Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.5% → 89.7%

Time: 24.1s

Alternatives: 17

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+35} \lor \neg \left(z \leq 2.2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t\_1} + \frac{z \cdot \left(t - a\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1.52e+35) (not (<= z 2.2e+28)))
     (-
      (+ (/ (/ y (/ z x)) (- b y)) (/ (- t a) (- b y)))
      (/ y (/ (pow (- b y) 2.0) (/ (- t a) z))))
     (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -1.52e+35) || !(z <= 2.2e+28)) {
		tmp = (((y / (z / x)) / (b - y)) + ((t - a) / (b - y))) - (y / (pow((b - y), 2.0) / ((t - a) / z)));
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-1.52d+35)) .or. (.not. (z <= 2.2d+28))) then
        tmp = (((y / (z / x)) / (b - y)) + ((t - a) / (b - y))) - (y / (((b - y) ** 2.0d0) / ((t - a) / z)))
    else
        tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -1.52e+35) || !(z <= 2.2e+28)) {
		tmp = (((y / (z / x)) / (b - y)) + ((t - a) / (b - y))) - (y / (Math.pow((b - y), 2.0) / ((t - a) / z)));
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -1.52e+35) or not (z <= 2.2e+28):
		tmp = (((y / (z / x)) / (b - y)) + ((t - a) / (b - y))) - (y / (math.pow((b - y), 2.0) / ((t - a) / z)))
	else:
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -1.52e+35) || !(z <= 2.2e+28))
		tmp = Float64(Float64(Float64(Float64(y / Float64(z / x)) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(Float64(t - a) / z))));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -1.52e+35) || ~((z <= 2.2e+28)))
		tmp = (((y / (z / x)) / (b - y)) + ((t - a) / (b - y))) - (y / (((b - y) ^ 2.0) / ((t - a) / z)));
	else
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.52e+35], N[Not[LessEqual[z, 2.2e+28]], $MachinePrecision]], N[(N[(N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5200000000000001e35 or 2.19999999999999986e28 < z

   1. Initial program 39.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 65.2%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 65.2%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 65.2%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. associate-/r* 68.9%

         \[\leadsto \left(\color{blue}{\frac{\frac{x \cdot y}{z}}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. *-commutative 68.9%

         \[\leadsto \left(\frac{\frac{\color{blue}{y \cdot x}}{z}}{b - y} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. associate-/l* 74.2%

         \[\leadsto \left(\frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{b - y} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. div-sub 75.0%

         \[\leadsto \left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      8. associate-/l* 90.7%

         \[\leadsto \left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{\frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}} \]

      9. *-commutative 90.7%

         \[\leadsto \left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}{t - a}} \]

      10. associate-/l* 90.7%

          \[\leadsto \left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\color{blue}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}} \]

   5. Simplified 90.7%

      \[\leadsto \color{blue}{\left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}} \]

