Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 89.9%

Time: 18.1s

Alternatives: 17

Speedup: 0.9×

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: 66.4% 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: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+17} \lor \neg \left(z \leq 3200000000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))))
   (if (or (<= z -5.7e+17) (not (<= z 3200000000000.0)))
     (+
      (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
      (/ (- t a) (- b y)))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -5.7e+17) || !(z <= 3200000000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 * (y - b))
    if ((z <= (-5.7d+17)) .or. (.not. (z <= 3200000000000.0d0))) then
        tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z) + ((t - a) / (b - y))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 * (y - b));
	double tmp;
	if ((z <= -5.7e+17) || !(z <= 3200000000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	tmp = 0
	if (z <= -5.7e+17) or not (z <= 3200000000000.0):
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	tmp = 0.0
	if ((z <= -5.7e+17) || !(z <= 3200000000000.0))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	tmp = 0.0;
	if ((z <= -5.7e+17) || ~((z <= 3200000000000.0)))
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.7e+17], N[Not[LessEqual[z, 3200000000000.0]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7e17 or 3.2e12 < z

   1. Initial program 44.0%

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

   3. Taylor expanded in z around -inf 70.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 70.1%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 70.1%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 70.1%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 78.1%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 91.2%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 91.2%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 91.2%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   if -5.7e17 < z < 3.2e12

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 88.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+17} \lor \neg \left(z \leq 3200000000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (/ (+ (* z (- t a)) (* x y)) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -1.15e+56)
     t_3
     (if (<= z 9.8e-154)
       t_2
       (if (<= z 2.8e-109)
         (* x (+ (/ y t_1) (/ (- t a) (* x b))))
         (if (<= z 1.1e+55) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = ((z * (t - a)) + (x * y)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15e+56) {
		tmp = t_3;
	} else if (z <= 9.8e-154) {
		tmp = t_2;
	} else if (z <= 2.8e-109) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (z <= 1.1e+55) {
		tmp = 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 = y - (z * (y - b))
    t_2 = ((z * (t - a)) + (x * y)) / t_1
    t_3 = (t - a) / (b - y)
    if (z <= (-1.15d+56)) then
        tmp = t_3
    else if (z <= 9.8d-154) then
        tmp = t_2
    else if (z <= 2.8d-109) then
        tmp = x * ((y / t_1) + ((t - a) / (x * b)))
    else if (z <= 1.1d+55) then
        tmp = 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 = y - (z * (y - b));
	double t_2 = ((z * (t - a)) + (x * y)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15e+56) {
		tmp = t_3;
	} else if (z <= 9.8e-154) {
		tmp = t_2;
	} else if (z <= 2.8e-109) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (z <= 1.1e+55) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = ((z * (t - a)) + (x * y)) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.15e+56:
		tmp = t_3
	elif z <= 9.8e-154:
		tmp = t_2
	elif z <= 2.8e-109:
		tmp = x * ((y / t_1) + ((t - a) / (x * b)))
	elif z <= 1.1e+55:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.15e+56)
		tmp = t_3;
	elseif (z <= 9.8e-154)
		tmp = t_2;
	elseif (z <= 2.8e-109)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(t - a) / Float64(x * b))));
	elseif (z <= 1.1e+55)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = ((z * (t - a)) + (x * y)) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.15e+56)
		tmp = t_3;
	elseif (z <= 9.8e-154)
		tmp = t_2;
	elseif (z <= 2.8e-109)
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	elseif (z <= 1.1e+55)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+56], t$95$3, If[LessEqual[z, 9.8e-154], t$95$2, If[LessEqual[z, 2.8e-109], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+55], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000007e56 or 1.10000000000000005e55 < z

   1. Initial program 38.7%

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

   3. Taylor expanded in z around inf 85.3%

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

   if -1.15000000000000007e56 < z < 9.79999999999999993e-154 or 2.79999999999999979e-109 < z < 1.10000000000000005e55

