

   10. Simplified 55.2%

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

   if -2.5e-141 < z < 6.9999999999999994e-95 or 2.1e-74 < z < 1.9e35

   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 66.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- x (* y z)) t)))
   (if (<= z -8.6e+116)
     (/ y a)
     (if (<= z -6.2e+19)
       t_2
       (if (<= z -2.3e-26)
         t_1
         (if (<= z 7.5e-90) t_2 (if (<= z 3.5e+54) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (z <= -8.6e+116) {
		tmp = y / a;
	} else if (z <= -6.2e+19) {
		tmp = t_2;
	} else if (z <= -2.3e-26) {
		tmp = t_1;
	} else if (z <= 7.5e-90) {
		tmp = t_2;
	} else if (z <= 3.5e+54) {
		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 / (t - (z * a))
    t_2 = (x - (y * z)) / t
    if (z <= (-8.6d+116)) then
        tmp = y / a
    else if (z <= (-6.2d+19)) then
        tmp = t_2
    else if (z <= (-2.3d-26)) then
        tmp = t_1
    else if (z <= 7.5d-90) then
        tmp = t_2
    else if (z <= 3.5d+54) 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 / (t - (z * a));
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (z <= -8.6e+116) {
		tmp = y / a;
	} else if (z <= -6.2e+19) {
		tmp = t_2;
	} else if (z <= -2.3e-26) {
		tmp = t_1;
	} else if (z <= 7.5e-90) {
		tmp = t_2;
	} else if (z <= 3.5e+54) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (x - (y * z)) / t
	tmp = 0
	if z <= -8.6e+116:
		tmp = y / a
	elif z <= -6.2e+19:
		tmp = t_2
	elif z <= -2.3e-26:
		tmp = t_1
	elif z <= 7.5e-90:
		tmp = t_2
	elif z <= 3.5e+54:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (z <= -8.6e+116)
		tmp = Float64(y / a);
	elseif (z <= -6.2e+19)
		tmp = t_2;
	elseif (z <= -2.3e-26)
		tmp = t_1;
	elseif (z <= 7.5e-90)
		tmp = t_2;
	elseif (z <= 3.5e+54)
		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 / (t - (z * a));
	t_2 = (x - (y * z)) / t;
	tmp = 0.0;
	if (z <= -8.6e+116)
		tmp = y / a;
	elseif (z <= -6.2e+19)
		tmp = t_2;
	elseif (z <= -2.3e-26)
		tmp = t_1;
	elseif (z <= 7.5e-90)
		tmp = t_2;
	elseif (z <= 3.5e+54)
		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[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -8.6e+116], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.2e+19], t$95$2, If[LessEqual[z, -2.3e-26], t$95$1, If[LessEqual[z, 7.5e-90], t$95$2, If[LessEqual[z, 3.5e+54], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6e116 or 3.5000000000000001e54 < z

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in z around inf 60.0%

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

   if -8.6e116 < z < -6.2e19 or -2.30000000000000009e-26 < z < 7.4999999999999999e-90

   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 t around inf 77.8%

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

   if -6.2e19 < z < -2.30000000000000009e-26 or 7.4999999999999999e-90 < z < 3.5000000000000001e54