   if -1.5200000000000001e35 < z < 2.19999999999999986e28

   1. Initial program 89.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+35} \lor \neg \left(z \leq 2.2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(\frac{\frac{y}{\frac{z}{x}}}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-19}:\\ \;\;\;\;\frac{t\_1}{t\_2} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;\frac{y \cdot x + t\_1}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_3
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (<= z -9.5e+95)
         t_3
         (if (<= z -1.06e-19)
           (+ (/ t_1 t_2) (* (/ x z) (/ y (- b y))))
           (if (<= z -1.95e-66)
             (+ x (* z (/ (- t a) y)))
             (if (<= z 1.75e+28) (/ (+ (* y x) t_1) t_2) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_3;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if (z <= -9.5e+95) {
		tmp = t_3;
	} else if (z <= -1.06e-19) {
		tmp = (t_1 / t_2) + ((x / z) * (y / (b - y)));
	} else if (z <= -1.95e-66) {
		tmp = x + (z * ((t - a) / y));
	} else if (z <= 1.75e+28) {
		tmp = ((y * x) + t_1) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_3
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-9.5d+95)) then
        tmp = t_3
    else if (z <= (-1.06d-19)) then
        tmp = (t_1 / t_2) + ((x / z) * (y / (b - y)))
    else if (z <= (-1.95d-66)) then
        tmp = x + (z * ((t - a) / y))
    else if (z <= 1.75d+28) then
        tmp = ((y * x) + t_1) / t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_3;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if (z <= -9.5e+95) {
		tmp = t_3;
	} else if (z <= -1.06e-19) {
		tmp = (t_1 / t_2) + ((x / z) * (y / (b - y)));
	} else if (z <= -1.95e-66) {
		tmp = x + (z * ((t - a) / y));
	} else if (z <= 1.75e+28) {
		tmp = ((y * x) + t_1) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_3
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif z <= -9.5e+95:
		tmp = t_3
	elif z <= -1.06e-19:
		tmp = (t_1 / t_2) + ((x / z) * (y / (b - y)))
	elif z <= -1.95e-66:
		tmp = x + (z * ((t - a) / y))
	elif z <= 1.75e+28:
		tmp = ((y * x) + t_1) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_3;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -9.5e+95)
		tmp = t_3;
	elseif (z <= -1.06e-19)
		tmp = Float64(Float64(t_1 / t_2) + Float64(Float64(x / z) * Float64(y / Float64(b - y))));
	elseif (z <= -1.95e-66)
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	elseif (z <= 1.75e+28)
		tmp = Float64(Float64(Float64(y * x) + t_1) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_3;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif (z <= -9.5e+95)
		tmp = t_3;
	elseif (z <= -1.06e-19)
		tmp = (t_1 / t_2) + ((x / z) * (y / (b - y)));
	elseif (z <= -1.95e-66)
		tmp = x + (z * ((t - a) / y));
	elseif (z <= 1.75e+28)
		tmp = ((y * x) + t_1) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$3, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e+95], t$95$3, If[LessEqual[z, -1.06e-19], N[(N[(t$95$1 / t$95$2), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-66], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+28], N[(N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -9.5000000000000004e95 or 1.75e28 < z

   1. Initial program 36.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.7%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -9.5000000000000004e95 < z < -1.06e-19

   1. Initial program 76.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

   4. Taylor expanded in z around inf 74.9%

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

      1. times-frac 87.8%

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

   6. Simplified 87.8%

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

   if -1.06e-19 < z < -1.94999999999999991e-66

   1. Initial program 76.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.1%

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

   4. Taylor expanded in x around 0 96.7%

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

      1. div-sub 96.8%

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

   6. Simplified 96.8%

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

   if -1.94999999999999991e-66 < z < 1.75e28

   1. Initial program 89.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 5 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+36} \lor \neg \left(z \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t\_1} + \frac{z \cdot \left(t - a\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_2
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -1.1e+36) (not (<= z 1.95e+28)))
         t_2
         (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_2;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.1e+36) || !(z <= 1.95e+28)) {
		tmp = t_2;
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_2
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-1.1d+36)) .or. (.not. (z <= 1.95d+28))) then
        tmp = t_2
    else
        tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_2;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.1e+36) || !(z <= 1.95e+28)) {
		tmp = t_2;
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_2
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -1.1e+36) or not (z <= 1.95e+28):
		tmp = t_2
	else:
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_2;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -1.1e+36) || !(z <= 1.95e+28))
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_2;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -1.1e+36) || ~((z <= 1.95e+28)))
		tmp = t_2;
	else
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$2, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.1e+36], N[Not[LessEqual[z, 1.95e+28]], $MachinePrecision]], t$95$2, N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -1.1e36 or 1.9499999999999999e28 < z

   1. Initial program 41.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.4%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -1.1e36 < z < 1.9499999999999999e28