   1. Initial program 87.4%

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

   if 9.79999999999999993e-154 < z < 2.79999999999999979e-109

   1. Initial program 41.8%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+42} \lor \neg \left(z \leq 3.4 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))))
   (if (or (<= z -5.5e+42) (not (<= z 3.4e+33)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -5.5e+42) || !(z <= 3.4e+33)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 * (y - b))
    if ((z <= (-5.5d+42)) .or. (.not. (z <= 3.4d+33))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 * (y - b));
	double tmp;
	if ((z <= -5.5e+42) || !(z <= 3.4e+33)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	tmp = 0
	if (z <= -5.5e+42) or not (z <= 3.4e+33):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	tmp = 0.0
	if ((z <= -5.5e+42) || !(z <= 3.4e+33))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	tmp = 0.0;
	if ((z <= -5.5e+42) || ~((z <= 3.4e+33)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.5e+42], N[Not[LessEqual[z, 3.4e+33]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000001e42 or 3.3999999999999999e33 < z

   1. Initial program 40.4%

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

   3. Taylor expanded in z around inf 82.9%

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

   if -5.50000000000000001e42 < z < 3.3999999999999999e33

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 87.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+42} \lor \neg \left(z \leq 3.4 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot t}{y}\\ t_2 := \frac{a}{y - b}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z t) y))) (t_2 (/ a (- y b))))
   (if (<= y -9e+16)
     t_1
     (if (<= y 2.2e-143)
       (/ (- t a) b)
       (if (<= y 7.5e-66)
         (/ t (- b y))
         (if (<= y 1.12e-47)
           t_2
           (if (<= y 7e+29) t_1 (if (<= y 7.2e+87) t_2 (/ x (- 1.0 z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = a / (y - b);
	double tmp;
	if (y <= -9e+16) {
		tmp = t_1;
	} else if (y <= 2.2e-143) {
		tmp = (t - a) / b;
	} else if (y <= 7.5e-66) {
		tmp = t / (b - y);
	} else if (y <= 1.12e-47) {
		tmp = t_2;
	} else if (y <= 7e+29) {
		tmp = t_1;
	} else if (y <= 7.2e+87) {
		tmp = t_2;
	} else {
		tmp = x / (1.0 - z);
	}
	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 = x + ((z * t) / y)
    t_2 = a / (y - b)
    if (y <= (-9d+16)) then
        tmp = t_1
    else if (y <= 2.2d-143) then
        tmp = (t - a) / b
    else if (y <= 7.5d-66) then
        tmp = t / (b - y)
    else if (y <= 1.12d-47) then
        tmp = t_2
    else if (y <= 7d+29) then
        tmp = t_1
    else if (y <= 7.2d+87) then
        tmp = t_2
    else
        tmp = x / (1.0d0 - z)
    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 + ((z * t) / y);
	double t_2 = a / (y - b);
	double tmp;
	if (y <= -9e+16) {
		tmp = t_1;
	} else if (y <= 2.2e-143) {
		tmp = (t - a) / b;
	} else if (y <= 7.5e-66) {
		tmp = t / (b - y);
	} else if (y <= 1.12e-47) {
		tmp = t_2;
	} else if (y <= 7e+29) {
		tmp = t_1;
	} else if (y <= 7.2e+87) {
		tmp = t_2;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z * t) / y)
	t_2 = a / (y - b)
	tmp = 0
	if y <= -9e+16:
		tmp = t_1
	elif y <= 2.2e-143:
		tmp = (t - a) / b
	elif y <= 7.5e-66:
		tmp = t / (b - y)
	elif y <= 1.12e-47:
		tmp = t_2
	elif y <= 7e+29:
		tmp = t_1
	elif y <= 7.2e+87:
		tmp = t_2
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * t) / y))
	t_2 = Float64(a / Float64(y - b))
	tmp = 0.0
	if (y <= -9e+16)
		tmp = t_1;
	elseif (y <= 2.2e-143)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 7.5e-66)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.12e-47)
		tmp = t_2;
	elseif (y <= 7e+29)
		tmp = t_1;
	elseif (y <= 7.2e+87)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * t) / y);
	t_2 = a / (y - b);
	tmp = 0.0;
	if (y <= -9e+16)
		tmp = t_1;
	elseif (y <= 2.2e-143)
		tmp = (t - a) / b;
	elseif (y <= 7.5e-66)
		tmp = t / (b - y);
	elseif (y <= 1.12e-47)
		tmp = t_2;
	elseif (y <= 7e+29)
		tmp = t_1;
	elseif (y <= 7.2e+87)
		tmp = t_2;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+16], t$95$1, If[LessEqual[y, 2.2e-143], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 7.5e-66], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-47], t$95$2, If[LessEqual[y, 7e+29], t$95$1, If[LessEqual[y, 7.2e+87], t$95$2, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9e16 or 1.12000000000000002e-47 < y < 6.99999999999999958e29