   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 75.9%

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

      1. *-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (* y (/ z (- (* z a) t)))))
   (if (<= z -2.55e+19)
     t_2
     (if (<= z -2.35e-26)
       t_1
       (if (<= z 1.08e-91) (/ (- x (* y z)) t) (if (<= z 1.5e+53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = y * (z / ((z * a) - t));
	double tmp;
	if (z <= -2.55e+19) {
		tmp = t_2;
	} else if (z <= -2.35e-26) {
		tmp = t_1;
	} else if (z <= 1.08e-91) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.5e+53) {
		tmp = 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 = x / (t - (z * a))
    t_2 = y * (z / ((z * a) - t))
    if (z <= (-2.55d+19)) then
        tmp = t_2
    else if (z <= (-2.35d-26)) then
        tmp = t_1
    else if (z <= 1.08d-91) then
        tmp = (x - (y * z)) / t
    else if (z <= 1.5d+53) then
        tmp = 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 = x / (t - (z * a));
	double t_2 = y * (z / ((z * a) - t));
	double tmp;
	if (z <= -2.55e+19) {
		tmp = t_2;
	} else if (z <= -2.35e-26) {
		tmp = t_1;
	} else if (z <= 1.08e-91) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.5e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = y * (z / ((z * a) - t))
	tmp = 0
	if z <= -2.55e+19:
		tmp = t_2
	elif z <= -2.35e-26:
		tmp = t_1
	elif z <= 1.08e-91:
		tmp = (x - (y * z)) / t
	elif z <= 1.5e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(y * Float64(z / Float64(Float64(z * a) - t)))
	tmp = 0.0
	if (z <= -2.55e+19)
		tmp = t_2;
	elseif (z <= -2.35e-26)
		tmp = t_1;
	elseif (z <= 1.08e-91)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1.5e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = y * (z / ((z * a) - t));
	tmp = 0.0;
	if (z <= -2.55e+19)
		tmp = t_2;
	elseif (z <= -2.35e-26)
		tmp = t_1;
	elseif (z <= 1.08e-91)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1.5e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+19], t$95$2, If[LessEqual[z, -2.35e-26], t$95$1, If[LessEqual[z, 1.08e-91], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.5e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e19 or 1.49999999999999999e53 < z

   1. Initial program 57.0%

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

      1. *-commutative 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in x around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. distribute-neg-frac2 65.2%

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

      5. cancel-sign-sub-inv 65.2%

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

      6. *-commutative 65.2%

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

      7. +-commutative 65.2%

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

      8. *-commutative 65.2%

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

      9. distribute-lft-neg-in 65.2%

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

      10. distribute-rgt-neg-in 65.2%

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

      11. fma-undefine 65.2%

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

      12. neg-sub0 65.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 65.2%

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

      14. distribute-rgt-neg-in 65.2%

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

      15. distribute-lft-neg-in 65.2%

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

      16. *-commutative 65.2%

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

      17. associate--r+ 65.2%

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

      18. neg-sub0 65.2%

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

      19. distribute-rgt-neg-out 65.2%

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

      20. remove-double-neg 65.2%

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

   7. Simplified 65.2%

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

   if -2.55e19 < z < -2.34999999999999995e-26 or 1.07999999999999998e-91 < z < 1.49999999999999999e53

   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 75.9%

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

      1. *-commutative 75.9%

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

   7. Simplified 75.9%

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

   if -2.34999999999999995e-26 < z < 1.07999999999999998e-91

   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 80.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-91}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -4e+18)
     (* y (/ z (- (* z a) t)))
     (if (<= z -2.05e-26)
       t_1
       (if (<= z 5.1e-90)
         (/ (- x (* y z)) t)
         (if (<= z 1.7e+35) t_1 (- (/ y a) (/ (/ x z) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -4e+18) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.05e-26) {
		tmp = t_1;
	} else if (z <= 5.1e-90) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.7e+35) {
		tmp = t_1;
	} else {
		tmp = (y / a) - ((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) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (z <= (-4d+18)) then
        tmp = y * (z / ((z * a) - t))
    else if (z <= (-2.05d-26)) then
        tmp = t_1
    else if (z <= 5.1d-90) then
        tmp = (x - (y * z)) / t
    else if (z <= 1.7d+35) then
        tmp = t_1
    else
        tmp = (y / a) - ((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 t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -4e+18) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.05e-26) {
		tmp = t_1;
	} else if (z <= 5.1e-90) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 1.7e+35) {
		tmp = t_1;
	} else {
		tmp = (y / a) - ((x / z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -4e+18:
		tmp = y * (z / ((z * a) - t))
	elif z <= -2.05e-26:
		tmp = t_1
	elif z <= 5.1e-90:
		tmp = (x - (y * z)) / t
	elif z <= 1.7e+35:
		tmp = t_1
	else:
		tmp = (y / a) - ((x / z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -4e+18)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (z <= -2.05e-26)
		tmp = t_1;
	elseif (z <= 5.1e-90)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 1.7e+35)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) - Float64(Float64(x / z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -4e+18)
		tmp = y * (z / ((z * a) - t));
	elseif (z <= -2.05e-26)
		tmp = t_1;
	elseif (z <= 5.1e-90)
		tmp = (x - (y * z)) / t;
	elseif (z <= 1.7e+35)
		tmp = t_1;
	else
		tmp = (y / a) - ((x / z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+18], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e-26], t$95$1, If[LessEqual[z, 5.1e-90], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.7e+35], t$95$1, N[(N[(y / a), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e18

