Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 89.1%

Time: 18.6s

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: 66.8% 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: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -10000000000000:\\ \;\;\;\;t\_2 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 210000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- a t) (- y b))))
   (if (<= z -10000000000000.0)
     (- t_2 (/ x z))
     (if (<= z 210000.0)
       (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1))))
       (+
        t_2
        (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -10000000000000.0) {
		tmp = t_2 - (x / z);
	} else if (z <= 210000.0) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else {
		tmp = t_2 + (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / 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 = y + (z * (b - y))
    t_2 = (a - t) / (y - b)
    if (z <= (-10000000000000.0d0)) then
        tmp = t_2 - (x / z)
    else if (z <= 210000.0d0) then
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    else
        tmp = t_2 + (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ** 2.0d0)))) / 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 = y + (z * (b - y));
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -10000000000000.0) {
		tmp = t_2 - (x / z);
	} else if (z <= 210000.0) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else {
		tmp = t_2 + (((x * (y / (b - y))) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (a - t) / (y - b)
	tmp = 0
	if z <= -10000000000000.0:
		tmp = t_2 - (x / z)
	elif z <= 210000.0:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	else:
		tmp = t_2 + (((x * (y / (b - y))) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -10000000000000.0)
		tmp = Float64(t_2 - Float64(x / z));
	elseif (z <= 210000.0)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	else
		tmp = Float64(t_2 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -10000000000000.0)
		tmp = t_2 - (x / z);
	elseif (z <= 210000.0)
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	else
		tmp = t_2 + (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10000000000000.0], N[(t$95$2 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 210000.0], 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], N[(t$95$2 + N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e13

   1. Initial program 52.0%

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

   3. Taylor expanded in z around -inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. mul-1-neg 65.2%

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

      3. distribute-lft-out-- 65.2%

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

      4. associate-/l* 69.4%

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

      5. associate-/l* 84.0%

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

      6. div-sub 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in y around inf 94.2%

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

   if -1e13 < z < 2.1e5

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 91.8%

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

   if 2.1e5 < z

   1. Initial program 41.5%

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

   3. Taylor expanded in z around -inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. mul-1-neg 59.0%

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

      3. distribute-lft-out-- 59.0%

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

      4. associate-/l* 67.6%

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

      5. associate-/l* 87.8%

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

      6. div-sub 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000000000:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 210000:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1200000000000 \lor \neg \left(z \leq 1.36 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1200000000000.0) (not (<= z 1.36e+25)))
     (- (/ (- a t) (- y b)) (/ x z))
     (* 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 * (b - y));
	double tmp;
	if ((z <= -1200000000000.0) || !(z <= 1.36e+25)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} 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 * (b - y))
    if ((z <= (-1200000000000.0d0)) .or. (.not. (z <= 1.36d+25))) then
        tmp = ((a - t) / (y - b)) - (x / z)
    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 * (b - y));
	double tmp;
	if ((z <= -1200000000000.0) || !(z <= 1.36e+25)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} 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 * (b - y))
	tmp = 0
	if (z <= -1200000000000.0) or not (z <= 1.36e+25):
		tmp = ((a - t) / (y - b)) - (x / z)
	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(b - y)))
	tmp = 0.0
	if ((z <= -1200000000000.0) || !(z <= 1.36e+25))
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z));
	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 * (b - y));
	tmp = 0.0;
	if ((z <= -1200000000000.0) || ~((z <= 1.36e+25)))
		tmp = ((a - t) / (y - b)) - (x / z);
	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[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1200000000000.0], N[Not[LessEqual[z, 1.36e+25]], $MachinePrecision]], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $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 < -1.2e12 or 1.36e25 < z

   1. Initial program 45.0%

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

   3. Taylor expanded in z around -inf 63.8%

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

      1. associate--l+ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. distribute-lft-out-- 63.8%