   1. Initial program 60.9%

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

   3. Taylor expanded in b around inf 51.7%

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

      1. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in y around inf 51.7%

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

      1. associate-/l* 50.5%

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

   8. Simplified 50.5%

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

   9. Taylor expanded in b around 0 54.5%

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

   10. Taylor expanded in t around inf 47.2%

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

   if -9e16 < y < 2.19999999999999989e-143

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 66.4%

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

   if 2.19999999999999989e-143 < y < 7.49999999999999995e-66

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 42.2%

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

      1. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in z around inf 63.2%

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

   if 7.49999999999999995e-66 < y < 1.12000000000000002e-47 or 6.99999999999999958e29 < y < 7.19999999999999988e87

   1. Initial program 71.9%

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

   3. Taylor expanded in t around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

      5. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around inf 58.3%

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

      1. associate-*r/ 58.3%

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

      2. neg-mul-1 58.3%

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

   8. Simplified 58.3%

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

   if 7.19999999999999988e87 < y

   1. Initial program 38.2%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-47}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot \left(a - t\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot \left(x - a \cdot \frac{z}{y}\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.98 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (/ (* z (- a t)) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5.8e-11)
     t_2
     (if (<= z 1.2e-306)
       t_1
       (if (<= z 8.5e-138)
         (/ (* y (- x (* a (/ z y)))) (+ y (* z b)))
         (if (<= z 1.98e-22) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * (a - t)) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.8e-11) {
		tmp = t_2;
	} else if (z <= 1.2e-306) {
		tmp = t_1;
	} else if (z <= 8.5e-138) {
		tmp = (y * (x - (a * (z / y)))) / (y + (z * b));
	} else if (z <= 1.98e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x - ((z * (a - t)) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-5.8d-11)) then
        tmp = t_2
    else if (z <= 1.2d-306) then
        tmp = t_1
    else if (z <= 8.5d-138) then
        tmp = (y * (x - (a * (z / y)))) / (y + (z * b))
    else if (z <= 1.98d-22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * (a - t)) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.8e-11) {
		tmp = t_2;
	} else if (z <= 1.2e-306) {
		tmp = t_1;
	} else if (z <= 8.5e-138) {
		tmp = (y * (x - (a * (z / y)))) / (y + (z * b));
	} else if (z <= 1.98e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((z * (a - t)) / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.8e-11:
		tmp = t_2
	elif z <= 1.2e-306:
		tmp = t_1
	elif z <= 8.5e-138:
		tmp = (y * (x - (a * (z / y)))) / (y + (z * b))
	elif z <= 1.98e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z * Float64(a - t)) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.8e-11)
		tmp = t_2;
	elseif (z <= 1.2e-306)
		tmp = t_1;
	elseif (z <= 8.5e-138)
		tmp = Float64(Float64(y * Float64(x - Float64(a * Float64(z / y)))) / Float64(y + Float64(z * b)));
	elseif (z <= 1.98e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((z * (a - t)) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.8e-11)
		tmp = t_2;
	elseif (z <= 1.2e-306)
		tmp = t_1;
	elseif (z <= 8.5e-138)
		tmp = (y * (x - (a * (z / y)))) / (y + (z * b));
	elseif (z <= 1.98e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-11], t$95$2, If[LessEqual[z, 1.2e-306], t$95$1, If[LessEqual[z, 8.5e-138], N[(N[(y * N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.98e-22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e-11 or 1.98000000000000001e-22 < z

   1. Initial program 46.7%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -5.8e-11 < z < 1.2e-306 or 8.50000000000000035e-138 < z < 1.98000000000000001e-22

   1. Initial program 85.3%

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

   3. Taylor expanded in b around inf 85.2%

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

      1. *-commutative 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in y around inf 80.8%

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

      1. associate-/l* 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in b around 0 73.1%

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

   if 1.2e-306 < z < 8.50000000000000035e-138

   1. Initial program 95.5%

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

   3. Taylor expanded in b around inf 95.5%

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

      1. *-commutative 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around inf 95.6%

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

      1. associate-/l* 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in t around 0 81.3%

