Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 87.4%

Time: 21.4s

Alternatives: 20

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -6800000000:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{t\_2}}{z} + t\_3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-127}:\\ \;\;\;\;\frac{x \cdot y + a \cdot \left(t \cdot \frac{z}{a} - z\right)}{t\_1}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{t\_4}{t\_1}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y + t\_4}{y + y \cdot \left(b \cdot \frac{z}{y} - z\right)}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t\_4}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 + \frac{y}{z} \cdot \frac{x}{b - y}\right) - y \cdot \frac{t - a}{z \cdot t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (pow (- b y) 2.0))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (* z (- t a))))
   (if (<= z -6800000000.0)
     (+ (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) t_2))) z) t_3)
     (if (<= z -7e-127)
       (/ (+ (* x y) (* a (- (* t (/ z a)) z))) t_1)
       (if (<= z 2.45e-254)
         (+ x (/ t_4 t_1))
         (if (<= z 2e-229)
           (/ (+ (* x y) t_4) (+ y (* y (- (* b (/ z y)) z))))
           (if (<= z 2.4e+36)
             (* x (+ (/ y t_1) (/ t_4 (* x t_1))))
             (-
              (+ t_3 (* (/ y z) (/ x (- b y))))
              (* y (/ (- t a) (* z 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 = pow((b - y), 2.0);
	double t_3 = (t - a) / (b - y);
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -6800000000.0) {
		tmp = (((x * (y / (b - y))) + (y * ((a - t) / t_2))) / z) + t_3;
	} else if (z <= -7e-127) {
		tmp = ((x * y) + (a * ((t * (z / a)) - z))) / t_1;
	} else if (z <= 2.45e-254) {
		tmp = x + (t_4 / t_1);
	} else if (z <= 2e-229) {
		tmp = ((x * y) + t_4) / (y + (y * ((b * (z / y)) - z)));
	} else if (z <= 2.4e+36) {
		tmp = x * ((y / t_1) + (t_4 / (x * t_1)));
	} else {
		tmp = (t_3 + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (b - y) ** 2.0d0
    t_3 = (t - a) / (b - y)
    t_4 = z * (t - a)
    if (z <= (-6800000000.0d0)) then
        tmp = (((x * (y / (b - y))) + (y * ((a - t) / t_2))) / z) + t_3
    else if (z <= (-7d-127)) then
        tmp = ((x * y) + (a * ((t * (z / a)) - z))) / t_1
    else if (z <= 2.45d-254) then
        tmp = x + (t_4 / t_1)
    else if (z <= 2d-229) then
        tmp = ((x * y) + t_4) / (y + (y * ((b * (z / y)) - z)))
    else if (z <= 2.4d+36) then
        tmp = x * ((y / t_1) + (t_4 / (x * t_1)))
    else
        tmp = (t_3 + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * 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 = Math.pow((b - y), 2.0);
	double t_3 = (t - a) / (b - y);
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -6800000000.0) {
		tmp = (((x * (y / (b - y))) + (y * ((a - t) / t_2))) / z) + t_3;
	} else if (z <= -7e-127) {
		tmp = ((x * y) + (a * ((t * (z / a)) - z))) / t_1;
	} else if (z <= 2.45e-254) {
		tmp = x + (t_4 / t_1);
	} else if (z <= 2e-229) {
		tmp = ((x * y) + t_4) / (y + (y * ((b * (z / y)) - z)));
	} else if (z <= 2.4e+36) {
		tmp = x * ((y / t_1) + (t_4 / (x * t_1)));
	} else {
		tmp = (t_3 + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * t_2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = math.pow((b - y), 2.0)
	t_3 = (t - a) / (b - y)
	t_4 = z * (t - a)
	tmp = 0
	if z <= -6800000000.0:
		tmp = (((x * (y / (b - y))) + (y * ((a - t) / t_2))) / z) + t_3
	elif z <= -7e-127:
		tmp = ((x * y) + (a * ((t * (z / a)) - z))) / t_1
	elif z <= 2.45e-254:
		tmp = x + (t_4 / t_1)
	elif z <= 2e-229:
		tmp = ((x * y) + t_4) / (y + (y * ((b * (z / y)) - z)))
	elif z <= 2.4e+36:
		tmp = x * ((y / t_1) + (t_4 / (x * t_1)))
	else:
		tmp = (t_3 + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * 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(b - y) ^ 2.0
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -6800000000.0)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / t_2))) / z) + t_3);
	elseif (z <= -7e-127)
		tmp = Float64(Float64(Float64(x * y) + Float64(a * Float64(Float64(t * Float64(z / a)) - z))) / t_1);
	elseif (z <= 2.45e-254)
		tmp = Float64(x + Float64(t_4 / t_1));
	elseif (z <= 2e-229)
		tmp = Float64(Float64(Float64(x * y) + t_4) / Float64(y + Float64(y * Float64(Float64(b * Float64(z / y)) - z))));
	elseif (z <= 2.4e+36)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(t_4 / Float64(x * t_1))));
	else
		tmp = Float64(Float64(t_3 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(y * Float64(Float64(t - a) / Float64(z * 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 = (b - y) ^ 2.0;
	t_3 = (t - a) / (b - y);
	t_4 = z * (t - a);
	tmp = 0.0;
	if (z <= -6800000000.0)
		tmp = (((x * (y / (b - y))) + (y * ((a - t) / t_2))) / z) + t_3;
	elseif (z <= -7e-127)
		tmp = ((x * y) + (a * ((t * (z / a)) - z))) / t_1;
	elseif (z <= 2.45e-254)
		tmp = x + (t_4 / t_1);
	elseif (z <= 2e-229)
		tmp = ((x * y) + t_4) / (y + (y * ((b * (z / y)) - z)));
	elseif (z <= 2.4e+36)
		tmp = x * ((y / t_1) + (t_4 / (x * t_1)));
	else
		tmp = (t_3 + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * 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[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6800000000.0], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[z, -7e-127], N[(N[(N[(x * y), $MachinePrecision] + N[(a * N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.45e-254], N[(x + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-229], N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / N[(y + N[(y * N[(N[(b * N[(z / y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+36], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$4 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.8e9

