Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.9% → 90.2%

Time: 21.8s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.9% 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: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+238}:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -350000000 \lor \neg \left(z \leq 7.6 \cdot 10^{+15}\right):\\ \;\;\;\;t\_1 + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.9e+238)
     (- t_1 (/ x z))
     (if (or (<= z -350000000.0) (not (<= z 7.6e+15)))
       (+
        t_1
        (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z))
       (*
        x
        (-
         (/ y (+ y (* z (- b y))))
         (/ (* z (- t a)) (* x (- (* z (- y b)) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+238) {
		tmp = t_1 - (x / z);
	} else if ((z <= -350000000.0) || !(z <= 7.6e+15)) {
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.9d+238)) then
        tmp = t_1 - (x / z)
    else if ((z <= (-350000000.0d0)) .or. (.not. (z <= 7.6d+15))) then
        tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z)
    else
        tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+238) {
		tmp = t_1 - (x / z);
	} else if ((z <= -350000000.0) || !(z <= 7.6e+15)) {
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.9e+238:
		tmp = t_1 - (x / z)
	elif (z <= -350000000.0) or not (z <= 7.6e+15):
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z)
	else:
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.9e+238)
		tmp = Float64(t_1 - Float64(x / z));
	elseif ((z <= -350000000.0) || !(z <= 7.6e+15))
		tmp = Float64(t_1 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(y + Float64(z * Float64(b - y)))) - Float64(Float64(z * Float64(t - a)) / Float64(x * Float64(Float64(z * Float64(y - b)) - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.9e+238)
		tmp = t_1 - (x / z);
	elseif ((z <= -350000000.0) || ~((z <= 7.6e+15)))
		tmp = t_1 + (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z);
	else
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+238], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -350000000.0], N[Not[LessEqual[z, 7.6e+15]], $MachinePrecision]], N[(t$95$1 + N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000002e238

   1. Initial program 33.7%

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

   3. Taylor expanded in z around -inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. mul-1-neg 69.2%

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

      3. distribute-lft-out-- 69.2%

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

      4. associate-/l* 69.2%

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

      5. associate-/l* 54.5%

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

      6. div-sub 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around inf 99.9%

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

   if -2.9000000000000002e238 < z < -3.5e8 or 7.6e15 < 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 z around -inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. mul-1-neg 70.0%

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

      3. distribute-lft-out-- 70.0%

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

      4. associate-/l* 73.4%

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

      5. associate-/l* 91.7%

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

      6. div-sub 92.6%

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

   5. Simplified 92.6%

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

   if -3.5e8 < z < 7.6e15

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 89.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+238}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -350000000 \lor \neg \left(z \leq 7.6 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -550000 \lor \neg \left(z \leq 1.3 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -550000.0) (not (<= z 1.3e+15)))
   (+
    (/ t (- b y))
    (-
     (* (/ x z) (/ y (- b y)))
     (+ (/ a (- b y)) (* y (/ (- t a) (* z (pow (- b y) 2.0)))))))
   (*
    x
    (-
     (/ y (+ y (* z (- b y))))
     (/ (* z (- t a)) (* x (- (* z (- y b)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -550000.0) || !(z <= 1.3e+15)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y * ((t - a) / (z * pow((b - y), 2.0))))));
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - 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 <= (-550000.0d0)) .or. (.not. (z <= 1.3d+15))) then
        tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y * ((t - a) / (z * ((b - y) ** 2.0d0))))))
    else
        tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - 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 <= -550000.0) || !(z <= 1.3e+15)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y * ((t - a) / (z * Math.pow((b - y), 2.0))))));
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -550000.0) or not (z <= 1.3e+15):
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y * ((t - a) / (z * math.pow((b - y), 2.0))))))
	else:
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -550000.0) || !(z <= 1.3e+15))
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) - Float64(Float64(a / Float64(b - y)) + Float64(y * Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0)))))));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(y + Float64(z * Float64(b - y)))) - Float64(Float64(z * Float64(t - a)) / Float64(x * Float64(Float64(z * Float64(y - b)) - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -550000.0) || ~((z <= 1.3e+15)))
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y * ((t - a) / (z * ((b - y) ^ 2.0))))));
	else
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -550000.0], N[Not[LessEqual[z, 1.3e+15]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e5 or 1.3e15 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. times-frac 72.4%