   1. Initial program 63.8%

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

      1. *-commutative 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in x around 0 50.2%

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

      1. mul-1-neg 50.2%

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

      2. associate-/l* 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. distribute-neg-frac2 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. *-commutative 72.1%

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

      7. +-commutative 72.1%

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

      8. *-commutative 72.1%

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

      9. distribute-lft-neg-in 72.1%

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

      10. distribute-rgt-neg-in 72.1%

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

      11. fma-undefine 72.1%

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

      12. neg-sub0 72.1%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 72.1%

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

      14. distribute-rgt-neg-in 72.1%

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

      15. distribute-lft-neg-in 72.1%

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

      16. *-commutative 72.1%

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

      17. associate--r+ 72.1%

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

      18. neg-sub0 72.1%

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

      19. distribute-rgt-neg-out 72.1%

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

      20. remove-double-neg 72.1%

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

   7. Simplified 72.1%

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

   if -4e18 < z < -2.0499999999999999e-26 or 5.0999999999999997e-90 < z < 1.7000000000000001e35

   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 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -2.0499999999999999e-26 < z < 5.0999999999999997e-90

   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 80.2%

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

   if 1.7000000000000001e35 < z

   1. Initial program 54.4%

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

      1. *-commutative 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in t around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

      3. neg-sub0 41.5%

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

      4. sub-neg 41.5%

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

      5. distribute-rgt-neg-out 41.5%

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

      6. +-commutative 41.5%

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

      7. associate--r+ 41.5%

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

      8. neg-sub0 41.5%

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

      9. distribute-rgt-neg-out 41.5%

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

      10. remove-double-neg 41.5%

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

      11. *-commutative 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in y around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-/r* 82.3%

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

   10. Simplified 82.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+184)
   (* y (/ z (- (* z a) t)))
   (if (<= z 1.1e+124)
     (/ (- x (* y z)) (- t (* z a)))
     (- (/ y a) (/ (/ x z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+184) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= 1.1e+124) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y / a) - ((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 (z <= (-2.3d+184)) then
        tmp = y * (z / ((z * a) - t))
    else if (z <= 1.1d+124) then
        tmp = (x - (y * z)) / (t - (z * a))
    else
        tmp = (y / a) - ((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 (z <= -2.3e+184) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= 1.1e+124) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y / a) - ((x / z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+184:
		tmp = y * (z / ((z * a) - t))
	elif z <= 1.1e+124:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = (y / a) - ((x / z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+184)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (z <= 1.1e+124)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y / a) - Float64(Float64(x / z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+184)
		tmp = y * (z / ((z * a) - t));
	elseif (z <= 1.1e+124)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = (y / a) - ((x / z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+184], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+124], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e184

   1. Initial program 47.1%

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

      1. *-commutative 47.1%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in x around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. associate-/l* 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. distribute-neg-frac2 80.3%