   1. Initial program 89.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+36} \lor \neg \left(z \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x - z \cdot \frac{a}{y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-134}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (- x (* z (/ a y)))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (<= z -1.8e-18)
         t_1
         (if (<= z 4.4e-197)
           t_2
           (if (<= z 6e-134)
             (/ (- t a) (/ y z))
             (if (<= z 8.5e-11) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x - (z * (a / y));
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.8e-18) {
		tmp = t_1;
	} else if (z <= 4.4e-197) {
		tmp = t_2;
	} else if (z <= 6e-134) {
		tmp = (t - a) / (y / z);
	} else if (z <= 8.5e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = x - (z * (a / y))
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-1.8d-18)) then
        tmp = t_1
    else if (z <= 4.4d-197) then
        tmp = t_2
    else if (z <= 6d-134) then
        tmp = (t - a) / (y / z)
    else if (z <= 8.5d-11) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x - (z * (a / y));
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.8e-18) {
		tmp = t_1;
	} else if (z <= 4.4e-197) {
		tmp = t_2;
	} else if (z <= 6e-134) {
		tmp = (t - a) / (y / z);
	} else if (z <= 8.5e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = x - (z * (a / y))
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif z <= -1.8e-18:
		tmp = t_1
	elif z <= 4.4e-197:
		tmp = t_2
	elif z <= 6e-134:
		tmp = (t - a) / (y / z)
	elif z <= 8.5e-11:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(x - Float64(z * Float64(a / y)))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -1.8e-18)
		tmp = t_1;
	elseif (z <= 4.4e-197)
		tmp = t_2;
	elseif (z <= 6e-134)
		tmp = Float64(Float64(t - a) / Float64(y / z));
	elseif (z <= 8.5e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = x - (z * (a / y));
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif (z <= -1.8e-18)
		tmp = t_1;
	elseif (z <= 4.4e-197)
		tmp = t_2;
	elseif (z <= 6e-134)
		tmp = (t - a) / (y / z);
	elseif (z <= 8.5e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-18], t$95$1, If[LessEqual[z, 4.4e-197], t$95$2, If[LessEqual[z, 6e-134], N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-11], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -1.80000000000000005e-18 or 8.50000000000000037e-11 < z

   1. Initial program 48.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.6%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -1.80000000000000005e-18 < z < 4.4000000000000001e-197 or 6e-134 < z < 8.50000000000000037e-11

   1. Initial program 87.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 63.4%

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

   4. Taylor expanded in a around inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. neg-mul-1 68.1%

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

   6. Simplified 68.1%

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

   if 4.4000000000000001e-197 < z < 6e-134

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. fma-def 77.7%

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

      4. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in z around 0 54.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-134}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+35} \lor \neg \left(z \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -4.5e+35) (not (<= z 2.1e+28)))
         t_1
         (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -4.5e+35) || !(z <= 2.1e+28)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-4.5d+35)) .or. (.not. (z <= 2.1d+28))) then
        tmp = t_1
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -4.5e+35) || !(z <= 2.1e+28)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -4.5e+35) or not (z <= 2.1e+28):
		tmp = t_1
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -4.5e+35) || !(z <= 2.1e+28))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -4.5e+35) || ~((z <= 2.1e+28)))
		tmp = t_1;
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.5e+35], N[Not[LessEqual[z, 2.1e+28]], $MachinePrecision]], t$95$1, N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -4.4999999999999997e35 or 2.09999999999999989e28 < z

   1. Initial program 41.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.4%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -4.4999999999999997e35 < z < 2.09999999999999989e28

   1. Initial program 89.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+35} \lor \neg \left(z \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+16} \lor \neg \left(z \leq 1.55\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -3.1e+16) (not (<= z 1.55)))
         t_1
         (/ (+ (* y x) (* z (- t a))) (+ y (* z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -3.1e+16) || !(z <= 1.55)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-3.1d+16)) .or. (.not. (z <= 1.55d0))) then
        tmp = t_1
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -3.1e+16) || !(z <= 1.55)) {
		tmp = t_1;
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -3.1e+16) or not (z <= 1.55):
		tmp = t_1
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -3.1e+16) || !(z <= 1.55))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -3.1e+16) || ~((z <= 1.55)))
		tmp = t_1;
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.1e+16], N[Not[LessEqual[z, 1.55]], $MachinePrecision]], t$95$1, N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -3.1e16 or 1.55000000000000004 < z