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

      3. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

   if -5.5e5 < z < 1.3e15

   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 x around inf 90.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -550000 \lor \neg \left(z \leq 1.3 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ t_2 := \frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-294}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z)))
        (t_2 (/ -1.0 (- (/ (+ z -1.0) x) (* b (/ z (* y x)))))))
   (if (<= z -620000000.0)
     t_1
     (if (<= z -1.85e-65)
       (/ (* z (- t a)) (+ y (* z (- b y))))
       (if (<= z -7.6e-294)
         t_2
         (if (<= z 3.5e-31)
           (/ (* y (+ x (* z (/ (- t a) y)))) y)
           (if (<= z 1e+15) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double t_2 = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	double tmp;
	if (z <= -620000000.0) {
		tmp = t_1;
	} else if (z <= -1.85e-65) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= -7.6e-294) {
		tmp = t_2;
	} else if (z <= 3.5e-31) {
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	} else if (z <= 1e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    t_2 = (-1.0d0) / (((z + (-1.0d0)) / x) - (b * (z / (y * x))))
    if (z <= (-620000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.85d-65)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= (-7.6d-294)) then
        tmp = t_2
    else if (z <= 3.5d-31) then
        tmp = (y * (x + (z * ((t - a) / y)))) / y
    else if (z <= 1d+15) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double t_2 = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	double tmp;
	if (z <= -620000000.0) {
		tmp = t_1;
	} else if (z <= -1.85e-65) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= -7.6e-294) {
		tmp = t_2;
	} else if (z <= 3.5e-31) {
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	} else if (z <= 1e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	t_2 = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))))
	tmp = 0
	if z <= -620000000.0:
		tmp = t_1
	elif z <= -1.85e-65:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= -7.6e-294:
		tmp = t_2
	elif z <= 3.5e-31:
		tmp = (y * (x + (z * ((t - a) / y)))) / y
	elif z <= 1e+15:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	t_2 = Float64(-1.0 / Float64(Float64(Float64(z + -1.0) / x) - Float64(b * Float64(z / Float64(y * x)))))
	tmp = 0.0
	if (z <= -620000000.0)
		tmp = t_1;
	elseif (z <= -1.85e-65)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -7.6e-294)
		tmp = t_2;
	elseif (z <= 3.5e-31)
		tmp = Float64(Float64(y * Float64(x + Float64(z * Float64(Float64(t - a) / y)))) / y);
	elseif (z <= 1e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	t_2 = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	tmp = 0.0;
	if (z <= -620000000.0)
		tmp = t_1;
	elseif (z <= -1.85e-65)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= -7.6e-294)
		tmp = t_2;
	elseif (z <= 3.5e-31)
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	elseif (z <= 1e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 / N[(N[(N[(z + -1.0), $MachinePrecision] / x), $MachinePrecision] - N[(b * N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -620000000.0], t$95$1, If[LessEqual[z, -1.85e-65], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-294], t$95$2, If[LessEqual[z, 3.5e-31], N[(N[(y * N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1e+15], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e8 or 1e15 < z

   1. Initial program 48.3%

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

   3. Taylor expanded in z around -inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. mul-1-neg 69.1%

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

      3. distribute-lft-out-- 69.1%

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

      4. associate-/l* 72.2%

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

      5. associate-/l* 87.0%

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

      6. div-sub 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in y around inf 88.1%

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

   if -6.2e8 < z < -1.85e-65

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.3%

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

   if -1.85e-65 < z < -7.6e-294 or 3.49999999999999985e-31 < z < 1e15

   1. Initial program 78.2%

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

      1. fma-define 78.2%

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

      2. clear-num 78.1%

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

      3. inv-pow 78.1%

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

      4. +-commutative 78.1%

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

      5. fma-undefine 78.1%

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

      6. fma-define 78.1%

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

      7. +-commutative 78.1%

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

      8. fma-define 78.1%

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

   4. Applied egg-rr 78.1%

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

      1. unpow-1 78.1%

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

      2. *-commutative 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in x around inf 49.4%