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

      5. cancel-sign-sub-inv 80.3%

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

      6. *-commutative 80.3%

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

      7. +-commutative 80.3%

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

      8. *-commutative 80.3%

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

      9. distribute-lft-neg-in 80.3%

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

      10. distribute-rgt-neg-in 80.3%

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

      11. fma-undefine 80.3%

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

      12. neg-sub0 80.3%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 80.3%

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

      14. distribute-rgt-neg-in 80.3%

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

      15. distribute-lft-neg-in 80.3%

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

      16. *-commutative 80.3%

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

      17. associate--r+ 80.3%

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

      18. neg-sub0 80.3%

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

      19. distribute-rgt-neg-out 80.3%

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

      20. remove-double-neg 80.3%

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

   7. Simplified 80.3%

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

   if -2.3e184 < z < 1.1e124

   1. Initial program 94.3%

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

   if 1.1e124 < z

   1. Initial program 46.3%

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

      1. *-commutative 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in t around 0 37.1%

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

      1. associate-*r/ 37.1%

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

      2. neg-mul-1 37.1%

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

      3. neg-sub0 37.1%

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

      4. sub-neg 37.1%

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

      5. distribute-rgt-neg-out 37.1%

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

      6. +-commutative 37.1%

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

      7. associate--r+ 37.1%

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

      8. neg-sub0 37.1%

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

      9. distribute-rgt-neg-out 37.1%

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

      10. remove-double-neg 37.1%

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

      11. *-commutative 37.1%

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

   7. Simplified 37.1%

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

   8. Taylor expanded in y around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-/r* 86.3%

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

   10. Simplified 86.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+116)
   (/ y a)
   (if (<= z -8.5e+18) (* y (/ z (- t))) (if (<= z 1.2e+36) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+116) {
		tmp = y / a;
	} else if (z <= -8.5e+18) {
		tmp = y * (z / -t);
	} else if (z <= 1.2e+36) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+116)) then
        tmp = y / a
    else if (z <= (-8.5d+18)) then
        tmp = y * (z / -t)
    else if (z <= 1.2d+36) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+116) {
		tmp = y / a;
	} else if (z <= -8.5e+18) {
		tmp = y * (z / -t);
	} else if (z <= 1.2e+36) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+116:
		tmp = y / a
	elif z <= -8.5e+18:
		tmp = y * (z / -t)
	elif z <= 1.2e+36:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+116)
		tmp = Float64(y / a);
	elseif (z <= -8.5e+18)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 1.2e+36)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+116)
		tmp = y / a;
	elseif (z <= -8.5e+18)
		tmp = y * (z / -t);
	elseif (z <= 1.2e+36)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+116], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.5e+18], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+36], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e116 or 1.19999999999999996e36 < z

   1. Initial program 54.1%

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

      1. *-commutative 54.1%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in z around inf 59.1%

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

   if -7.5e116 < z < -8.5e18

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate-/l* 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

      4. distribute-neg-frac2 65.7%

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

      5. cancel-sign-sub-inv 65.7%

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

      6. *-commutative 65.7%

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

      7. +-commutative 65.7%

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

      8. *-commutative 65.7%

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

      9. distribute-lft-neg-in 65.7%

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

      10. distribute-rgt-neg-in 65.7%

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

      11. fma-undefine 65.7%

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

      12. neg-sub0 65.7%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 65.7%

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

      14. distribute-rgt-neg-in 65.7%

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

      15. distribute-lft-neg-in 65.7%

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

      16. *-commutative 65.7%

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

      17. associate--r+ 65.7%

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

      18. neg-sub0 65.7%

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

      19. distribute-rgt-neg-out 65.7%

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

      20. remove-double-neg 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. mul-1-neg 52.5%