   1. Initial program 43.5%

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

   3. Taylor expanded in z around -inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. mul-1-neg 66.8%

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

      3. distribute-lft-out-- 66.8%

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

      4. associate-/l* 69.0%

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

      5. associate-/l* 90.2%

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

      6. div-sub 90.2%

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

   5. Simplified 90.2%

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

   if -6.8e9 < z < -6.99999999999999979e-127

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 95.2%

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

      1. +-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. unsub-neg 95.2%

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

      4. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

   if -6.99999999999999979e-127 < z < 2.4499999999999999e-254

   1. Initial program 88.0%

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

   3. Taylor expanded in x around 0 88.0%

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

   4. Taylor expanded in z around 0 99.9%

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

   if 2.4499999999999999e-254 < z < 2.00000000000000014e-229

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. unsub-neg 99.6%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 2.00000000000000014e-229 < z < 2.39999999999999992e36

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 95.9%

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

   if 2.39999999999999992e36 < z

   1. Initial program 40.3%

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

   3. Taylor expanded in z around inf 71.2%

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

      1. associate--r+ 71.2%

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

      2. +-commutative 71.2%

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

      3. associate--l+ 71.2%

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

      4. *-commutative 71.2%

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

      5. times-frac 77.7%

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

      6. div-sub 77.7%

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

      7. associate-/l* 95.3%

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

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6800000000:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-127}:\\ \;\;\;\;\frac{x \cdot y + a \cdot \left(t \cdot \frac{z}{a} - z\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + y \cdot \left(b \cdot \frac{z}{y} - z\right)}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0 \lor \neg \left(t\_3 \leq 2 \cdot 10^{+244}\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{t\_1} + \frac{x \cdot y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ y t_1) (/ (- t a) (* x b))))
     (if (<= t_3 -5e-291)
       t_3
       (if (or (<= t_3 0.0) (not (<= t_3 2e+244)))
         (-
          (+ (/ (- t a) (- b y)) (* (/ y z) (/ x (- b y))))
          (* y (/ (- t a) (* z (pow (- b y) 2.0)))))
         (+ (/ t_2 t_1) (/ (* x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_3 <= -5e-291) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 2e+244)) {
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * pow((b - y), 2.0))));
	} else {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	}
	return tmp;
}