   1. Initial program 45.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.4%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -3.1e16 < z < 1.55000000000000004

   1. Initial program 89.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 87.1%

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

      1. *-commutative 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+16} \lor \neg \left(z \leq 1.55\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-147}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3.5e+204)
     t_1
     (if (<= z -4.5e-13)
       (/ (- a) b)
       (if (<= z 4.4e-197)
         x
         (if (<= z 1.55e-147)
           (/ t b)
           (if (<= z 0.00145) (+ x (* z x)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.5e+204) {
		tmp = t_1;
	} else if (z <= -4.5e-13) {
		tmp = -a / b;
	} else if (z <= 4.4e-197) {
		tmp = x;
	} else if (z <= 1.55e-147) {
		tmp = t / b;
	} else if (z <= 0.00145) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-3.5d+204)) then
        tmp = t_1
    else if (z <= (-4.5d-13)) then
        tmp = -a / b
    else if (z <= 4.4d-197) then
        tmp = x
    else if (z <= 1.55d-147) then
        tmp = t / b
    else if (z <= 0.00145d0) then
        tmp = x + (z * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.5e+204) {
		tmp = t_1;
	} else if (z <= -4.5e-13) {
		tmp = -a / b;
	} else if (z <= 4.4e-197) {
		tmp = x;
	} else if (z <= 1.55e-147) {
		tmp = t / b;
	} else if (z <= 0.00145) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3.5e+204:
		tmp = t_1
	elif z <= -4.5e-13:
		tmp = -a / b
	elif z <= 4.4e-197:
		tmp = x
	elif z <= 1.55e-147:
		tmp = t / b
	elif z <= 0.00145:
		tmp = x + (z * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e+204)
		tmp = t_1;
	elseif (z <= -4.5e-13)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 4.4e-197)
		tmp = x;
	elseif (z <= 1.55e-147)
		tmp = Float64(t / b);
	elseif (z <= 0.00145)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3.5e+204)
		tmp = t_1;
	elseif (z <= -4.5e-13)
		tmp = -a / b;
	elseif (z <= 4.4e-197)
		tmp = x;
	elseif (z <= 1.55e-147)
		tmp = t / b;
	elseif (z <= 0.00145)
		tmp = x + (z * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+204], t$95$1, If[LessEqual[z, -4.5e-13], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 4.4e-197], x, If[LessEqual[z, 1.55e-147], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.00145], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.49999999999999989e204 or 0.00145 < z

   1. Initial program 36.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 24.9%

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

      1. *-commutative 24.9%

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

   5. Simplified 24.9%

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

   6. Taylor expanded in z around inf 51.3%

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

   if -3.49999999999999989e204 < z < -4.5e-13

   1. Initial program 64.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.1%

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

      1. mul-1-neg 42.1%

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

      2. distribute-lft-neg-out 42.1%

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

      3. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in y around 0 34.1%

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

      1. mul-1-neg 34.1%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

      2. distribute-neg-frac 34.1%

         \[\leadsto \color{blue}{\frac{-a}{b}} \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]

   if -4.5e-13 < z < 4.4000000000000001e-197

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 55.5%

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

   if 4.4000000000000001e-197 < z < 1.5500000000000001e-147

   1. Initial program 99.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in y around 0 39.2%

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

   if 1.5500000000000001e-147 < z < 0.00145

   1. Initial program 95.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 67.9%

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

   4. Taylor expanded in y around inf 40.2%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   6. Simplified 40.2%

      \[\leadsto x + \color{blue}{z \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-147}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-18} \lor \neg \left(z \leq 5.2 \cdot 10^{-8}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -3.8e-18) (not (<= z 5.2e-8)))
         t_1
         (+ x (* z (/ (- t a) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -3.8e-18) || !(z <= 5.2e-8)) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-3.8d-18)) .or. (.not. (z <= 5.2d-8))) then
        tmp = t_1
    else
        tmp = x + (z * ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -3.8e-18) || !(z <= 5.2e-8)) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -3.8e-18) or not (z <= 5.2e-8):
		tmp = t_1
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -3.8e-18) || !(z <= 5.2e-8))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -3.8e-18) || ~((z <= 5.2e-8)))
		tmp = t_1;
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.8e-18], N[Not[LessEqual[z, 5.2e-8]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -3.7999999999999998e-18 or 5.2000000000000002e-8 < z