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

       1. mul-1-neg 81.3%

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

       2. unsub-neg 81.3%

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

       3. associate-/l* 81.3%

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

   11. Simplified 81.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot \left(x - a \cdot \frac{z}{y}\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.98 \cdot 10^{-22}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+218}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.4e-9)
   x
   (if (<= y -8.5e-223)
     (/ t b)
     (if (<= y -5.2e-275)
       (/ a (- b))
       (if (<= y 7.5e-51) (/ t b) (if (<= y 1.5e+218) x (/ x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.4e-9) {
		tmp = x;
	} else if (y <= -8.5e-223) {
		tmp = t / b;
	} else if (y <= -5.2e-275) {
		tmp = a / -b;
	} else if (y <= 7.5e-51) {
		tmp = t / b;
	} else if (y <= 1.5e+218) {
		tmp = x;
	} else {
		tmp = x / -z;
	}
	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 <= (-7.4d-9)) then
        tmp = x
    else if (y <= (-8.5d-223)) then
        tmp = t / b
    else if (y <= (-5.2d-275)) then
        tmp = a / -b
    else if (y <= 7.5d-51) then
        tmp = t / b
    else if (y <= 1.5d+218) then
        tmp = x
    else
        tmp = x / -z
    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 <= -7.4e-9) {
		tmp = x;
	} else if (y <= -8.5e-223) {
		tmp = t / b;
	} else if (y <= -5.2e-275) {
		tmp = a / -b;
	} else if (y <= 7.5e-51) {
		tmp = t / b;
	} else if (y <= 1.5e+218) {
		tmp = x;
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.4e-9:
		tmp = x
	elif y <= -8.5e-223:
		tmp = t / b
	elif y <= -5.2e-275:
		tmp = a / -b
	elif y <= 7.5e-51:
		tmp = t / b
	elif y <= 1.5e+218:
		tmp = x
	else:
		tmp = x / -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.4e-9)
		tmp = x;
	elseif (y <= -8.5e-223)
		tmp = Float64(t / b);
	elseif (y <= -5.2e-275)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 7.5e-51)
		tmp = Float64(t / b);
	elseif (y <= 1.5e+218)
		tmp = x;
	else
		tmp = Float64(x / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.4e-9)
		tmp = x;
	elseif (y <= -8.5e-223)
		tmp = t / b;
	elseif (y <= -5.2e-275)
		tmp = a / -b;
	elseif (y <= 7.5e-51)
		tmp = t / b;
	elseif (y <= 1.5e+218)
		tmp = x;
	else
		tmp = x / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.4e-9], x, If[LessEqual[y, -8.5e-223], N[(t / b), $MachinePrecision], If[LessEqual[y, -5.2e-275], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 7.5e-51], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.5e+218], x, N[(x / (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.4e-9 or 7.49999999999999976e-51 < y < 1.5e218

   1. Initial program 59.5%

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

   3. Taylor expanded in z around 0 33.4%

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

   if -7.4e-9 < y < -8.5000000000000003e-223 or -5.19999999999999985e-275 < y < 7.49999999999999976e-51

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf 37.8%

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

      1. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in y around 0 43.8%

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

   if -8.5000000000000003e-223 < y < -5.19999999999999985e-275

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

   if 1.5e218 < y

   1. Initial program 19.7%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in z around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. mul-1-neg 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+218}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-14} \lor \neg \left(z \leq -8.5 \cdot 10^{-54} \lor \neg \left(z \leq -5.7 \cdot 10^{-103}\right) \land z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-14)
         (not
          (or (<= z -8.5e-54) (and (not (<= z -5.7e-103)) (<= z 6.4e-21)))))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-14) || !((z <= -8.5e-54) || (!(z <= -5.7e-103) && (z <= 6.4e-21)))) {
		tmp = (t - a) / (b - y);
	} 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) :: tmp
    if ((z <= (-3d-14)) .or. (.not. (z <= (-8.5d-54)) .or. (.not. (z <= (-5.7d-103))) .and. (z <= 6.4d-21))) then
        tmp = (t - a) / (b - y)
    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 tmp;
	if ((z <= -3e-14) || !((z <= -8.5e-54) || (!(z <= -5.7e-103) && (z <= 6.4e-21)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e-14) or not ((z <= -8.5e-54) or (not (z <= -5.7e-103) and (z <= 6.4e-21))):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-14) || !((z <= -8.5e-54) || (!(z <= -5.7e-103) && (z <= 6.4e-21))))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e-14) || ~(((z <= -8.5e-54) || (~((z <= -5.7e-103)) && (z <= 6.4e-21)))))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-14], N[Not[Or[LessEqual[z, -8.5e-54], And[N[Not[LessEqual[z, -5.7e-103]], $MachinePrecision], LessEqual[z, 6.4e-21]]]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999998e-14 or -8.5e-54 < z < -5.6999999999999996e-103 or 6.4000000000000003e-21 < z