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 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_3 <= -5e-291) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 2e+244)) {
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((y / t_1) + ((t - a) / (x * b)))
	elif t_3 <= -5e-291:
		tmp = t_3
	elif (t_3 <= 0.0) or not (t_3 <= 2e+244):
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * math.pow((b - y), 2.0))))
	else:
		tmp = (t_2 / t_1) + ((x * y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(t - a) / Float64(x * b))));
	elseif (t_3 <= -5e-291)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || !(t_3 <= 2e+244))
		tmp = Float64(Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(y * Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(Float64(t_2 / t_1) + Float64(Float64(x * y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	elseif (t_3 <= -5e-291)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || ~((t_3 <= 2e+244)))
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) - (y * ((t - a) / (z * ((b - y) ^ 2.0))));
	else
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-291], t$95$3, If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 2e+244]], $MachinePrecision]], N[(N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 69.0%

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

   4. Taylor expanded in y around 0 77.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-291

   1. Initial program 99.4%

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

   if -5.0000000000000003e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.2%

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

   3. Taylor expanded in z around inf 49.4%

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

      1. associate--r+ 49.4%

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

      2. +-commutative 49.4%

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

      3. associate--l+ 49.4%

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

      4. *-commutative 49.4%

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

      5. times-frac 59.8%

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

      6. div-sub 59.8%

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

      7. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{t\_3}{t\_1} + \frac{x \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 - \frac{x}{z}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1)))
   (if (<= t_4 (- INFINITY))
     (* x (+ (/ y t_1) (/ (- t a) (* x b))))
     (if (<= t_4 -5e-291)
       t_4
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 2e+244)
           (+ (/ t_3 t_1) (/ (* x y) t_1))
           (- (- t_2 (/ x z)) (* y (/ (- t a) (* z (pow (- b y) 2.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_4 <= -5e-291) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+244) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else {
		tmp = (t_2 - (x / z)) - (y * ((t - a) / (z * pow((b - y), 2.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_4 <= -5e-291) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+244) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else {
		tmp = (t_2 - (x / z)) - (y * ((t - a) / (z * Math.pow((b - y), 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	tmp = 0
	if t_4 <= -math.inf:
		tmp = x * ((y / t_1) + ((t - a) / (x * b)))
	elif t_4 <= -5e-291:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = t_2
	elif t_4 <= 2e+244:
		tmp = (t_3 / t_1) + ((x * y) / t_1)
	else:
		tmp = (t_2 - (x / z)) - (y * ((t - a) / (z * math.pow((b - y), 2.0))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(t - a) / Float64(x * b))));
	elseif (t_4 <= -5e-291)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+244)
		tmp = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1));
	else
		tmp = Float64(Float64(t_2 - Float64(x / z)) - Float64(y * Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0)))));
	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);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	elseif (t_4 <= -5e-291)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+244)
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	else
		tmp = (t_2 - (x / z)) - (y * ((t - a) / (z * ((b - y) ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -5e-291], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 2e+244], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 - N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 69.0%

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

   4. Taylor expanded in y around 0 77.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-291

   1. Initial program 99.4%

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

   if -5.0000000000000003e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 21.3%

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

   3. Taylor expanded in z around inf 86.7%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

   if 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.6%

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

   3. Taylor expanded in z around inf 39.9%

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

      1. associate--r+ 39.9%

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

      2. +-commutative 39.9%

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

      3. associate--l+ 39.9%

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

      4. *-commutative 39.9%

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

      5. times-frac 49.8%

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

      6. div-sub 49.8%

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

      7. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. mul-1-neg 77.1%

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

   8. Simplified 77.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} - \frac{x}{z}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0 \lor \neg \left(t\_3 \leq 2 \cdot 10^{+244}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{t\_1} + \frac{x \cdot y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ y t_1) (/ (- t a) (* x b))))
     (if (<= t_3 -5e-291)
       t_3
       (if (or (<= t_3 0.0) (not (<= t_3 2e+244)))
         (/ (- t a) (- b y))
         (+ (/ t_2 t_1) (/ (* x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_3 <= -5e-291) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 2e+244)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	}
	return tmp;
}