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

   10. Simplified 52.5%

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

   if -8.5e18 < z < 1.19999999999999996e36

   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 54.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+116)
   (/ y a)
   (if (<= z -7.8e+18) (* z (/ (- y) t)) (if (<= z 1.9e+35) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+116) {
		tmp = y / a;
	} else if (z <= -7.8e+18) {
		tmp = z * (-y / t);
	} else if (z <= 1.9e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+116)) then
        tmp = y / a
    else if (z <= (-7.8d+18)) then
        tmp = z * (-y / t)
    else if (z <= 1.9d+35) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+116) {
		tmp = y / a;
	} else if (z <= -7.8e+18) {
		tmp = z * (-y / t);
	} else if (z <= 1.9e+35) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+116:
		tmp = y / a
	elif z <= -7.8e+18:
		tmp = z * (-y / t)
	elif z <= 1.9e+35:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+116)
		tmp = Float64(y / a);
	elseif (z <= -7.8e+18)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 1.9e+35)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+116)
		tmp = y / a;
	elseif (z <= -7.8e+18)
		tmp = z * (-y / t);
	elseif (z <= 1.9e+35)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+116], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.8e+18], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+35], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000002e116 or 1.9e35 < z

   1. Initial program 54.1%

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

      1. *-commutative 54.1%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in z around inf 59.1%

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

   if -8.5000000000000002e116 < z < -7.8e18

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-neg-frac2 76.1%

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

      3. cancel-sign-sub-inv 76.1%

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

      4. *-commutative 76.1%

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

      5. +-commutative 76.1%

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

      6. *-commutative 76.1%

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

      7. distribute-lft-neg-in 76.1%

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

      8. distribute-rgt-neg-in 76.1%

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

      9. fma-undefine 76.1%

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

      10. neg-sub0 76.1%

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

      11. fma-undefine 76.1%

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

      12. distribute-rgt-neg-in 76.1%

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

      13. distribute-lft-neg-in 76.1%

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

      14. *-commutative 76.1%

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

      15. associate--r+ 76.1%

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

      16. neg-sub0 76.1%

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

      17. distribute-rgt-neg-out 76.1%

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

      18. remove-double-neg 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in t around inf 62.9%

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

   9. Taylor expanded in z around inf 62.8%

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

       1. +-commutative 62.8%

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

       2. mul-1-neg 62.8%

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

       3. unsub-neg 62.8%

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

   11. Simplified 62.8%

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

   12. Taylor expanded in x around 0 52.5%

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

       1. associate-*r/ 52.5%

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

       2. mul-1-neg 52.5%

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

   14. Simplified 52.5%

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

   if -7.8e18 < z < 1.9e35

   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 54.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+116} \lor \neg \left(z \leq 1.3 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+116) (not (<= z 1.3e+54))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+116) || !(z <= 1.3e+54)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+116)) .or. (.not. (z <= 1.3d+54))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+116) || !(z <= 1.3e+54)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+116) or not (z <= 1.3e+54):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+116) || !(z <= 1.3e+54))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+116) || ~((z <= 1.3e+54)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+116], N[Not[LessEqual[z, 1.3e+54]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000032e116 or 1.30000000000000003e54 < z

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in z around inf 60.0%

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

   if -9.00000000000000032e116 < z < 1.30000000000000003e54

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

   7. Simplified 66.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+116} \lor \neg \left(z \leq 1.3 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5000000000000.0) (not (<= z 1.9e+35))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5000000000000.0) || !(z <= 1.9e+35)) {
		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 <= (-5000000000000.0d0)) .or. (.not. (z <= 1.9d+35))) 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 <= -5000000000000.0) || !(z <= 1.9e+35)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5000000000000.0) or not (z <= 1.9e+35):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5000000000000.0) || !(z <= 1.9e+35))
		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 <= -5000000000000.0) || ~((z <= 1.9e+35)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5000000000000.0], N[Not[LessEqual[z, 1.9e+35]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e12 or 1.9e35 < z

   1. Initial program 59.6%

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

      1. *-commutative 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in z around inf 53.1%

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

   if -5e12 < z < 1.9e35

   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 55.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

   1. *-commutative 81.6%

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

3. Simplified 81.6%

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

5. Taylor expanded in z around 0 34.1%

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

6. Final simplification 34.1%

   \[\leadsto \frac{x}{t} \]
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 2024055 
(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))))