   1. Initial program 49.3%

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

   3. Taylor expanded in z around inf 77.4%

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

   if -2.9999999999999998e-14 < z < -8.5e-54 or -5.6999999999999996e-103 < z < 6.4000000000000003e-21

   1. Initial program 88.2%

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

   3. Taylor expanded in b around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in y around inf 85.5%

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

      1. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in b around 0 74.8%

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

   10. Taylor expanded in t around 0 60.6%

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

       1. mul-1-neg 60.6%

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

       2. unsub-neg 60.6%

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

   12. Simplified 60.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-14} \lor \neg \left(z \leq -8.5 \cdot 10^{-54} \lor \neg \left(z \leq -5.7 \cdot 10^{-103}\right) \land z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+55} \lor \neg \left(z \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e+55) (not (<= z 3.1e+55)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+55) || !(z <= 3.1e+55)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - 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 <= (-1.9d+55)) .or. (.not. (z <= 3.1d+55))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - 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 <= -1.9e+55) || !(z <= 3.1e+55)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e+55) or not (z <= 3.1e+55):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e+55) || !(z <= 3.1e+55))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y - Float64(z * Float64(y - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e+55) || ~((z <= 3.1e+55)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e+55], N[Not[LessEqual[z, 3.1e+55]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e55 or 3.09999999999999994e55 < z

   1. Initial program 38.7%

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

   3. Taylor expanded in z around inf 85.3%

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

   if -1.9e55 < z < 3.09999999999999994e55

   1. Initial program 85.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+55} \lor \neg \left(z \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -60000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -60000000000000.0)
     t_1
     (if (<= y 4e-137)
       (/ (- t a) b)
       (if (<= y 4.8e-66)
         (/ t (- b y))
         (if (<= y 4e-47) (/ a (- y 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 <= -60000000000000.0) {
		tmp = t_1;
	} else if (y <= 4e-137) {
		tmp = (t - a) / b;
	} else if (y <= 4.8e-66) {
		tmp = t / (b - y);
	} else if (y <= 4e-47) {
		tmp = a / (y - 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 <= (-60000000000000.0d0)) then
        tmp = t_1
    else if (y <= 4d-137) then
        tmp = (t - a) / b
    else if (y <= 4.8d-66) then
        tmp = t / (b - y)
    else if (y <= 4d-47) then
        tmp = a / (y - 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 <= -60000000000000.0) {
		tmp = t_1;
	} else if (y <= 4e-137) {
		tmp = (t - a) / b;
	} else if (y <= 4.8e-66) {
		tmp = t / (b - y);
	} else if (y <= 4e-47) {
		tmp = a / (y - 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 <= -60000000000000.0:
		tmp = t_1
	elif y <= 4e-137:
		tmp = (t - a) / b
	elif y <= 4.8e-66:
		tmp = t / (b - y)
	elif y <= 4e-47:
		tmp = a / (y - 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 <= -60000000000000.0)
		tmp = t_1;
	elseif (y <= 4e-137)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 4.8e-66)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 4e-47)
		tmp = Float64(a / Float64(y - 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 <= -60000000000000.0)
		tmp = t_1;
	elseif (y <= 4e-137)
		tmp = (t - a) / b;
	elseif (y <= 4.8e-66)
		tmp = t / (b - y);
	elseif (y <= 4e-47)
		tmp = a / (y - 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, -60000000000000.0], t$95$1, If[LessEqual[y, 4e-137], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.8e-66], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-47], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e13 or 3.9999999999999999e-47 < y

   1. Initial program 55.2%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

   5. Simplified 48.4%

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

   if -6e13 < y < 3.99999999999999991e-137

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 66.3%

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

   if 3.99999999999999991e-137 < y < 4.80000000000000052e-66

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 44.5%

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

      1. *-commutative 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in z around inf 66.9%