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

   8. Taylor expanded in y around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/l* 69.1%

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

      5. sub-neg 69.1%

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

      6. metadata-eval 69.1%

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

   10. Simplified 69.1%

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

   if -7.6e-294 < z < 3.49999999999999985e-31

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 90.0%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in z around 0 63.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-294}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -420000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{t\_1}{t\_2}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{t\_1 + y \cdot x}{y - z \cdot y}\\ \mathbf{elif}\;z \leq 10^{+22}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -420000000000.0)
     t_3
     (if (<= z -2.6e-68)
       (/ t_1 t_2)
       (if (<= z -1.95e-146)
         (/ -1.0 (- (/ (+ z -1.0) x) (* b (/ z (* y x)))))
         (if (<= z 4.2e-175)
           (/ (+ t_1 (* y x)) (- y (* z y)))
           (if (<= z 1e+22) (/ (+ (* y x) (* z t)) t_2) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -420000000000.0) {
		tmp = t_3;
	} else if (z <= -2.6e-68) {
		tmp = t_1 / t_2;
	} else if (z <= -1.95e-146) {
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	} else if (z <= 4.2e-175) {
		tmp = (t_1 + (y * x)) / (y - (z * y));
	} else if (z <= 1e+22) {
		tmp = ((y * x) + (z * t)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-420000000000.0d0)) then
        tmp = t_3
    else if (z <= (-2.6d-68)) then
        tmp = t_1 / t_2
    else if (z <= (-1.95d-146)) then
        tmp = (-1.0d0) / (((z + (-1.0d0)) / x) - (b * (z / (y * x))))
    else if (z <= 4.2d-175) then
        tmp = (t_1 + (y * x)) / (y - (z * y))
    else if (z <= 1d+22) then
        tmp = ((y * x) + (z * t)) / t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -420000000000.0) {
		tmp = t_3;
	} else if (z <= -2.6e-68) {
		tmp = t_1 / t_2;
	} else if (z <= -1.95e-146) {
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	} else if (z <= 4.2e-175) {
		tmp = (t_1 + (y * x)) / (y - (z * y));
	} else if (z <= 1e+22) {
		tmp = ((y * x) + (z * t)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -420000000000.0:
		tmp = t_3
	elif z <= -2.6e-68:
		tmp = t_1 / t_2
	elif z <= -1.95e-146:
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))))
	elif z <= 4.2e-175:
		tmp = (t_1 + (y * x)) / (y - (z * y))
	elif z <= 1e+22:
		tmp = ((y * x) + (z * t)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -420000000000.0)
		tmp = t_3;
	elseif (z <= -2.6e-68)
		tmp = Float64(t_1 / t_2);
	elseif (z <= -1.95e-146)
		tmp = Float64(-1.0 / Float64(Float64(Float64(z + -1.0) / x) - Float64(b * Float64(z / Float64(y * x)))));
	elseif (z <= 4.2e-175)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / Float64(y - Float64(z * y)));
	elseif (z <= 1e+22)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -420000000000.0)
		tmp = t_3;
	elseif (z <= -2.6e-68)
		tmp = t_1 / t_2;
	elseif (z <= -1.95e-146)
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	elseif (z <= 4.2e-175)
		tmp = (t_1 + (y * x)) / (y - (z * y));
	elseif (z <= 1e+22)
		tmp = ((y * x) + (z * t)) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -420000000000.0], t$95$3, If[LessEqual[z, -2.6e-68], N[(t$95$1 / t$95$2), $MachinePrecision], If[LessEqual[z, -1.95e-146], N[(-1.0 / N[(N[(N[(z + -1.0), $MachinePrecision] / x), $MachinePrecision] - N[(b * N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-175], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+22], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2e11 or 1e22 < z

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. distribute-lft-out-- 69.4%

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

      4. associate-/l* 72.5%

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

      5. associate-/l* 87.6%

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

      6. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 88.7%

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

   if -4.2e11 < z < -2.5999999999999998e-68

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.3%

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

   if -2.5999999999999998e-68 < z < -1.95000000000000001e-146

   1. Initial program 63.1%

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

      1. fma-define 63.2%

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

      2. clear-num 63.0%

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

      3. inv-pow 63.0%

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

      4. +-commutative 63.0%

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

      5. fma-undefine 63.0%

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

      6. fma-define 62.9%

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

      7. +-commutative 62.9%

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

      8. fma-define 63.0%

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

   4. Applied egg-rr 63.0%

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

      1. unpow-1 63.0%

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

      2. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x around inf 39.0%

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

   8. Taylor expanded in y around -inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. associate-/l* 75.7%

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

      5. sub-neg 75.7%

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

      6. metadata-eval 75.7%

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

   10. Simplified 75.7%

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

   if -1.95000000000000001e-146 < z < 4.2e-175

   1. Initial program 91.5%

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

   3. Taylor expanded in b around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. distribute-lft-neg-out 80.2%

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

      3. *-commutative 80.2%

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

   5. Simplified 80.2%

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

   if 4.2e-175 < z < 1e22

   1. Initial program 85.3%

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

   3. Taylor expanded in a around 0 65.6%

      \[\leadsto \color{blue}{\frac{t \cdot z + x \cdot y}{y + z \cdot \left(b - y\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420000000000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-146}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot y}\\ \mathbf{elif}\;z \leq 10^{+22}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -350000000.0) (not (<= z 4.5e+15)))
   (- (/ (- t a) (- b y)) (/ x z))
   (*
    x
    (-
     (/ y (+ y (* z (- b y))))
     (/ (* z (- t a)) (* x (- (* z (- y b)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -350000000.0) || !(z <= 4.5e+15)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - 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 <= (-350000000.0d0)) .or. (.not. (z <= 4.5d+15))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - 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 <= -350000000.0) || !(z <= 4.5e+15)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -350000000.0) or not (z <= 4.5e+15):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -350000000.0) || !(z <= 4.5e+15))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(y + Float64(z * Float64(b - y)))) - Float64(Float64(z * Float64(t - a)) / Float64(x * Float64(Float64(z * Float64(y - b)) - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -350000000.0) || ~((z <= 4.5e+15)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = x * ((y / (y + (z * (b - y)))) - ((z * (t - a)) / (x * ((z * (y - b)) - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -350000000.0], N[Not[LessEqual[z, 4.5e+15]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e8 or 4.5e15 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in z around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. distribute-lft-out-- 69.4%