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 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if (t_3 <= -5e-291) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 2e+244)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((y / t_1) + ((t - a) / (x * b)))
	elif t_3 <= -5e-291:
		tmp = t_3
	elif (t_3 <= 0.0) or not (t_3 <= 2e+244):
		tmp = (t - a) / (b - y)
	else:
		tmp = (t_2 / t_1) + ((x * y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(t - a) / Float64(x * b))));
	elseif (t_3 <= -5e-291)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || !(t_3 <= 2e+244))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(t_2 / t_1) + Float64(Float64(x * y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	elseif (t_3 <= -5e-291)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || ~((t_3 <= 2e+244)))
		tmp = (t - a) / (b - y);
	else
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-291], t$95$3, If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 2e+244]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 69.0%

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

   4. Taylor expanded in y around 0 77.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-291

   1. Initial program 99.4%

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

   if -5.0000000000000003e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.2%

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

   3. Taylor expanded in z around inf 78.5%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-291} \lor \neg \left(t\_2 \leq 0\right) \land t\_2 \leq 2 \cdot 10^{+244}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (+ (* x y) (* z (- t a))) t_1)))
   (if (<= t_2 (- INFINITY))
     (* x (+ (/ y t_1) (/ (- t a) (* x b))))
     (if (or (<= t_2 -5e-291) (and (not (<= t_2 0.0)) (<= t_2 2e+244)))
       t_2
       (/ (- t a) (- b y))))))

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 = ((x * y) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if ((t_2 <= -5e-291) || (!(t_2 <= 0.0) && (t_2 <= 2e+244))) {
		tmp = t_2;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

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 = ((x * y) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	} else if ((t_2 <= -5e-291) || (!(t_2 <= 0.0) && (t_2 <= 2e+244))) {
		tmp = t_2;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x * ((y / t_1) + ((t - a) / (x * b)))
	elif (t_2 <= -5e-291) or (not (t_2 <= 0.0) and (t_2 <= 2e+244)):
		tmp = t_2
	else:
		tmp = (t - a) / (b - y)
	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(x * y) + Float64(z * Float64(t - a))) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(t - a) / Float64(x * b))));
	elseif ((t_2 <= -5e-291) || (!(t_2 <= 0.0) && (t_2 <= 2e+244)))
		tmp = t_2;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x * ((y / t_1) + ((t - a) / (x * b)));
	elseif ((t_2 <= -5e-291) || (~((t_2 <= 0.0)) && (t_2 <= 2e+244)))
		tmp = t_2;
	else
		tmp = (t - a) / (b - y);
	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[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -5e-291], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 2e+244]]], t$95$2, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 69.0%

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

   4. Taylor expanded in y around 0 77.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-291 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   1. Initial program 99.4%

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

   if -5.0000000000000003e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.2%

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

   3. Taylor expanded in z around inf 78.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{x \cdot b}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-291} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + t\_1}{t\_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{t\_1}{t\_2}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) t_1) t_2))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -1.2e+15)
     t_4
     (if (<= z -1.3e-120)
       t_3
       (if (<= z 2.45e-254) (+ x (/ t_1 t_2)) (if (<= z 1.3e+92) t_3 t_4))))))