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

      4. associate-/l* 69.8%

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

      5. associate-/l* 86.2%

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

      6. div-sub 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 89.3%

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

   if -1.2e12 < z < 1.36e25

   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 x around inf 90.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1200000000000 \lor \neg \left(z \leq 1.36 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\left(b \cdot \frac{z}{y} - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -1.9e-44)
     t_1
     (if (<= z 4.3e-26)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 1.4e+19)
         (/ (- (* x (/ y z)) a) b)
         (if (<= z 1.12e+101) (/ x (+ (- (* b (/ z y)) z) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.9e-44) {
		tmp = t_1;
	} else if (z <= 4.3e-26) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.4e+19) {
		tmp = ((x * (y / z)) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = x / (((b * (z / y)) - z) + 1.0);
	} 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 = (a - t) / (y - b)
    if (z <= (-1.9d-44)) then
        tmp = t_1
    else if (z <= 4.3d-26) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.4d+19) then
        tmp = ((x * (y / z)) - a) / b
    else if (z <= 1.12d+101) then
        tmp = x / (((b * (z / y)) - z) + 1.0d0)
    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 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.9e-44) {
		tmp = t_1;
	} else if (z <= 4.3e-26) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.4e+19) {
		tmp = ((x * (y / z)) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = x / (((b * (z / y)) - z) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -1.9e-44:
		tmp = t_1
	elif z <= 4.3e-26:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.4e+19:
		tmp = ((x * (y / z)) - a) / b
	elif z <= 1.12e+101:
		tmp = x / (((b * (z / y)) - z) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -1.9e-44)
		tmp = t_1;
	elseif (z <= 4.3e-26)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.4e+19)
		tmp = Float64(Float64(Float64(x * Float64(y / z)) - a) / b);
	elseif (z <= 1.12e+101)
		tmp = Float64(x / Float64(Float64(Float64(b * Float64(z / y)) - z) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -1.9e-44)
		tmp = t_1;
	elseif (z <= 4.3e-26)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.4e+19)
		tmp = ((x * (y / z)) - a) / b;
	elseif (z <= 1.12e+101)
		tmp = x / (((b * (z / y)) - z) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e-44], t$95$1, If[LessEqual[z, 4.3e-26], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+19], N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.12e+101], N[(x / N[(N[(N[(b * N[(z / y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e-44 or 1.1199999999999999e101 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in z around inf 82.4%

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

   if -1.9e-44 < z < 4.29999999999999988e-26

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 62.9%

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

   4. Taylor expanded in x around 0 74.8%

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

   if 4.29999999999999988e-26 < z < 1.4e19

   1. Initial program 84.5%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. associate-/l* 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in b around inf 60.7%

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

      1. associate-*r/ 60.7%

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

   8. Simplified 60.7%

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

   9. Taylor expanded in t around 0 58.7%

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

       1. associate-*r/ 58.7%

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

   11. Simplified 58.7%

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

   if 1.4e19 < z < 1.1199999999999999e101

   1. Initial program 42.9%

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

      1. sub-neg 42.9%

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

      2. distribute-lft-in 42.7%

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

   4. Applied egg-rr 42.7%

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

   5. Taylor expanded in y around inf 37.5%

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

      1. associate-+r+ 37.5%

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

      2. mul-1-neg 37.5%

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

      3. unsub-neg 37.5%

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

      4. associate-/l* 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in x around inf 49.5%

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

      1. associate--l+ 49.5%

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

      2. associate-*r/ 64.8%

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

   10. Simplified 64.8%

       \[\leadsto \color{blue}{\frac{x}{1 + \left(b \cdot \frac{z}{y} - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\left(b \cdot \frac{z}{y} - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{\left(t + x \cdot \frac{y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\left(b \cdot \frac{z}{y} - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -9e-42)
     t_1
     (if (<= z 1.8e-74)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 1.9e+19)
         (/ (- (+ t (* x (/ y z))) a) b)
         (if (<= z 1.12e+101) (/ x (+ (- (* b (/ z y)) z) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -9e-42) {
		tmp = t_1;
	} else if (z <= 1.8e-74) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.9e+19) {
		tmp = ((t + (x * (y / z))) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = x / (((b * (z / y)) - z) + 1.0);
	} 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 = (a - t) / (y - b)
    if (z <= (-9d-42)) then
        tmp = t_1
    else if (z <= 1.8d-74) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.9d+19) then
        tmp = ((t + (x * (y / z))) - a) / b
    else if (z <= 1.12d+101) then
        tmp = x / (((b * (z / y)) - z) + 1.0d0)
    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 = (a - t) / (y - b);
	double tmp;
	if (z <= -9e-42) {
		tmp = t_1;
	} else if (z <= 1.8e-74) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.9e+19) {
		tmp = ((t + (x * (y / z))) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = x / (((b * (z / y)) - z) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -9e-42:
		tmp = t_1
	elif z <= 1.8e-74:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.9e+19:
		tmp = ((t + (x * (y / z))) - a) / b
	elif z <= 1.12e+101:
		tmp = x / (((b * (z / y)) - z) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -9e-42)
		tmp = t_1;
	elseif (z <= 1.8e-74)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.9e+19)
		tmp = Float64(Float64(Float64(t + Float64(x * Float64(y / z))) - a) / b);
	elseif (z <= 1.12e+101)
		tmp = Float64(x / Float64(Float64(Float64(b * Float64(z / y)) - z) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -9e-42)
		tmp = t_1;
	elseif (z <= 1.8e-74)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.9e+19)
		tmp = ((t + (x * (y / z))) - a) / b;
	elseif (z <= 1.12e+101)
		tmp = x / (((b * (z / y)) - z) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-42], t$95$1, If[LessEqual[z, 1.8e-74], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+19], N[(N[(N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.12e+101], N[(x / N[(N[(N[(b * N[(z / y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9e-42 or 1.1199999999999999e101 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in z around inf 82.4%