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

      4. associate-/l* 72.5%

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

      5. associate-/l* 87.1%

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

      6. div-sub 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around inf 88.2%

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

   if -3.5e8 < z < 4.5e15

   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 x around inf 90.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(t - a\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-130}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{elif}\;z \leq 10^{+22}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -2300000000.0)
     t_2
     (if (<= z -1.3e-68)
       (/ (* z (- t a)) t_1)
       (if (<= z -3.4e-130)
         (/ -1.0 (- (/ (+ z -1.0) x) (* b (/ z (* y x)))))
         (if (<= z 1e+22) (/ (+ (* y x) (* z t)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -2300000000.0) {
		tmp = t_2;
	} else if (z <= -1.3e-68) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -3.4e-130) {
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	} else if (z <= 1e+22) {
		tmp = ((y * x) + (z * t)) / 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 = y + (z * (b - y))
    t_2 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-2300000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.3d-68)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= (-3.4d-130)) then
        tmp = (-1.0d0) / (((z + (-1.0d0)) / x) - (b * (z / (y * x))))
    else if (z <= 1d+22) then
        tmp = ((y * x) + (z * t)) / 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 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -2300000000.0) {
		tmp = t_2;
	} else if (z <= -1.3e-68) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -3.4e-130) {
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	} else if (z <= 1e+22) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -2300000000.0:
		tmp = t_2
	elif z <= -1.3e-68:
		tmp = (z * (t - a)) / t_1
	elif z <= -3.4e-130:
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))))
	elif z <= 1e+22:
		tmp = ((y * x) + (z * t)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -2300000000.0)
		tmp = t_2;
	elseif (z <= -1.3e-68)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= -3.4e-130)
		tmp = Float64(-1.0 / Float64(Float64(Float64(z + -1.0) / x) - Float64(b * Float64(z / Float64(y * x)))));
	elseif (z <= 1e+22)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -2300000000.0)
		tmp = t_2;
	elseif (z <= -1.3e-68)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= -3.4e-130)
		tmp = -1.0 / (((z + -1.0) / x) - (b * (z / (y * x))));
	elseif (z <= 1e+22)
		tmp = ((y * x) + (z * t)) / t_1;
	else
		tmp = t_2;
	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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2300000000.0], t$95$2, If[LessEqual[z, -1.3e-68], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, -3.4e-130], N[(-1.0 / N[(N[(N[(z + -1.0), $MachinePrecision] / x), $MachinePrecision] - N[(b * N[(z / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+22], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e9 or 1e22 < z

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. distribute-lft-out-- 69.4%

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

      4. associate-/l* 72.5%

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

      5. associate-/l* 87.6%

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

      6. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 88.7%

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

   if -2.3e9 < z < -1.2999999999999999e-68

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.3%

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

   if -1.2999999999999999e-68 < z < -3.40000000000000005e-130

   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. Step-by-step derivation

      1. fma-define 60.3%

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

      2. clear-num 60.1%

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

      3. inv-pow 60.1%

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

      4. +-commutative 60.1%

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

      5. fma-undefine 60.1%

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

      6. fma-define 60.0%

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

      7. +-commutative 60.0%

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

      8. fma-define 60.1%

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

   4. Applied egg-rr 60.1%

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

      1. unpow-1 60.1%

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

      2. *-commutative 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in x around inf 36.1%