   1. Initial program 48.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.6%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -3.7999999999999998e-18 < z < 5.2000000000000002e-8

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.0%

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

   4. Taylor expanded in x around 0 71.8%

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

      1. div-sub 72.8%

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

   6. Simplified 72.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-18} \lor \neg \left(z \leq 5.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-30} \lor \neg \left(z \leq 8.8 \cdot 10^{-10}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -8.5e-30) (not (<= z 8.8e-10)))
         t_1
         (+ x (* z (/ t y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -8.5e-30) || !(z <= 8.8e-10)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-8.5d-30)) .or. (.not. (z <= 8.8d-10))) then
        tmp = t_1
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -8.5e-30) || !(z <= 8.8e-10)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -8.5e-30) or not (z <= 8.8e-10):
		tmp = t_1
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -8.5e-30) || !(z <= 8.8e-10))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -8.5e-30) || ~((z <= 8.8e-10)))
		tmp = t_1;
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.5e-30], N[Not[LessEqual[z, 8.8e-10]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -8.49999999999999931e-30 or 8.7999999999999996e-10 < z

   1. Initial program 49.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -8.49999999999999931e-30 < z < 8.7999999999999996e-10

   1. Initial program 88.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 59.9%

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

   4. Taylor expanded in t around inf 59.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-30} \lor \neg \left(z \leq 8.8 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+208)
     t_1
     (if (<= z -1.85e+202)
       (/ x (- 1.0 z))
       (if (or (<= z -2.3e-19) (not (<= z 3.2e-10)))
         t_1
         (- x (/ (* z a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -2.3e-19) || !(z <= 3.2e-10)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d+208)) then
        tmp = t_1
    else if (z <= (-1.85d+202)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-2.3d-19)) .or. (.not. (z <= 3.2d-10))) then
        tmp = t_1
    else
        tmp = x - ((z * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e+208) {
		tmp = t_1;
	} else if (z <= -1.85e+202) {
		tmp = x / (1.0 - z);
	} else if ((z <= -2.3e-19) || !(z <= 3.2e-10)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+208:
		tmp = t_1
	elif z <= -1.85e+202:
		tmp = x / (1.0 - z)
	elif (z <= -2.3e-19) or not (z <= 3.2e-10):
		tmp = t_1
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -2.3e-19) || !(z <= 3.2e-10))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e+208)
		tmp = t_1;
	elseif (z <= -1.85e+202)
		tmp = x / (1.0 - z);
	elseif ((z <= -2.3e-19) || ~((z <= 3.2e-10)))
		tmp = t_1;
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+208], t$95$1, If[LessEqual[z, -1.85e+202], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.3e-19], N[Not[LessEqual[z, 3.2e-10]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e208 or -1.8499999999999999e202 < z < -2.2999999999999998e-19 or 3.19999999999999981e-10 < z

   1. Initial program 48.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.6%

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

   if -2.6e208 < z < -1.8499999999999999e202

   1. Initial program 0.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -2.2999999999999998e-19 < z < 3.19999999999999981e-10