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

   if 4.80000000000000052e-66 < y < 3.9999999999999999e-47

   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 t around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. mul-1-neg 99.5%

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

      3. unsub-neg 99.5%

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

      4. *-commutative 99.5%

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

      5. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in z around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. neg-mul-1 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -60000000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -7000000000000.0)
     t_2
     (if (<= y 4e-137)
       t_1
       (if (<= y 5.8e-94) (/ t (- b y)) (if (<= y 1.6e-45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -7000000000000.0) {
		tmp = t_2;
	} else if (y <= 4e-137) {
		tmp = t_1;
	} else if (y <= 5.8e-94) {
		tmp = t / (b - y);
	} else if (y <= 1.6e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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
    t_2 = x / (1.0d0 - z)
    if (y <= (-7000000000000.0d0)) then
        tmp = t_2
    else if (y <= 4d-137) then
        tmp = t_1
    else if (y <= 5.8d-94) then
        tmp = t / (b - y)
    else if (y <= 1.6d-45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -7000000000000.0) {
		tmp = t_2;
	} else if (y <= 4e-137) {
		tmp = t_1;
	} else if (y <= 5.8e-94) {
		tmp = t / (b - y);
	} else if (y <= 1.6e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -7000000000000.0:
		tmp = t_2
	elif y <= 4e-137:
		tmp = t_1
	elif y <= 5.8e-94:
		tmp = t / (b - y)
	elif y <= 1.6e-45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7000000000000.0)
		tmp = t_2;
	elseif (y <= 4e-137)
		tmp = t_1;
	elseif (y <= 5.8e-94)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.6e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7000000000000.0)
		tmp = t_2;
	elseif (y <= 4e-137)
		tmp = t_1;
	elseif (y <= 5.8e-94)
		tmp = t / (b - y);
	elseif (y <= 1.6e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7000000000000.0], t$95$2, If[LessEqual[y, 4e-137], t$95$1, If[LessEqual[y, 5.8e-94], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e12 or 1.60000000000000004e-45 < y

   1. Initial program 55.2%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

   5. Simplified 48.4%

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

   if -7e12 < y < 3.99999999999999991e-137 or 5.79999999999999991e-94 < y < 1.60000000000000004e-45

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 64.8%

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

   if 3.99999999999999991e-137 < y < 5.79999999999999991e-94

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in z around inf 75.4%

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

Alternative 11: 43.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-221}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.55e-44)
     t_1
     (if (<= y -1.12e-221)
       (/ t b)
       (if (<= y -4.6e-275)
         (/ a (- b))
         (if (<= y 2.6e-54) (/ t (- b 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 <= -1.55e-44) {
		tmp = t_1;
	} else if (y <= -1.12e-221) {
		tmp = t / b;
	} else if (y <= -4.6e-275) {
		tmp = a / -b;
	} else if (y <= 2.6e-54) {
		tmp = t / (b - 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 <= (-1.55d-44)) then
        tmp = t_1
    else if (y <= (-1.12d-221)) then
        tmp = t / b
    else if (y <= (-4.6d-275)) then
        tmp = a / -b
    else if (y <= 2.6d-54) then
        tmp = t / (b - 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 <= -1.55e-44) {
		tmp = t_1;
	} else if (y <= -1.12e-221) {
		tmp = t / b;
	} else if (y <= -4.6e-275) {
		tmp = a / -b;
	} else if (y <= 2.6e-54) {
		tmp = t / (b - 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 <= -1.55e-44:
		tmp = t_1
	elif y <= -1.12e-221:
		tmp = t / b
	elif y <= -4.6e-275:
		tmp = a / -b
	elif y <= 2.6e-54:
		tmp = t / (b - 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 <= -1.55e-44)
		tmp = t_1;
	elseif (y <= -1.12e-221)
		tmp = Float64(t / b);
	elseif (y <= -4.6e-275)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 2.6e-54)
		tmp = Float64(t / Float64(b - 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 <= -1.55e-44)
		tmp = t_1;
	elseif (y <= -1.12e-221)
		tmp = t / b;
	elseif (y <= -4.6e-275)
		tmp = a / -b;
	elseif (y <= 2.6e-54)
		tmp = t / (b - 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, -1.55e-44], t$95$1, If[LessEqual[y, -1.12e-221], N[(t / b), $MachinePrecision], If[LessEqual[y, -4.6e-275], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 2.6e-54], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.54999999999999992e-44 or 2.60000000000000002e-54 < y