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

   8. Taylor expanded in y around -inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. associate-/l* 75.7%

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

      5. sub-neg 75.7%

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

      6. metadata-eval 75.7%

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

   10. Simplified 75.7%

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

   if -3.40000000000000005e-130 < z < 1e22

   1. Initial program 88.6%

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

   3. Taylor expanded in a around 0 68.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-130}:\\ \;\;\;\;\frac{-1}{\frac{z + -1}{x} - b \cdot \frac{z}{y \cdot x}}\\ \mathbf{elif}\;z \leq 10^{+22}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -1.6e-9)
     t_1
     (if (<= z -9.5e-67)
       (/ (* z t) (+ y (* z (- b y))))
       (if (<= z -6.5e-294)
         x
         (if (<= z 5.8e-11) (/ (* y (+ x (* z (/ (- t a) y)))) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -1.6e-9) {
		tmp = t_1;
	} else if (z <= -9.5e-67) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= -6.5e-294) {
		tmp = x;
	} else if (z <= 5.8e-11) {
		tmp = (y * (x + (z * ((t - a) / y)))) / 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 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-1.6d-9)) then
        tmp = t_1
    else if (z <= (-9.5d-67)) then
        tmp = (z * t) / (y + (z * (b - y)))
    else if (z <= (-6.5d-294)) then
        tmp = x
    else if (z <= 5.8d-11) then
        tmp = (y * (x + (z * ((t - a) / y)))) / 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 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -1.6e-9) {
		tmp = t_1;
	} else if (z <= -9.5e-67) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= -6.5e-294) {
		tmp = x;
	} else if (z <= 5.8e-11) {
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -1.6e-9:
		tmp = t_1
	elif z <= -9.5e-67:
		tmp = (z * t) / (y + (z * (b - y)))
	elif z <= -6.5e-294:
		tmp = x
	elif z <= 5.8e-11:
		tmp = (y * (x + (z * ((t - a) / y)))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.6e-9)
		tmp = t_1;
	elseif (z <= -9.5e-67)
		tmp = Float64(Float64(z * t) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -6.5e-294)
		tmp = x;
	elseif (z <= 5.8e-11)
		tmp = Float64(Float64(y * Float64(x + Float64(z * Float64(Float64(t - a) / y)))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -1.6e-9)
		tmp = t_1;
	elseif (z <= -9.5e-67)
		tmp = (z * t) / (y + (z * (b - y)));
	elseif (z <= -6.5e-294)
		tmp = x;
	elseif (z <= 5.8e-11)
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-9], t$95$1, If[LessEqual[z, -9.5e-67], N[(N[(z * t), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-294], x, If[LessEqual[z, 5.8e-11], N[(N[(y * N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.60000000000000006e-9 or 5.8e-11 < 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 68.4%

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

      1. associate--l+ 68.4%

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

      2. mul-1-neg 68.4%

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

      3. distribute-lft-out-- 68.4%

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

      4. associate-/l* 70.5%

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

      5. associate-/l* 85.1%

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

      6. div-sub 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around inf 86.2%

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

   if -1.60000000000000006e-9 < z < -9.4999999999999994e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -9.4999999999999994e-67 < z < -6.4999999999999995e-294

   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 0 67.1%

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

   if -6.4999999999999995e-294 < z < 5.8e-11

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. associate-/l* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in z around 0 61.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -4500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -4500000000.0)
     t_1
     (if (<= z -4.5e-68)
       (/ (* z (- t a)) (+ y (* z (- b y))))
       (if (<= z -8e-294)
         x
         (if (<= z 9.2e-9) (/ (* y (+ x (* z (/ (- t a) y)))) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4500000000.0) {
		tmp = t_1;
	} else if (z <= -4.5e-68) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= -8e-294) {
		tmp = x;
	} else if (z <= 9.2e-9) {
		tmp = (y * (x + (z * ((t - a) / y)))) / 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 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-4500000000.0d0)) then
        tmp = t_1
    else if (z <= (-4.5d-68)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= (-8d-294)) then
        tmp = x
    else if (z <= 9.2d-9) then
        tmp = (y * (x + (z * ((t - a) / y)))) / 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 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4500000000.0) {
		tmp = t_1;
	} else if (z <= -4.5e-68) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= -8e-294) {
		tmp = x;
	} else if (z <= 9.2e-9) {
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -4500000000.0:
		tmp = t_1
	elif z <= -4.5e-68:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= -8e-294:
		tmp = x
	elif z <= 9.2e-9:
		tmp = (y * (x + (z * ((t - a) / y)))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -4500000000.0)
		tmp = t_1;
	elseif (z <= -4.5e-68)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -8e-294)
		tmp = x;
	elseif (z <= 9.2e-9)
		tmp = Float64(Float64(y * Float64(x + Float64(z * Float64(Float64(t - a) / y)))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -4500000000.0)
		tmp = t_1;
	elseif (z <= -4.5e-68)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= -8e-294)
		tmp = x;
	elseif (z <= 9.2e-9)
		tmp = (y * (x + (z * ((t - a) / y)))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4500000000.0], t$95$1, If[LessEqual[z, -4.5e-68], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-294], x, If[LessEqual[z, 9.2e-9], N[(N[(y * N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5e9 or 9.1999999999999997e-9 < z

   1. Initial program 50.3%

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

   3. Taylor expanded in z around -inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. mul-1-neg 68.4%

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

      3. distribute-lft-out-- 68.4%

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

      4. associate-/l* 70.6%

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

      5. associate-/l* 85.5%

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

      6. div-sub 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in y around inf 86.6%