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

   if -9e-42 < z < 1.8000000000000001e-74

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 63.5%

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

   4. Taylor expanded in x around 0 76.5%

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

   if 1.8000000000000001e-74 < z < 1.9e19

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in b around inf 59.1%

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

      1. associate-*r/ 59.1%

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

   8. Simplified 59.1%

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

   if 1.9e19 < z < 1.1199999999999999e101

   1. Initial program 42.9%

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

      1. sub-neg 42.9%

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

      2. distribute-lft-in 42.7%

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

   4. Applied egg-rr 42.7%

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

   5. Taylor expanded in y around inf 37.5%

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

      1. associate-+r+ 37.5%

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

      2. mul-1-neg 37.5%

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

      3. unsub-neg 37.5%

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

      4. associate-/l* 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in x around inf 49.5%

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

      1. associate--l+ 49.5%

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

      2. associate-*r/ 64.8%

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

   10. Simplified 64.8%

       \[\leadsto \color{blue}{\frac{x}{1 + \left(b \cdot \frac{z}{y} - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-42}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{\left(t + x \cdot \frac{y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{\left(b \cdot \frac{z}{y} - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \frac{-1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.8e+253)
     t_1
     (if (<= z -8.2e+232)
       (/ a (- b))
       (if (<= z -2.9e-53)
         t_1
         (if (<= z 1.15e-73) x (if (<= z 7.2e+106) (* a (/ -1.0 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 <= -1.8e+253) {
		tmp = t_1;
	} else if (z <= -8.2e+232) {
		tmp = a / -b;
	} else if (z <= -2.9e-53) {
		tmp = t_1;
	} else if (z <= 1.15e-73) {
		tmp = x;
	} else if (z <= 7.2e+106) {
		tmp = a * (-1.0 / 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 <= (-1.8d+253)) then
        tmp = t_1
    else if (z <= (-8.2d+232)) then
        tmp = a / -b
    else if (z <= (-2.9d-53)) then
        tmp = t_1
    else if (z <= 1.15d-73) then
        tmp = x
    else if (z <= 7.2d+106) then
        tmp = a * ((-1.0d0) / 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 <= -1.8e+253) {
		tmp = t_1;
	} else if (z <= -8.2e+232) {
		tmp = a / -b;
	} else if (z <= -2.9e-53) {
		tmp = t_1;
	} else if (z <= 1.15e-73) {
		tmp = x;
	} else if (z <= 7.2e+106) {
		tmp = a * (-1.0 / 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 <= -1.8e+253:
		tmp = t_1
	elif z <= -8.2e+232:
		tmp = a / -b
	elif z <= -2.9e-53:
		tmp = t_1
	elif z <= 1.15e-73:
		tmp = x
	elif z <= 7.2e+106:
		tmp = a * (-1.0 / 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 <= -1.8e+253)
		tmp = t_1;
	elseif (z <= -8.2e+232)
		tmp = Float64(a / Float64(-b));
	elseif (z <= -2.9e-53)
		tmp = t_1;
	elseif (z <= 1.15e-73)
		tmp = x;
	elseif (z <= 7.2e+106)
		tmp = Float64(a * Float64(-1.0 / 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 <= -1.8e+253)
		tmp = t_1;
	elseif (z <= -8.2e+232)
		tmp = a / -b;
	elseif (z <= -2.9e-53)
		tmp = t_1;
	elseif (z <= 1.15e-73)
		tmp = x;
	elseif (z <= 7.2e+106)
		tmp = a * (-1.0 / 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, -1.8e+253], t$95$1, If[LessEqual[z, -8.2e+232], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, -2.9e-53], t$95$1, If[LessEqual[z, 1.15e-73], x, If[LessEqual[z, 7.2e+106], N[(a * N[(-1.0 / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e253 or -8.20000000000000005e232 < z < -2.8999999999999998e-53 or 7.2000000000000002e106 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in z around inf 81.3%