   1. Initial program 56.8%

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

   3. Taylor expanded in y around inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

   5. Simplified 46.0%

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

   if -1.54999999999999992e-44 < y < -1.12000000000000003e-221

   1. Initial program 70.3%

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

   3. Taylor expanded in t around inf 37.5%

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

      1. *-commutative 37.5%

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

   5. Simplified 37.5%

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

   6. Taylor expanded in y around 0 47.8%

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

   if -1.12000000000000003e-221 < y < -4.59999999999999979e-275

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

   if -4.59999999999999979e-275 < y < 2.60000000000000002e-54

   1. Initial program 82.2%

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

   3. Taylor expanded in t around inf 39.8%

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

      1. *-commutative 39.8%

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

   5. Simplified 39.8%

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

   6. Taylor expanded in z around inf 49.7%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-221}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.85:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.1e-13)
     t_1
     (if (<= z 4.2e-94)
       x
       (if (<= z 3.2e-37) (/ t b) (if (<= z 2.85) (/ a (- b)) 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 <= -2.1e-13) {
		tmp = t_1;
	} else if (z <= 4.2e-94) {
		tmp = x;
	} else if (z <= 3.2e-37) {
		tmp = t / b;
	} else if (z <= 2.85) {
		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 = t / (b - y)
    if (z <= (-2.1d-13)) then
        tmp = t_1
    else if (z <= 4.2d-94) then
        tmp = x
    else if (z <= 3.2d-37) then
        tmp = t / b
    else if (z <= 2.85d0) 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 = t / (b - y);
	double tmp;
	if (z <= -2.1e-13) {
		tmp = t_1;
	} else if (z <= 4.2e-94) {
		tmp = x;
	} else if (z <= 3.2e-37) {
		tmp = t / b;
	} else if (z <= 2.85) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.1e-13:
		tmp = t_1
	elif z <= 4.2e-94:
		tmp = x
	elif z <= 3.2e-37:
		tmp = t / b
	elif z <= 2.85:
		tmp = a / -b
	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 <= -2.1e-13)
		tmp = t_1;
	elseif (z <= 4.2e-94)
		tmp = x;
	elseif (z <= 3.2e-37)
		tmp = Float64(t / b);
	elseif (z <= 2.85)
		tmp = Float64(a / Float64(-b));
	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 <= -2.1e-13)
		tmp = t_1;
	elseif (z <= 4.2e-94)
		tmp = x;
	elseif (z <= 3.2e-37)
		tmp = t / b;
	elseif (z <= 2.85)
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e-13], t$95$1, If[LessEqual[z, 4.2e-94], x, If[LessEqual[z, 3.2e-37], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.85], N[(a / (-b)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999989e-13 or 2.85000000000000009 < z

   1. Initial program 45.8%

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

   3. Taylor expanded in t around inf 24.2%

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

      1. *-commutative 24.2%

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

   5. Simplified 24.2%

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

   6. Taylor expanded in z around inf 43.8%

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

   if -2.09999999999999989e-13 < z < 4.2000000000000002e-94

   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 44.7%

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

   if 4.2000000000000002e-94 < z < 3.1999999999999999e-37

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 43.6%

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

   if 3.1999999999999999e-37 < z < 2.85000000000000009

   1. Initial program 80.8%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

      5. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around 0 43.5%

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

      1. associate-*r/ 43.5%

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

      2. neg-mul-1 43.5%

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

   8. Simplified 43.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.85:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+29} \lor \neg \left(z \leq 0.0035\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+29) (not (<= z 0.0035)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e+29) || !(z <= 0.0035)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (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) :: tmp
    if ((z <= (-5.4d+29)) .or. (.not. (z <= 0.0035d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (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 tmp;
	if ((z <= -5.4e+29) || !(z <= 0.0035)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.4e+29) or not (z <= 0.0035):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e+29) || !(z <= 0.0035))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.4e+29) || ~((z <= 0.0035)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e+29], N[Not[LessEqual[z, 0.0035]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e29 or 0.00350000000000000007 < z