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

   if -4.5e9 < z < -4.49999999999999999e-68

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.3%

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

   if -4.49999999999999999e-68 < z < -8.00000000000000013e-294

   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 0 67.1%

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

   if -8.00000000000000013e-294 < z < 9.1999999999999997e-9

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. associate-/l* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in z around 0 61.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4500000000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot \left(x + z \cdot \frac{t - a}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+16} \lor \neg \left(z \leq 1.28 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e+16) (not (<= z 1.28e+26)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (+ (* z (- t a)) (* y x)) (+ y (- (* z b) (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e+16) || !(z <= 1.28e+26)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + ((z * b) - (z * 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 <= (-2.4d+16)) .or. (.not. (z <= 1.28d+26))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + ((z * b) - (z * 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 <= -2.4e+16) || !(z <= 1.28e+26)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + ((z * b) - (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e+16) or not (z <= 1.28e+26):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + ((z * b) - (z * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e+16) || !(z <= 1.28e+26))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(Float64(z * b) - Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.4e+16) || ~((z <= 1.28e+26)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + ((z * b) - (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e+16], N[Not[LessEqual[z, 1.28e+26]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(N[(z * b), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e16 or 1.28e26 < z

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. distribute-lft-out-- 69.4%

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

      4. associate-/l* 72.5%

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

      5. associate-/l* 87.6%

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

      6. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 88.7%

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

   if -2.4e16 < z < 1.28e26

   1. Initial program 85.7%

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

      1. sub-neg 85.7%

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

      2. distribute-lft-in 85.7%

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

   4. Applied egg-rr 85.7%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+16} \lor \neg \left(z \leq 1.28 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+16} \lor \neg \left(z \leq 3.8 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.3e+16) (not (<= z 3.8e+23)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.3e+16) || !(z <= 3.8e+23)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (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 <= (-3.3d+16)) .or. (.not. (z <= 3.8d+23))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((z * (t - a)) + (y * x)) / (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 <= -3.3e+16) || !(z <= 3.8e+23)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.3e+16) or not (z <= 3.8e+23):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.3e+16) || !(z <= 3.8e+23))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / 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 <= -3.3e+16) || ~((z <= 3.8e+23)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.3e+16], N[Not[LessEqual[z, 3.8e+23]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e16 or 3.79999999999999975e23 < z

   1. Initial program 47.5%

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

   3. Taylor expanded in z around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. mul-1-neg 69.4%

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

      3. distribute-lft-out-- 69.4%

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

      4. associate-/l* 72.5%

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

      5. associate-/l* 87.6%

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

      6. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 88.7%

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

   if -3.3e16 < z < 3.79999999999999975e23

   1. Initial program 85.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+16} \lor \neg \left(z \leq 3.8 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -4.8e-9)
     t_1
     (if (<= z -7.5e-66)
       (/ (* z t) (+ y (* z (- b y))))
       (if (<= z 1.45e-37) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.8e-9) {
		tmp = t_1;
	} else if (z <= -7.5e-66) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= 1.45e-37) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-4.8d-9)) then
        tmp = t_1
    else if (z <= (-7.5d-66)) then
        tmp = (z * t) / (y + (z * (b - y)))
    else if (z <= 1.45d-37) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.8e-9) {
		tmp = t_1;
	} else if (z <= -7.5e-66) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= 1.45e-37) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -4.8e-9:
		tmp = t_1
	elif z <= -7.5e-66:
		tmp = (z * t) / (y + (z * (b - y)))
	elif z <= 1.45e-37:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -4.8e-9)
		tmp = t_1;
	elseif (z <= -7.5e-66)
		tmp = Float64(Float64(z * t) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 1.45e-37)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -4.8e-9)
		tmp = t_1;
	elseif (z <= -7.5e-66)
		tmp = (z * t) / (y + (z * (b - y)));
	elseif (z <= 1.45e-37)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-9], t$95$1, If[LessEqual[z, -7.5e-66], N[(N[(z * t), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-37], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e-9 or 1.45000000000000002e-37 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in z around -inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. mul-1-neg 67.1%

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

      3. distribute-lft-out-- 67.1%

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

      4. associate-/l* 69.9%

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

      5. associate-/l* 84.1%

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

      6. div-sub 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around inf 84.4%

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

   if -4.8e-9 < z < -7.49999999999999995e-66

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -7.49999999999999995e-66 < z < 1.45000000000000002e-37