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

   4. Taylor expanded in t around inf 47.6%

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

   if -1.8e253 < z < -8.20000000000000005e232

   1. Initial program 44.9%

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

   3. Taylor expanded in a around inf 41.0%

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

      1. mul-1-neg 41.0%

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

      2. associate-/l* 41.2%

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

      3. distribute-rgt-neg-in 41.2%

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

      4. mul-1-neg 41.2%

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

      5. associate-*r/ 41.2%

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

      6. mul-1-neg 41.2%

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

      7. +-commutative 41.2%

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

      8. fma-define 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in b around inf 69.4%

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

      1. associate-*r/ 69.4%

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

      2. mul-1-neg 69.4%

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

   8. Simplified 69.4%

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

   if -2.8999999999999998e-53 < z < 1.14999999999999994e-73

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 59.0%

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

   if 1.14999999999999994e-73 < z < 7.2000000000000002e106

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 30.3%

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

      1. mul-1-neg 30.3%

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

      2. associate-/l* 38.9%

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

      3. distribute-rgt-neg-in 38.9%

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

      4. mul-1-neg 38.9%

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

      5. associate-*r/ 38.9%

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

      6. mul-1-neg 38.9%

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

      7. +-commutative 38.9%

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

      8. fma-define 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in b around inf 33.6%

      \[\leadsto a \cdot \color{blue}{\frac{-1}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+253}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \frac{-1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+120} \lor \neg \left(z \leq 4.4 \cdot 10^{+223}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -5.2e+231)
     t_1
     (if (<= z -2.4e-54)
       (/ t b)
       (if (<= z 1.15e-73)
         x
         (if (or (<= z 7.2e+120) (not (<= z 4.4e+223))) t_1 (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -5.2e+231) {
		tmp = t_1;
	} else if (z <= -2.4e-54) {
		tmp = t / b;
	} else if (z <= 1.15e-73) {
		tmp = x;
	} else if ((z <= 7.2e+120) || !(z <= 4.4e+223)) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-5.2d+231)) then
        tmp = t_1
    else if (z <= (-2.4d-54)) then
        tmp = t / b
    else if (z <= 1.15d-73) then
        tmp = x
    else if ((z <= 7.2d+120) .or. (.not. (z <= 4.4d+223))) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -5.2e+231) {
		tmp = t_1;
	} else if (z <= -2.4e-54) {
		tmp = t / b;
	} else if (z <= 1.15e-73) {
		tmp = x;
	} else if ((z <= 7.2e+120) || !(z <= 4.4e+223)) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -5.2e+231:
		tmp = t_1
	elif z <= -2.4e-54:
		tmp = t / b
	elif z <= 1.15e-73:
		tmp = x
	elif (z <= 7.2e+120) or not (z <= 4.4e+223):
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -5.2e+231)
		tmp = t_1;
	elseif (z <= -2.4e-54)
		tmp = Float64(t / b);
	elseif (z <= 1.15e-73)
		tmp = x;
	elseif ((z <= 7.2e+120) || !(z <= 4.4e+223))
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -5.2e+231)
		tmp = t_1;
	elseif (z <= -2.4e-54)
		tmp = t / b;
	elseif (z <= 1.15e-73)
		tmp = x;
	elseif ((z <= 7.2e+120) || ~((z <= 4.4e+223)))
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -5.2e+231], t$95$1, If[LessEqual[z, -2.4e-54], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.15e-73], x, If[Or[LessEqual[z, 7.2e+120], N[Not[LessEqual[z, 4.4e+223]], $MachinePrecision]], t$95$1, N[(t / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e231 or 1.14999999999999994e-73 < z < 7.20000000000000031e120 or 4.3999999999999999e223 < z

   1. Initial program 49.2%

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

   3. Taylor expanded in a around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. associate-/l* 34.2%

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

      3. distribute-rgt-neg-in 34.2%

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

      4. mul-1-neg 34.2%

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

      5. associate-*r/ 34.2%

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

      6. mul-1-neg 34.2%

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

      7. +-commutative 34.2%

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

      8. fma-define 34.2%

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

   5. Simplified 34.2%

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

   6. Taylor expanded in b around inf 36.7%

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

      1. associate-*r/ 36.7%

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

      2. mul-1-neg 36.7%

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

   8. Simplified 36.7%

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

   if -5.1999999999999997e231 < z < -2.40000000000000013e-54 or 7.20000000000000031e120 < z < 4.3999999999999999e223