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 = ((x * y) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+15) {
		tmp = t_4;
	} else if (z <= -1.3e-120) {
		tmp = t_3;
	} else if (z <= 2.45e-254) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.3e+92) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = ((x * y) + t_1) / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-1.2d+15)) then
        tmp = t_4
    else if (z <= (-1.3d-120)) then
        tmp = t_3
    else if (z <= 2.45d-254) then
        tmp = x + (t_1 / t_2)
    else if (z <= 1.3d+92) then
        tmp = t_3
    else
        tmp = t_4
    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 = ((x * y) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+15) {
		tmp = t_4;
	} else if (z <= -1.3e-120) {
		tmp = t_3;
	} else if (z <= 2.45e-254) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.3e+92) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + t_1) / t_2
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.2e+15:
		tmp = t_4
	elif z <= -1.3e-120:
		tmp = t_3
	elif z <= 2.45e-254:
		tmp = x + (t_1 / t_2)
	elif z <= 1.3e+92:
		tmp = t_3
	else:
		tmp = t_4
	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(x * y) + t_1) / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.2e+15)
		tmp = t_4;
	elseif (z <= -1.3e-120)
		tmp = t_3;
	elseif (z <= 2.45e-254)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 1.3e+92)
		tmp = t_3;
	else
		tmp = t_4;
	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 = ((x * y) + t_1) / t_2;
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.2e+15)
		tmp = t_4;
	elseif (z <= -1.3e-120)
		tmp = t_3;
	elseif (z <= 2.45e-254)
		tmp = x + (t_1 / t_2);
	elseif (z <= 1.3e+92)
		tmp = t_3;
	else
		tmp = t_4;
	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[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+15], t$95$4, If[LessEqual[z, -1.3e-120], t$95$3, If[LessEqual[z, 2.45e-254], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+92], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e15 or 1.2999999999999999e92 < z

   1. Initial program 38.8%

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

   3. Taylor expanded in z around inf 86.1%

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

   if -1.2e15 < z < -1.3000000000000001e-120 or 2.4499999999999999e-254 < z < 1.2999999999999999e92

   1. Initial program 87.8%

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

   if -1.3000000000000001e-120 < z < 2.4499999999999999e-254

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in z around 0 99.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := x + \frac{z \cdot \left(t - a\right)}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-150}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t\_1}\\ \mathbf{elif}\;z \leq 3800:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ x (/ (* z (- t a)) t_1)))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2800000000.0)
     t_3
     (if (<= z 2.45e-254)
       t_2
       (if (<= z 1.1e-150)
         (/ (+ (* x y) (* z t)) t_1)
         (if (<= z 3800.0) t_2 t_3))))))

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 = x + ((z * (t - a)) / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2800000000.0) {
		tmp = t_3;
	} else if (z <= 2.45e-254) {
		tmp = t_2;
	} else if (z <= 1.1e-150) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else if (z <= 3800.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = x + ((z * (t - a)) / t_1)
    t_3 = (t - a) / (b - y)
    if (z <= (-2800000000.0d0)) then
        tmp = t_3
    else if (z <= 2.45d-254) then
        tmp = t_2
    else if (z <= 1.1d-150) then
        tmp = ((x * y) + (z * t)) / t_1
    else if (z <= 3800.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x + ((z * (t - a)) / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2800000000.0) {
		tmp = t_3;
	} else if (z <= 2.45e-254) {
		tmp = t_2;
	} else if (z <= 1.1e-150) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else if (z <= 3800.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x + ((z * (t - a)) / t_1)
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2800000000.0:
		tmp = t_3
	elif z <= 2.45e-254:
		tmp = t_2
	elif z <= 1.1e-150:
		tmp = ((x * y) + (z * t)) / t_1
	elif z <= 3800.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(x + Float64(Float64(z * Float64(t - a)) / t_1))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2800000000.0)
		tmp = t_3;
	elseif (z <= 2.45e-254)
		tmp = t_2;
	elseif (z <= 1.1e-150)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_1);
	elseif (z <= 3800.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = x + ((z * (t - a)) / t_1);
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2800000000.0)
		tmp = t_3;
	elseif (z <= 2.45e-254)
		tmp = t_2;
	elseif (z <= 1.1e-150)
		tmp = ((x * y) + (z * t)) / t_1;
	elseif (z <= 3800.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2800000000.0], t$95$3, If[LessEqual[z, 2.45e-254], t$95$2, If[LessEqual[z, 1.1e-150], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3800.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e9 or 3800 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in z around inf 83.7%