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.0%

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

   4. Taylor expanded in a around inf 64.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+208}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+150}:\\ \;\;\;\;\frac{t - a}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.12e-29)
     t_1
     (if (<= y 2.2e-141)
       (/ (- t a) b)
       (if (<= y 2.1e+68)
         (+ x (* z (/ t y)))
         (if (<= y 1.26e+150) (/ (- t a) (- y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.12e-29) {
		tmp = t_1;
	} else if (y <= 2.2e-141) {
		tmp = (t - a) / b;
	} else if (y <= 2.1e+68) {
		tmp = x + (z * (t / y));
	} else if (y <= 1.26e+150) {
		tmp = (t - a) / -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.12d-29)) then
        tmp = t_1
    else if (y <= 2.2d-141) then
        tmp = (t - a) / b
    else if (y <= 2.1d+68) then
        tmp = x + (z * (t / y))
    else if (y <= 1.26d+150) then
        tmp = (t - a) / -y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.12e-29) {
		tmp = t_1;
	} else if (y <= 2.2e-141) {
		tmp = (t - a) / b;
	} else if (y <= 2.1e+68) {
		tmp = x + (z * (t / y));
	} else if (y <= 1.26e+150) {
		tmp = (t - a) / -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.12e-29:
		tmp = t_1
	elif y <= 2.2e-141:
		tmp = (t - a) / b
	elif y <= 2.1e+68:
		tmp = x + (z * (t / y))
	elif y <= 1.26e+150:
		tmp = (t - a) / -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.12e-29)
		tmp = t_1;
	elseif (y <= 2.2e-141)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 2.1e+68)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= 1.26e+150)
		tmp = Float64(Float64(t - a) / Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.12e-29)
		tmp = t_1;
	elseif (y <= 2.2e-141)
		tmp = (t - a) / b;
	elseif (y <= 2.1e+68)
		tmp = x + (z * (t / y));
	elseif (y <= 1.26e+150)
		tmp = (t - a) / -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e-29], t$95$1, If[LessEqual[y, 2.2e-141], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.1e+68], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+150], N[(N[(t - a), $MachinePrecision] / (-y)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.11999999999999995e-29 or 1.26e150 < y

   1. Initial program 55.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   5. Simplified 57.5%

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

   if -1.11999999999999995e-29 < y < 2.20000000000000009e-141

   1. Initial program 71.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.0%

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

   if 2.20000000000000009e-141 < y < 2.10000000000000001e68

   1. Initial program 87.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 50.7%

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

   4. Taylor expanded in t around inf 35.8%

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

   if 2.10000000000000001e68 < y < 1.26e150

   1. Initial program 43.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 27.9%

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

      1. *-commutative 27.9%

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

      2. +-commutative 27.9%

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

      3. fma-def 27.9%

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

      4. associate-/l* 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in b around 0 23.8%

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

      1. mul-1-neg 23.8%

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

      2. *-rgt-identity 23.8%

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

      3. distribute-rgt-neg-in 23.8%

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

      4. mul-1-neg 23.8%

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

      5. distribute-lft-in 23.8%

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

      6. mul-1-neg 23.8%

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

      7. unsub-neg 23.8%

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

   8. Simplified 23.8%

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

   9. Taylor expanded in z around inf 49.3%

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

       1. neg-mul-1 49.3%

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

   11. Simplified 49.3%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+68}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+150}:\\ \;\;\;\;\frac{t - a}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-144} \lor \neg \left(z \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e-15)
   (/ (- a) b)
   (if (<= z 4.4e-197)
     x
     (if (or (<= z 6.2e-144) (not (<= z 2e-6))) (/ t b) (+ x (* z x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e-15) {
		tmp = -a / b;
	} else if (z <= 4.4e-197) {
		tmp = x;
	} else if ((z <= 6.2e-144) || !(z <= 2e-6)) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.4d-15)) then
        tmp = -a / b
    else if (z <= 4.4d-197) then
        tmp = x
    else if ((z <= 6.2d-144) .or. (.not. (z <= 2d-6))) then
        tmp = t / b
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e-15) {
		tmp = -a / b;
	} else if (z <= 4.4e-197) {
		tmp = x;
	} else if ((z <= 6.2e-144) || !(z <= 2e-6)) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.4e-15:
		tmp = -a / b
	elif z <= 4.4e-197:
		tmp = x
	elif (z <= 6.2e-144) or not (z <= 2e-6):
		tmp = t / b
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e-15)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 4.4e-197)
		tmp = x;
	elseif ((z <= 6.2e-144) || !(z <= 2e-6))
		tmp = Float64(t / b);
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.4e-15)
		tmp = -a / b;
	elseif (z <= 4.4e-197)
		tmp = x;
	elseif ((z <= 6.2e-144) || ~((z <= 2e-6)))
		tmp = t / b;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e-15], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 4.4e-197], x, If[Or[LessEqual[z, 6.2e-144], N[Not[LessEqual[z, 2e-6]], $MachinePrecision]], N[(t / b), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.39999999999999971e-15