   1. Initial program 60.2%

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

   3. Taylor expanded in y around 0 38.8%

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

   4. Taylor expanded in t around inf 31.4%

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

   if -2.40000000000000013e-54 < z < 1.14999999999999994e-73

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 59.0%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+231}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+120} \lor \neg \left(z \leq 4.4 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \frac{-1}{b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -6e+231)
     t_1
     (if (<= z -7.6e-55)
       (/ t b)
       (if (<= z 1.1e-73)
         x
         (if (<= z 1.45e+109)
           (* a (/ -1.0 b))
           (if (<= z 5.5e+223) (/ t b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -6e+231) {
		tmp = t_1;
	} else if (z <= -7.6e-55) {
		tmp = t / b;
	} else if (z <= 1.1e-73) {
		tmp = x;
	} else if (z <= 1.45e+109) {
		tmp = a * (-1.0 / b);
	} else if (z <= 5.5e+223) {
		tmp = t / 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 = a / -b
    if (z <= (-6d+231)) then
        tmp = t_1
    else if (z <= (-7.6d-55)) then
        tmp = t / b
    else if (z <= 1.1d-73) then
        tmp = x
    else if (z <= 1.45d+109) then
        tmp = a * ((-1.0d0) / b)
    else if (z <= 5.5d+223) then
        tmp = t / 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 = a / -b;
	double tmp;
	if (z <= -6e+231) {
		tmp = t_1;
	} else if (z <= -7.6e-55) {
		tmp = t / b;
	} else if (z <= 1.1e-73) {
		tmp = x;
	} else if (z <= 1.45e+109) {
		tmp = a * (-1.0 / b);
	} else if (z <= 5.5e+223) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -6e+231:
		tmp = t_1
	elif z <= -7.6e-55:
		tmp = t / b
	elif z <= 1.1e-73:
		tmp = x
	elif z <= 1.45e+109:
		tmp = a * (-1.0 / b)
	elif z <= 5.5e+223:
		tmp = t / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -6e+231)
		tmp = t_1;
	elseif (z <= -7.6e-55)
		tmp = Float64(t / b);
	elseif (z <= 1.1e-73)
		tmp = x;
	elseif (z <= 1.45e+109)
		tmp = Float64(a * Float64(-1.0 / b));
	elseif (z <= 5.5e+223)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -6e+231)
		tmp = t_1;
	elseif (z <= -7.6e-55)
		tmp = t / b;
	elseif (z <= 1.1e-73)
		tmp = x;
	elseif (z <= 1.45e+109)
		tmp = a * (-1.0 / b);
	elseif (z <= 5.5e+223)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -6e+231], t$95$1, If[LessEqual[z, -7.6e-55], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.1e-73], x, If[LessEqual[z, 1.45e+109], N[(a * N[(-1.0 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+223], N[(t / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000003e231 or 5.4999999999999999e223 < z

   1. Initial program 24.7%

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

   3. Taylor expanded in a around inf 20.5%

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

      1. mul-1-neg 20.5%

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

      2. associate-/l* 27.5%

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

      3. distribute-rgt-neg-in 27.5%

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

      4. mul-1-neg 27.5%

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

      5. associate-*r/ 27.5%

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

      6. mul-1-neg 27.5%

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

      7. +-commutative 27.5%

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

      8. fma-define 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in b around inf 41.0%

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

      1. associate-*r/ 41.0%

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

      2. mul-1-neg 41.0%

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

   8. Simplified 41.0%

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

   if -6.0000000000000003e231 < z < -7.5999999999999993e-55 or 1.45e109 < z < 5.4999999999999999e223

   1. Initial program 60.2%

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

   3. Taylor expanded in y around 0 38.8%

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

   4. Taylor expanded in t around inf 31.4%

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

   if -7.5999999999999993e-55 < z < 1.1e-73

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 59.0%

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

   if 1.1e-73 < z < 1.45e109

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 30.3%

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

      1. mul-1-neg 30.3%

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

      2. associate-/l* 38.9%

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

      3. distribute-rgt-neg-in 38.9%

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

      4. mul-1-neg 38.9%

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

      5. associate-*r/ 38.9%

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

      6. mul-1-neg 38.9%

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

      7. +-commutative 38.9%

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

      8. fma-define 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in b around inf 33.6%