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

   if -2.8e9 < z < 2.4499999999999999e-254 or 1.1e-150 < z < 3800

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 87.6%

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

   4. Taylor expanded in z around 0 84.3%

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

   if 2.4499999999999999e-254 < z < 1.1e-150

   1. Initial program 91.7%

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

   3. Taylor expanded in a around 0 83.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-150}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3800:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-160}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-241}:\\ \;\;\;\;\frac{x + \frac{z \cdot t}{y}}{1 - z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -135000000000.0)
     t_2
     (if (<= z -1.55e-160)
       (/ (* z (- t a)) t_1)
       (if (<= z 5.6e-241)
         (/ (+ x (/ (* z t) y)) (- 1.0 z))
         (if (<= z 1.08e-29) (* x (/ y 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);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_2;
	} else if (z <= -1.55e-160) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 5.6e-241) {
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	} else if (z <= 1.08e-29) {
		tmp = x * (y / 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)
    if (z <= (-135000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.55d-160)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= 5.6d-241) then
        tmp = (x + ((z * t) / y)) / (1.0d0 - z)
    else if (z <= 1.08d-29) then
        tmp = x * (y / 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);
	double tmp;
	if (z <= -135000000000.0) {
		tmp = t_2;
	} else if (z <= -1.55e-160) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 5.6e-241) {
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	} else if (z <= 1.08e-29) {
		tmp = x * (y / 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)
	tmp = 0
	if z <= -135000000000.0:
		tmp = t_2
	elif z <= -1.55e-160:
		tmp = (z * (t - a)) / t_1
	elif z <= 5.6e-241:
		tmp = (x + ((z * t) / y)) / (1.0 - z)
	elif z <= 1.08e-29:
		tmp = x * (y / 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(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -135000000000.0)
		tmp = t_2;
	elseif (z <= -1.55e-160)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= 5.6e-241)
		tmp = Float64(Float64(x + Float64(Float64(z * t) / y)) / Float64(1.0 - z));
	elseif (z <= 1.08e-29)
		tmp = Float64(x * Float64(y / 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);
	tmp = 0.0;
	if (z <= -135000000000.0)
		tmp = t_2;
	elseif (z <= -1.55e-160)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= 5.6e-241)
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	elseif (z <= 1.08e-29)
		tmp = x * (y / 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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -135000000000.0], t$95$2, If[LessEqual[z, -1.55e-160], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 5.6e-241], N[(N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-29], N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e11 or 1.07999999999999995e-29 < z

   1. Initial program 45.8%

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

   3. Taylor expanded in z around inf 81.9%

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

   if -1.35e11 < z < -1.55e-160

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -1.55e-160 < z < 5.5999999999999998e-241

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around -inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. sub-neg 64.3%

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

      4. metadata-eval 64.3%

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

   8. Simplified 64.3%

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

   9. Taylor expanded in a around 0 79.1%

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

       1. mul-1-neg 79.1%

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

       2. sub-neg 79.1%

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

       3. metadata-eval 79.1%

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

   11. Simplified 79.1%

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

   if 5.5999999999999998e-241 < z < 1.07999999999999995e-29

   1. Initial program 84.2%

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

   3. Taylor expanded in t around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in x around inf 54.1%

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

      1. associate-/l* 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -135000000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-160}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-241}:\\ \;\;\;\;\frac{x + \frac{z \cdot t}{y}}{1 - z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{x + \frac{z \cdot t}{y}}{1 - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.6e-160)
     t_1
     (if (<= z 9.5e-240)
       (/ (+ x (/ (* z t) y)) (- 1.0 z))
       (if (<= z 1.18e-29) (* x (/ y (+ y (* z (- b 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);
	double tmp;
	if (z <= -1.6e-160) {
		tmp = t_1;
	} else if (z <= 9.5e-240) {
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	} else if (z <= 1.18e-29) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.6d-160)) then
        tmp = t_1
    else if (z <= 9.5d-240) then
        tmp = (x + ((z * t) / y)) / (1.0d0 - z)
    else if (z <= 1.18d-29) then
        tmp = x * (y / (y + (z * (b - y))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.6e-160) {
		tmp = t_1;
	} else if (z <= 9.5e-240) {
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	} else if (z <= 1.18e-29) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.6e-160:
		tmp = t_1
	elif z <= 9.5e-240:
		tmp = (x + ((z * t) / y)) / (1.0 - z)
	elif z <= 1.18e-29:
		tmp = x * (y / (y + (z * (b - y))))
	else:
		tmp = t_1
	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 <= -1.6e-160)
		tmp = t_1;
	elseif (z <= 9.5e-240)
		tmp = Float64(Float64(x + Float64(Float64(z * t) / y)) / Float64(1.0 - z));
	elseif (z <= 1.18e-29)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - 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);
	tmp = 0.0;
	if (z <= -1.6e-160)
		tmp = t_1;
	elseif (z <= 9.5e-240)
		tmp = (x + ((z * t) / y)) / (1.0 - z);
	elseif (z <= 1.18e-29)
		tmp = x * (y / (y + (z * (b - y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-160], t$95$1, If[LessEqual[z, 9.5e-240], N[(N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e-29], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000004e-160 or 1.17999999999999996e-29 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in z around inf 76.9%