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0 57.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-50} \lor \neg \left(z \leq 2.95 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4e+87)
   (/ (- a t) y)
   (if (or (<= z -2.4e-50) (not (<= z 2.95e-52)))
     (/ (- t a) b)
     (/ x (- 1.0 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4e+87) {
		tmp = (a - t) / y;
	} else if ((z <= -2.4e-50) || !(z <= 2.95e-52)) {
		tmp = (t - a) / b;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4d+87)) then
        tmp = (a - t) / y
    else if ((z <= (-2.4d-50)) .or. (.not. (z <= 2.95d-52))) then
        tmp = (t - a) / b
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4e+87) {
		tmp = (a - t) / y;
	} else if ((z <= -2.4e-50) || !(z <= 2.95e-52)) {
		tmp = (t - a) / b;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4e+87:
		tmp = (a - t) / y
	elif (z <= -2.4e-50) or not (z <= 2.95e-52):
		tmp = (t - a) / b
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4e+87)
		tmp = Float64(Float64(a - t) / y);
	elseif ((z <= -2.4e-50) || !(z <= 2.95e-52))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4e+87)
		tmp = (a - t) / y;
	elseif ((z <= -2.4e-50) || ~((z <= 2.95e-52)))
		tmp = (t - a) / b;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4e+87], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, -2.4e-50], N[Not[LessEqual[z, 2.95e-52]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999998e87

   1. Initial program 38.0%

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

   3. Taylor expanded in b around 0 25.2%

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

      1. mul-1-neg 25.2%

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

      2. distribute-lft-neg-out 25.2%

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

      3. *-commutative 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in z around inf 58.0%

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

      1. associate-*r/ 58.0%

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

      2. mul-1-neg 58.0%

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

   8. Simplified 58.0%

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

   if -3.9999999999999998e87 < z < -2.40000000000000002e-50 or 2.9500000000000001e-52 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in y around 0 53.5%

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

   if -2.40000000000000002e-50 < z < 2.9500000000000001e-52

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-50} \lor \neg \left(z \leq 2.95 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.45e-50)
   (/ t b)
   (if (<= z 7.5e-51) x (if (<= z 3.8e+180) (/ a (- b)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e-50) {
		tmp = t / b;
	} else if (z <= 7.5e-51) {
		tmp = x;
	} else if (z <= 3.8e+180) {
		tmp = a / -b;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.45d-50)) then
        tmp = t / b
    else if (z <= 7.5d-51) then
        tmp = x
    else if (z <= 3.8d+180) then
        tmp = a / -b
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e-50) {
		tmp = t / b;
	} else if (z <= 7.5e-51) {
		tmp = x;
	} else if (z <= 3.8e+180) {
		tmp = a / -b;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.45e-50:
		tmp = t / b
	elif z <= 7.5e-51:
		tmp = x
	elif z <= 3.8e+180:
		tmp = a / -b
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.45e-50)
		tmp = Float64(t / b);
	elseif (z <= 7.5e-51)
		tmp = x;
	elseif (z <= 3.8e+180)
		tmp = Float64(a / Float64(-b));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.45e-50)
		tmp = t / b;
	elseif (z <= 7.5e-51)
		tmp = x;
	elseif (z <= 3.8e+180)
		tmp = a / -b;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.45e-50], N[(t / b), $MachinePrecision], If[LessEqual[z, 7.5e-51], x, If[LessEqual[z, 3.8e+180], N[(a / (-b)), $MachinePrecision], N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4500000000000001e-50 or 3.8e180 < z

   1. Initial program 49.6%

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

      1. fma-define 49.6%

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

      2. clear-num 49.5%

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

      3. inv-pow 49.5%

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

      4. +-commutative 49.5%

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

      5. fma-undefine 49.5%

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

      6. fma-define 49.5%

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

      7. +-commutative 49.5%

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

      8. fma-define 49.5%

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

   4. Applied egg-rr 49.5%

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

      1. unpow-1 49.5%

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

      2. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in y around 0 46.5%

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

   8. Taylor expanded in t around inf 33.6%

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

   if -3.4500000000000001e-50 < z < 7.49999999999999976e-51

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0 55.9%

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

   if 7.49999999999999976e-51 < z < 3.8e180

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-lft-neg-out 40.1%

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

      3. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around 0 48.4%

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

      1. associate-*r/ 48.4%

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

      2. neg-mul-1 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.4e-50)
   (/ t b)
   (if (<= z 4.5e+44)
     (/ x (- 1.0 z))
     (if (<= z 1.35e+180) (/ a (- b)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.4e-50) {
		tmp = t / b;
	} else if (z <= 4.5e+44) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.35e+180) {
		tmp = a / -b;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.4d-50)) then
        tmp = t / b
    else if (z <= 4.5d+44) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.35d+180) then
        tmp = a / -b
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.4e-50) {
		tmp = t / b;
	} else if (z <= 4.5e+44) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.35e+180) {
		tmp = a / -b;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.4e-50:
		tmp = t / b
	elif z <= 4.5e+44:
		tmp = x / (1.0 - z)
	elif z <= 1.35e+180:
		tmp = a / -b
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.4e-50)
		tmp = Float64(t / b);
	elseif (z <= 4.5e+44)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.35e+180)
		tmp = Float64(a / Float64(-b));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.4e-50)
		tmp = t / b;
	elseif (z <= 4.5e+44)
		tmp = x / (1.0 - z);
	elseif (z <= 1.35e+180)
		tmp = a / -b;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.4e-50], N[(t / b), $MachinePrecision], If[LessEqual[z, 4.5e+44], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+180], N[(a / (-b)), $MachinePrecision], N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000014e-50 or 1.35000000000000008e180 < z