   1. Initial program 49.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 31.8%

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

      1. mul-1-neg 31.8%

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

      2. distribute-lft-neg-out 31.8%

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

      3. *-commutative 31.8%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in y around 0 29.6%

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

      1. mul-1-neg 29.6%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

      2. distribute-neg-frac 29.6%

         \[\leadsto \color{blue}{\frac{-a}{b}} \]

   8. Simplified 29.6%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]

   if -4.39999999999999971e-15 < z < 4.4000000000000001e-197

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 55.5%

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

   if 4.4000000000000001e-197 < z < 6.2000000000000001e-144 or 1.99999999999999991e-6 < z

   1. Initial program 50.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 30.7%

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

      1. *-commutative 30.7%

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

   5. Simplified 30.7%

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

   6. Taylor expanded in y around 0 31.2%

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

   if 6.2000000000000001e-144 < z < 1.99999999999999991e-6

   1. Initial program 95.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 67.9%

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

   4. Taylor expanded in y around inf 40.2%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   6. Simplified 40.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-144} \lor \neg \left(z \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197} \lor \neg \left(z \leq 1.55 \cdot 10^{-147}\right) \land z \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e-11)
   (/ (- a) b)
   (if (or (<= z 4.4e-197) (and (not (<= z 1.55e-147)) (<= z 4.5e-6)))
     x
     (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = -a / b;
	} else if ((z <= 4.4e-197) || (!(z <= 1.55e-147) && (z <= 4.5e-6))) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.8d-11)) then
        tmp = -a / b
    else if ((z <= 4.4d-197) .or. (.not. (z <= 1.55d-147)) .and. (z <= 4.5d-6)) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = -a / b;
	} else if ((z <= 4.4e-197) || (!(z <= 1.55e-147) && (z <= 4.5e-6))) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e-11:
		tmp = -a / b
	elif (z <= 4.4e-197) or (not (z <= 1.55e-147) and (z <= 4.5e-6)):
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= 4.4e-197) || (!(z <= 1.55e-147) && (z <= 4.5e-6)))
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e-11)
		tmp = -a / b;
	elseif ((z <= 4.4e-197) || (~((z <= 1.55e-147)) && (z <= 4.5e-6)))
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e-11], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, 4.4e-197], And[N[Not[LessEqual[z, 1.55e-147]], $MachinePrecision], LessEqual[z, 4.5e-6]]], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999992e-11

   1. Initial program 49.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 31.8%

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

      1. mul-1-neg 31.8%

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

      2. distribute-lft-neg-out 31.8%

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

      3. *-commutative 31.8%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in y around 0 29.6%

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

      1. mul-1-neg 29.6%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

      2. distribute-neg-frac 29.6%

         \[\leadsto \color{blue}{\frac{-a}{b}} \]

   8. Simplified 29.6%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]

   if -1.79999999999999992e-11 < z < 4.4000000000000001e-197 or 1.5500000000000001e-147 < z < 4.50000000000000011e-6

   1. Initial program 88.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 52.0%

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

   if 4.4000000000000001e-197 < z < 1.5500000000000001e-147 or 4.50000000000000011e-6 < z