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

   if -1.60000000000000004e-160 < z < 9.5000000000000005e-240

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around -inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. sub-neg 64.3%

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

      4. metadata-eval 64.3%

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

   8. Simplified 64.3%

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

   9. Taylor expanded in a around 0 79.1%

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

       1. mul-1-neg 79.1%

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

       2. sub-neg 79.1%

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

       3. metadata-eval 79.1%

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

   11. Simplified 79.1%

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

   if 9.5000000000000005e-240 < z < 1.17999999999999996e-29

   1. Initial program 84.2%

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

   3. Taylor expanded in t around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in x around inf 54.1%

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

      1. associate-/l* 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{x + \frac{z \cdot t}{y}}{1 - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{+64}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-160} \lor \neg \left(z \leq 4.4 \cdot 10^{-44}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.25e+186)
     t_1
     (if (<= z -3.85e+64)
       (- (/ a b))
       (if (or (<= z -1.6e-160) (not (<= z 4.4e-44))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.25e+186) {
		tmp = t_1;
	} else if (z <= -3.85e+64) {
		tmp = -(a / b);
	} else if ((z <= -1.6e-160) || !(z <= 4.4e-44)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-1.25d+186)) then
        tmp = t_1
    else if (z <= (-3.85d+64)) then
        tmp = -(a / b)
    else if ((z <= (-1.6d-160)) .or. (.not. (z <= 4.4d-44))) then
        tmp = t_1
    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 t_1 = t / (b - y);
	double tmp;
	if (z <= -1.25e+186) {
		tmp = t_1;
	} else if (z <= -3.85e+64) {
		tmp = -(a / b);
	} else if ((z <= -1.6e-160) || !(z <= 4.4e-44)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1.25e+186:
		tmp = t_1
	elif z <= -3.85e+64:
		tmp = -(a / b)
	elif (z <= -1.6e-160) or not (z <= 4.4e-44):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.25e+186)
		tmp = t_1;
	elseif (z <= -3.85e+64)
		tmp = Float64(-Float64(a / b));
	elseif ((z <= -1.6e-160) || !(z <= 4.4e-44))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.25e+186)
		tmp = t_1;
	elseif (z <= -3.85e+64)
		tmp = -(a / b);
	elseif ((z <= -1.6e-160) || ~((z <= 4.4e-44)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+186], t$95$1, If[LessEqual[z, -3.85e+64], (-N[(a / b), $MachinePrecision]), If[Or[LessEqual[z, -1.6e-160], N[Not[LessEqual[z, 4.4e-44]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999988e186 or -3.85e64 < z < -1.60000000000000004e-160 or 4.40000000000000024e-44 < z

   1. Initial program 55.4%

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

   3. Taylor expanded in x around inf 49.8%

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

   4. Taylor expanded in z around inf 61.4%

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

      1. div-sub 62.1%

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

      2. *-commutative 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in t around inf 44.4%