   1. Initial program 49.6%

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

      1. fma-define 49.6%

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

      2. clear-num 49.5%

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

      3. inv-pow 49.5%

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

      4. +-commutative 49.5%

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

      5. fma-undefine 49.5%

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

      6. fma-define 49.5%

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

      7. +-commutative 49.5%

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

      8. fma-define 49.5%

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

   4. Applied egg-rr 49.5%

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

      1. unpow-1 49.5%

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

      2. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in y around 0 46.5%

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

   8. Taylor expanded in t around inf 33.6%

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

   if -3.40000000000000014e-50 < z < 4.5e44

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

   5. Simplified 53.1%

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

   if 4.5e44 < z < 1.35000000000000008e180

   1. Initial program 55.6%

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

   3. Taylor expanded in a around inf 44.2%

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

      1. mul-1-neg 44.2%

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

      2. distribute-lft-neg-out 44.2%

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

      3. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in y around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-68} \lor \neg \left(z \leq 2.6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.2e-68) (not (<= z 2.6e-35))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e-68) || !(z <= 2.6e-35)) {
		tmp = (t - a) / (b - y);
	} 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 <= (-9.2d-68)) .or. (.not. (z <= 2.6d-35))) then
        tmp = (t - a) / (b - y)
    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 <= -9.2e-68) || !(z <= 2.6e-35)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.2e-68) or not (z <= 2.6e-35):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.2e-68) || !(z <= 2.6e-35))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.2e-68) || ~((z <= 2.6e-35)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.2e-68], N[Not[LessEqual[z, 2.6e-35]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999987e-68 or 2.60000000000000005e-35 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 77.4%

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

   if -9.19999999999999987e-68 < z < 2.60000000000000005e-35

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0 57.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-68} \lor \neg \left(z \leq 2.6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50} \lor \neg \left(z \leq 8.2 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-50) (not (<= z 8.2e-51))) (/ (- t a) b) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-50) || !(z <= 8.2e-51)) {
		tmp = (t - a) / b;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3d-50)) .or. (.not. (z <= 8.2d-51))) then
        tmp = (t - a) / b
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-50) || !(z <= 8.2e-51)) {
		tmp = (t - a) / b;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e-50) or not (z <= 8.2e-51):
		tmp = (t - a) / b
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-50) || !(z <= 8.2e-51))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e-50) || ~((z <= 8.2e-51)))
		tmp = (t - a) / b;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-50], N[Not[LessEqual[z, 8.2e-51]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-50 or 8.19999999999999947e-51 < 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 y around 0 50.6%

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

   if -2.9999999999999999e-50 < z < 8.19999999999999947e-51

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50} \lor \neg \left(z \leq 8.2 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50} \lor \neg \left(z \leq 3.1 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-50) (not (<= z 3.1e-38))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-50) || !(z <= 3.1e-38)) {
		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 <= (-3d-50)) .or. (.not. (z <= 3.1d-38))) 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 <= -3e-50) || !(z <= 3.1e-38)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e-50) or not (z <= 3.1e-38):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-50) || !(z <= 3.1e-38))
		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 <= -3e-50) || ~((z <= 3.1e-38)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-50], N[Not[LessEqual[z, 3.1e-38]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-50 or 3.09999999999999983e-38 < z

   1. Initial program 54.6%

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

      1. fma-define 54.6%

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

      2. clear-num 54.6%

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

      3. inv-pow 54.6%

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

      4. +-commutative 54.6%

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

      5. fma-undefine 54.6%

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

      6. fma-define 54.6%

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

      7. +-commutative 54.6%

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

      8. fma-define 54.6%

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

   4. Applied egg-rr 54.6%

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

      1. unpow-1 54.6%

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

      2. *-commutative 54.6%

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

   6. Simplified 54.6%

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

   7. Taylor expanded in y around 0 50.4%

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

   8. Taylor expanded in t around inf 28.7%

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

   if -2.9999999999999999e-50 < z < 3.09999999999999983e-38

   1. Initial program 84.1%

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

   3. Taylor expanded in z around 0 55.9%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50} \lor \neg \left(z \leq 3.1 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.2% 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 67.8%

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

3. Taylor expanded in z around 0 27.0%

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

4. Final simplification 27.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(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)))))