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf 81.7%

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

   if -5.4e29 < z < 0.00350000000000000007

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 84.5%

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

      1. *-commutative 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+29} \lor \neg \left(z \leq 0.0035\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.75e-9)
   x
   (if (<= y -2.3e-223)
     (/ t b)
     (if (<= y -5.5e-275) (/ a (- b)) (if (<= y 3.9e-56) (/ t b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.75e-9) {
		tmp = x;
	} else if (y <= -2.3e-223) {
		tmp = t / b;
	} else if (y <= -5.5e-275) {
		tmp = a / -b;
	} else if (y <= 3.9e-56) {
		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 <= (-1.75d-9)) then
        tmp = x
    else if (y <= (-2.3d-223)) then
        tmp = t / b
    else if (y <= (-5.5d-275)) then
        tmp = a / -b
    else if (y <= 3.9d-56) 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 <= -1.75e-9) {
		tmp = x;
	} else if (y <= -2.3e-223) {
		tmp = t / b;
	} else if (y <= -5.5e-275) {
		tmp = a / -b;
	} else if (y <= 3.9e-56) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.75e-9:
		tmp = x
	elif y <= -2.3e-223:
		tmp = t / b
	elif y <= -5.5e-275:
		tmp = a / -b
	elif y <= 3.9e-56:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.75e-9)
		tmp = x;
	elseif (y <= -2.3e-223)
		tmp = Float64(t / b);
	elseif (y <= -5.5e-275)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 3.9e-56)
		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 <= -1.75e-9)
		tmp = x;
	elseif (y <= -2.3e-223)
		tmp = t / b;
	elseif (y <= -5.5e-275)
		tmp = a / -b;
	elseif (y <= 3.9e-56)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.75e-9], x, If[LessEqual[y, -2.3e-223], N[(t / b), $MachinePrecision], If[LessEqual[y, -5.5e-275], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 3.9e-56], N[(t / b), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e-9 or 3.9e-56 < y

   1. Initial program 56.3%

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

   3. Taylor expanded in z around 0 31.5%

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

   if -1.75e-9 < y < -2.3e-223 or -5.49999999999999988e-275 < y < 3.9e-56

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf 37.8%

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

      1. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in y around 0 43.8%

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

   if -2.3e-223 < y < -5.49999999999999988e-275

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-13} \lor \neg \left(z \leq 6.7 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e-13) (not (<= z 6.7e-21)))
   (/ (- t a) (- b y))
   (- x (/ (* z (- a t)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e-13) || !(z <= 6.7e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - 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) :: tmp
    if ((z <= (-3.6d-13)) .or. (.not. (z <= 6.7d-21))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * (a - 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 tmp;
	if ((z <= -3.6e-13) || !(z <= 6.7e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.6e-13) or not (z <= 6.7e-21):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * (a - t)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e-13) || !(z <= 6.7e-21))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.6e-13) || ~((z <= 6.7e-21)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * (a - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e-13], N[Not[LessEqual[z, 6.7e-21]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5999999999999998e-13 or 6.6999999999999997e-21 < z

   1. Initial program 46.7%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -3.5999999999999998e-13 < z < 6.6999999999999997e-21

   1. Initial program 88.2%

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

   3. Taylor expanded in b around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in y around inf 85.0%

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

      1. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in b around 0 71.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-13} \lor \neg \left(z \leq 6.7 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.6e-9) x (if (<= y 1.9e-58) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e-9) {
		tmp = x;
	} else if (y <= 1.9e-58) {
		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 <= (-4.6d-9)) then
        tmp = x
    else if (y <= 1.9d-58) 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 <= -4.6e-9) {
		tmp = x;
	} else if (y <= 1.9e-58) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.6e-9:
		tmp = x
	elif y <= 1.9e-58:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.6e-9)
		tmp = x;
	elseif (y <= 1.9e-58)
		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 <= -4.6e-9)
		tmp = x;
	elseif (y <= 1.9e-58)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.6e-9], x, If[LessEqual[y, 1.9e-58], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e-9 or 1.8999999999999999e-58 < y

   1. Initial program 56.3%

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

   3. Taylor expanded in z around 0 31.5%

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

   if -4.5999999999999998e-9 < y < 1.8999999999999999e-58

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 35.5%

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

      1. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around 0 40.6%

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

Alternative 17: 25.4% 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 66.0%

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

3. Taylor expanded in z around 0 21.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 73.9% 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 2024085 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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