   1. Initial program 50.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 30.7%

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

      1. *-commutative 30.7%

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

   5. Simplified 30.7%

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

   6. Taylor expanded in y around 0 31.2%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197} \lor \neg \left(z \leq 1.55 \cdot 10^{-147}\right) \land z \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-235}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-137}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.1e-38)
     t_1
     (if (<= y 3.7e-235)
       (/ t (- b y))
       (if (<= y 1.35e-137) (/ (- a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e-38) {
		tmp = t_1;
	} else if (y <= 3.7e-235) {
		tmp = t / (b - y);
	} else if (y <= 1.35e-137) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.1d-38)) then
        tmp = t_1
    else if (y <= 3.7d-235) then
        tmp = t / (b - y)
    else if (y <= 1.35d-137) then
        tmp = -a / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e-38) {
		tmp = t_1;
	} else if (y <= 3.7e-235) {
		tmp = t / (b - y);
	} else if (y <= 1.35e-137) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.1e-38:
		tmp = t_1
	elif y <= 3.7e-235:
		tmp = t / (b - y)
	elif y <= 1.35e-137:
		tmp = -a / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.1e-38)
		tmp = t_1;
	elseif (y <= 3.7e-235)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.35e-137)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.1e-38)
		tmp = t_1;
	elseif (y <= 3.7e-235)
		tmp = t / (b - y);
	elseif (y <= 1.35e-137)
		tmp = -a / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-38], t$95$1, If[LessEqual[y, 3.7e-235], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-137], N[((-a) / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999983e-38 or 1.34999999999999996e-137 < y

   1. Initial program 60.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

   5. Simplified 47.3%

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

   if -3.09999999999999983e-38 < y < 3.7000000000000001e-235

   1. Initial program 69.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 34.6%

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

      1. *-commutative 34.6%

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

   5. Simplified 34.6%

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

   6. Taylor expanded in z around inf 53.9%

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

   if 3.7000000000000001e-235 < y < 1.34999999999999996e-137

   1. Initial program 81.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. distribute-lft-neg-out 45.6%

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

      3. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in y around 0 59.3%

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

      1. mul-1-neg 59.3%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

      2. distribute-neg-frac 59.3%

         \[\leadsto \color{blue}{\frac{-a}{b}} \]

   8. Simplified 59.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-235}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-137}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-30} \lor \neg \left(y \leq 2.4 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e-30) (not (<= y 2.4e-137))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e-30) || !(y <= 2.4e-137)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.5d-30)) .or. (.not. (y <= 2.4d-137))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e-30) || !(y <= 2.4e-137)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e-30) or not (y <= 2.4e-137):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e-30) || !(y <= 2.4e-137))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e-30) || ~((y <= 2.4e-137)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e-30], N[Not[LessEqual[y, 2.4e-137]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999931e-30 or 2.4e-137 < y

   1. Initial program 59.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

   5. Simplified 47.9%

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

   if -8.49999999999999931e-30 < y < 2.4e-137

   1. Initial program 72.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.4%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-30} \lor \neg \left(y \leq 2.4 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.4e-46) x (if (<= y 2.05e-137) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.4e-46) {
		tmp = x;
	} else if (y <= 2.05e-137) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.4d-46)) then
        tmp = x
    else if (y <= 2.05d-137) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.4e-46) {
		tmp = x;
	} else if (y <= 2.05e-137) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.4e-46:
		tmp = x
	elif y <= 2.05e-137:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.4e-46)
		tmp = x;
	elseif (y <= 2.05e-137)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.4e-46)
		tmp = x;
	elseif (y <= 2.05e-137)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.4e-46], x, If[LessEqual[y, 2.05e-137], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999998e-46 or 2.0499999999999999e-137 < y

   1. Initial program 60.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 29.8%

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

   if -6.3999999999999998e-46 < y < 2.0499999999999999e-137

   1. Initial program 71.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.8%

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

      1. *-commutative 35.8%

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

   5. Simplified 35.8%

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

   6. Taylor expanded in y around 0 45.4%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 24.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 64.4%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 22.0%

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

4. Final simplification 22.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

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