      \[\leadsto a \cdot \color{blue}{\frac{-1}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+231}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \frac{-1}{b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+223}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -4.8e-41)
     t_1
     (if (<= z 4.5e-26)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 1.6e+23)
         (/ (- (* x (/ y z)) a) b)
         (if (<= z 1.12e+101) (- (/ t (- b y)) (/ x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -4.8e-41) {
		tmp = t_1;
	} else if (z <= 4.5e-26) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.6e+23) {
		tmp = ((x * (y / z)) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = (t / (b - y)) - (x / z);
	} 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 = (a - t) / (y - b)
    if (z <= (-4.8d-41)) then
        tmp = t_1
    else if (z <= 4.5d-26) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.6d+23) then
        tmp = ((x * (y / z)) - a) / b
    else if (z <= 1.12d+101) then
        tmp = (t / (b - y)) - (x / z)
    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 = (a - t) / (y - b);
	double tmp;
	if (z <= -4.8e-41) {
		tmp = t_1;
	} else if (z <= 4.5e-26) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.6e+23) {
		tmp = ((x * (y / z)) - a) / b;
	} else if (z <= 1.12e+101) {
		tmp = (t / (b - y)) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -4.8e-41:
		tmp = t_1
	elif z <= 4.5e-26:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.6e+23:
		tmp = ((x * (y / z)) - a) / b
	elif z <= 1.12e+101:
		tmp = (t / (b - y)) - (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -4.8e-41)
		tmp = t_1;
	elseif (z <= 4.5e-26)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.6e+23)
		tmp = Float64(Float64(Float64(x * Float64(y / z)) - a) / b);
	elseif (z <= 1.12e+101)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -4.8e-41)
		tmp = t_1;
	elseif (z <= 4.5e-26)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.6e+23)
		tmp = ((x * (y / z)) - a) / b;
	elseif (z <= 1.12e+101)
		tmp = (t / (b - y)) - (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-41], t$95$1, If[LessEqual[z, 4.5e-26], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+23], N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.12e+101], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.80000000000000044e-41 or 1.1199999999999999e101 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in z around inf 82.4%

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

   if -4.80000000000000044e-41 < z < 4.4999999999999999e-26

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 62.9%

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

   4. Taylor expanded in x around 0 74.8%

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

   if 4.4999999999999999e-26 < z < 1.6e23

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 79.9%

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

      1. associate--l+ 79.9%

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

      2. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in b around inf 59.5%

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

      1. associate-*r/ 59.5%

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around 0 57.8%

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

       1. associate-*r/ 57.8%

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

   11. Simplified 57.8%

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

   if 1.6e23 < z < 1.1199999999999999e101

   1. Initial program 42.0%

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

   3. Taylor expanded in z around -inf 47.5%

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

      1. associate--l+ 47.5%

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

      2. mul-1-neg 47.5%

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

      3. distribute-lft-out-- 47.5%

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

      4. associate-/l* 58.7%

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

      5. associate-/l* 82.8%

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

      6. div-sub 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf 82.1%

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

   7. Taylor expanded in t around inf 65.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} - a}{b}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+21} \lor \neg \left(z \leq 6.2 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.4e+21) (not (<= z 6.2e+23)))
   (- (/ (- a t) (- y b)) (/ x z))
   (/ (- (* x y) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.4e+21) || !(z <= 6.2e+23)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.4d+21)) .or. (.not. (z <= 6.2d+23))) then
        tmp = ((a - t) / (y - b)) - (x / z)
    else
        tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.4e+21) || !(z <= 6.2e+23)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.4e+21) or not (z <= 6.2e+23):
		tmp = ((a - t) / (y - b)) - (x / z)
	else:
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.4e+21) || !(z <= 6.2e+23))
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.4e+21) || ~((z <= 6.2e+23)))
		tmp = ((a - t) / (y - b)) - (x / z);
	else
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.4e+21], N[Not[LessEqual[z, 6.2e+23]], $MachinePrecision]], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4e21 or 6.19999999999999941e23 < z

   1. Initial program 42.3%

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

   3. Taylor expanded in z around -inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. distribute-lft-out-- 63.7%

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

      4. associate-/l* 70.0%

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

      5. associate-/l* 86.4%

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

      6. div-sub 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around inf 89.0%

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

   if -7.4e21 < z < 6.19999999999999941e23

   1. Initial program 87.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+21} \lor \neg \left(z \leq 6.2 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ t (- b y))))
   (if (<= t -5.6e+41)
     t_2
     (if (<= t -9.6e-204)
       t_1
       (if (<= t 5.2e-209) (/ a (- b)) (if (<= t 4.4e+104) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = t / (b - y);
	double tmp;
	if (t <= -5.6e+41) {
		tmp = t_2;
	} else if (t <= -9.6e-204) {
		tmp = t_1;
	} else if (t <= 5.2e-209) {
		tmp = a / -b;
	} else if (t <= 4.4e+104) {
		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 / (1.0d0 - z)
    t_2 = t / (b - y)
    if (t <= (-5.6d+41)) then
        tmp = t_2
    else if (t <= (-9.6d-204)) then
        tmp = t_1
    else if (t <= 5.2d-209) then
        tmp = a / -b
    else if (t <= 4.4d+104) 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 / (1.0 - z);
	double t_2 = t / (b - y);
	double tmp;
	if (t <= -5.6e+41) {
		tmp = t_2;
	} else if (t <= -9.6e-204) {
		tmp = t_1;
	} else if (t <= 5.2e-209) {
		tmp = a / -b;
	} else if (t <= 4.4e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = t / (b - y)
	tmp = 0
	if t <= -5.6e+41:
		tmp = t_2
	elif t <= -9.6e-204:
		tmp = t_1
	elif t <= 5.2e-209:
		tmp = a / -b
	elif t <= 4.4e+104:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (t <= -5.6e+41)
		tmp = t_2;
	elseif (t <= -9.6e-204)
		tmp = t_1;
	elseif (t <= 5.2e-209)
		tmp = Float64(a / Float64(-b));
	elseif (t <= 4.4e+104)
		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 / (1.0 - z);
	t_2 = t / (b - y);
	tmp = 0.0;
	if (t <= -5.6e+41)
		tmp = t_2;
	elseif (t <= -9.6e-204)
		tmp = t_1;
	elseif (t <= 5.2e-209)
		tmp = a / -b;
	elseif (t <= 4.4e+104)
		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[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+41], t$95$2, If[LessEqual[t, -9.6e-204], t$95$1, If[LessEqual[t, 5.2e-209], N[(a / (-b)), $MachinePrecision], If[LessEqual[t, 4.4e+104], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5999999999999999e41 or 4.40000000000000001e104 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 64.9%

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

   4. Taylor expanded in t around inf 56.2%

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

   if -5.5999999999999999e41 < t < -9.6e-204 or 5.19999999999999969e-209 < t < 4.40000000000000001e104

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. unsub-neg 45.8%

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

   5. Simplified 45.8%

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

   if -9.6e-204 < t < 5.19999999999999969e-209

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/l* 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. mul-1-neg 60.2%

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

      5. associate-*r/ 60.2%

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

      6. mul-1-neg 60.2%

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

      7. +-commutative 60.2%

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

      8. fma-define 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in b around inf 49.0%

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

      1. associate-*r/ 49.0%

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

      2. mul-1-neg 49.0%

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

   8. Simplified 49.0%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-41} \lor \neg \left(z \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e-41) (not (<= z 1.1e-16)))
   (- (/ (- a t) (- y b)) (/ x z))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-41) || !(z <= 1.1e-16)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d-41)) .or. (.not. (z <= 1.1d-16))) then
        tmp = ((a - t) / (y - b)) - (x / z)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-41) || !(z <= 1.1e-16)) {
		tmp = ((a - t) / (y - b)) - (x / z);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e-41) or not (z <= 1.1e-16):
		tmp = ((a - t) / (y - b)) - (x / z)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e-41) || !(z <= 1.1e-16))
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e-41) || ~((z <= 1.1e-16)))
		tmp = ((a - t) / (y - b)) - (x / z);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e-41], N[Not[LessEqual[z, 1.1e-16]], $MachinePrecision]], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999999e-41 or 1.1e-16 < z

   1. Initial program 51.7%

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

   3. Taylor expanded in z around -inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. mul-1-neg 60.8%

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

      3. distribute-lft-out-- 60.8%

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

      4. associate-/l* 66.0%

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

      5. associate-/l* 82.5%

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

      6. div-sub 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around inf 83.5%

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

   if -6.9999999999999999e-41 < z < 1.1e-16

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 61.8%

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

   4. Taylor expanded in x around 0 74.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-41} \lor \neg \left(z \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -6.2e-40)
     t_1
     (if (<= y 2.1e-93) (/ (- t a) b) (if (<= y 5.6e+49) (/ (- a t) 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 <= -6.2e-40) {
		tmp = t_1;
	} else if (y <= 2.1e-93) {
		tmp = (t - a) / b;
	} else if (y <= 5.6e+49) {
		tmp = (a - t) / 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 <= (-6.2d-40)) then
        tmp = t_1
    else if (y <= 2.1d-93) then
        tmp = (t - a) / b
    else if (y <= 5.6d+49) then
        tmp = (a - t) / 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 <= -6.2e-40) {
		tmp = t_1;
	} else if (y <= 2.1e-93) {
		tmp = (t - a) / b;
	} else if (y <= 5.6e+49) {
		tmp = (a - t) / 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 <= -6.2e-40:
		tmp = t_1
	elif y <= 2.1e-93:
		tmp = (t - a) / b
	elif y <= 5.6e+49:
		tmp = (a - t) / 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 <= -6.2e-40)
		tmp = t_1;
	elseif (y <= 2.1e-93)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 5.6e+49)
		tmp = Float64(Float64(a - t) / 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 <= -6.2e-40)
		tmp = t_1;
	elseif (y <= 2.1e-93)
		tmp = (t - a) / b;
	elseif (y <= 5.6e+49)
		tmp = (a - t) / 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, -6.2e-40], t$95$1, If[LessEqual[y, 2.1e-93], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5.6e+49], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000021e-40 or 5.5999999999999996e49 < y

   1. Initial program 50.5%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. unsub-neg 52.5%

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

   5. Simplified 52.5%

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

   if -6.20000000000000021e-40 < y < 2.1000000000000001e-93

   1. Initial program 81.9%

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

   3. Taylor expanded in y around 0 63.9%

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

   if 2.1000000000000001e-93 < y < 5.5999999999999996e49

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 55.2%

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

   4. Taylor expanded in b around 0 41.1%

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

      1. mul-1-neg 41.1%

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

   6. Simplified 41.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-93}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-41} \lor \neg \left(z \leq 7.4 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e-41) (not (<= z 7.4e-17)))
   (/ (- a t) (- y b))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-41) || !(z <= 7.4e-17)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d-41)) .or. (.not. (z <= 7.4d-17))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-41) || !(z <= 7.4e-17)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e-41) or not (z <= 7.4e-17):
		tmp = (a - t) / (y - b)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e-41) || !(z <= 7.4e-17))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e-41) || ~((z <= 7.4e-17)))
		tmp = (a - t) / (y - b);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e-41], N[Not[LessEqual[z, 7.4e-17]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999999e-41 or 7.3999999999999995e-17 < z

   1. Initial program 51.7%

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

   3. Taylor expanded in z around inf 75.1%

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

   if -6.9999999999999999e-41 < z < 7.3999999999999995e-17

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 61.8%

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

   4. Taylor expanded in x around 0 74.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-41} \lor \neg \left(z \leq 7.4 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-55} \lor \neg \left(z \leq 4.8 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5e-55) (not (<= z 4.8e-76))) (/ (- a t) (- y b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5e-55) || !(z <= 4.8e-76)) {
		tmp = (a - t) / (y - 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 ((z <= (-5d-55)) .or. (.not. (z <= 4.8d-76))) then
        tmp = (a - t) / (y - 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 ((z <= -5e-55) || !(z <= 4.8e-76)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5e-55) or not (z <= 4.8e-76):
		tmp = (a - t) / (y - b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5e-55) || !(z <= 4.8e-76))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5e-55) || ~((z <= 4.8e-76)))
		tmp = (a - t) / (y - b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5e-55], N[Not[LessEqual[z, 4.8e-76]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-55 or 4.80000000000000026e-76 < z

   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 z around inf 72.5%

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

   if -5.0000000000000002e-55 < z < 4.80000000000000026e-76

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 59.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-55} \lor \neg \left(z \leq 4.8 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-38} \lor \neg \left(y \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e-38) (not (<= y 1.12e-26)))
   (/ x (- 1.0 z))
   (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-38) || !(y <= 1.12e-26)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d-38)) .or. (.not. (y <= 1.12d-26))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-38) || !(y <= 1.12e-26)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e-38) or not (y <= 1.12e-26):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e-38) || !(y <= 1.12e-26))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e-38) || ~((y <= 1.12e-26)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e-38], N[Not[LessEqual[y, 1.12e-26]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000001e-38 or 1.12e-26 < y

   1. Initial program 54.0%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unsub-neg 48.9%

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

   5. Simplified 48.9%

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

   if -1.15000000000000001e-38 < y < 1.12e-26

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0 59.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-38} \lor \neg \left(y \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-53} \lor \neg \left(z \leq 5.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-53) (not (<= z 5.2e+20))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-53) || !(z <= 5.2e+20)) {
		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 ((z <= (-2.3d-53)) .or. (.not. (z <= 5.2d+20))) 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 ((z <= -2.3e-53) || !(z <= 5.2e+20)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e-53) or not (z <= 5.2e+20):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-53) || !(z <= 5.2e+20))
		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 ((z <= -2.3e-53) || ~((z <= 5.2e+20)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-53], N[Not[LessEqual[z, 5.2e+20]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-53 or 5.2e20 < z

   1. Initial program 50.1%

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

   3. Taylor expanded in y around 0 40.9%

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

   4. Taylor expanded in t around inf 25.2%

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

   if -2.3000000000000001e-53 < z < 5.2e20

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 51.2%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-53} \lor \neg \left(z \leq 5.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 24.8% 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 65.9%

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

3. Taylor expanded in z around 0 25.0%

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

4. Final simplification 25.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 74.2% 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 2024067 
(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)))))