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

   if -1.24999999999999988e186 < z < -3.85e64

   1. Initial program 52.9%

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

   3. Taylor expanded in a around inf 28.8%

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

      1. mul-1-neg 28.8%

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

      2. distribute-lft-neg-out 28.8%

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

      3. *-commutative 28.8%

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

   5. Simplified 28.8%

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

   6. Taylor expanded in y around 0 36.7%

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

      1. associate-*r/ 36.7%

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

      2. mul-1-neg 36.7%

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

   8. Simplified 36.7%

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

   if -1.60000000000000004e-160 < z < 4.40000000000000024e-44

   1. Initial program 86.3%

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

   3. Taylor expanded in z around 0 51.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+186}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{+64}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-160} \lor \neg \left(z \leq 4.4 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4600000000 \lor \neg \left(z \leq 24000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4600000000.0) (not (<= z 24000.0)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4600000000.0) || !(z <= 24000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4600000000.0d0)) .or. (.not. (z <= 24000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4600000000.0) || !(z <= 24000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4600000000.0) or not (z <= 24000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4600000000.0) || !(z <= 24000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4600000000.0) || ~((z <= 24000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4600000000.0], N[Not[LessEqual[z, 24000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e9 or 24000 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in z around inf 83.7%

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

   if -4.6e9 < z < 24000

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 88.4%

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

   4. Taylor expanded in z around 0 79.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4600000000 \lor \neg \left(z \leq 24000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-160} \lor \neg \left(z \leq 10^{-29}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.35e-160) (not (<= z 1e-29)))
   (/ (- t a) (- b y))
   (* x (/ y (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e-160) || !(z <= 1e-29)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (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 <= (-1.35d-160)) .or. (.not. (z <= 1d-29))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * (y / (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 <= -1.35e-160) || !(z <= 1e-29)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.35e-160) or not (z <= 1e-29):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * (y / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.35e-160) || !(z <= 1e-29))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(y / 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 <= -1.35e-160) || ~((z <= 1e-29)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * (y / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.35e-160], N[Not[LessEqual[z, 1e-29]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000005e-160 or 9.99999999999999943e-30 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in z around inf 76.9%

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

   if -1.35000000000000005e-160 < z < 9.99999999999999943e-30

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      3. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around inf 49.6%

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

      1. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-160} \lor \neg \left(z \leq 10^{-29}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-105}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.1e+56)
     t_1
     (if (<= y -1.7e-105)
       (/ a (- y b))
       (if (<= y 2.6e+48) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+56) {
		tmp = t_1;
	} else if (y <= -1.7e-105) {
		tmp = a / (y - b);
	} else if (y <= 2.6e+48) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.1d+56)) then
        tmp = t_1
    else if (y <= (-1.7d-105)) then
        tmp = a / (y - b)
    else if (y <= 2.6d+48) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+56) {
		tmp = t_1;
	} else if (y <= -1.7e-105) {
		tmp = a / (y - b);
	} else if (y <= 2.6e+48) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.1e+56:
		tmp = t_1
	elif y <= -1.7e-105:
		tmp = a / (y - b)
	elif y <= 2.6e+48:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.1e+56)
		tmp = t_1;
	elseif (y <= -1.7e-105)
		tmp = Float64(a / Float64(y - b));
	elseif (y <= 2.6e+48)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.1e+56)
		tmp = t_1;
	elseif (y <= -1.7e-105)
		tmp = a / (y - b);
	elseif (y <= 2.6e+48)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+56], t$95$1, If[LessEqual[y, -1.7e-105], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+48], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000005e56 or 2.59999999999999995e48 < y

   1. Initial program 44.3%

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

   3. Taylor expanded in y around inf 48.1%

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

      1. mul-1-neg 48.1%

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

      2. unsub-neg 48.1%

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

   5. Simplified 48.1%

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

   if -3.10000000000000005e56 < y < -1.69999999999999996e-105

   1. Initial program 73.4%

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

   3. Taylor expanded in a around inf 31.6%

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

      1. mul-1-neg 31.6%

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

      2. distribute-lft-neg-out 31.6%

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

      3. *-commutative 31.6%

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

   5. Simplified 31.6%

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

   6. Taylor expanded in z around inf 44.7%

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

      1. associate-*r/ 44.7%

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

      2. mul-1-neg 44.7%

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

   8. Simplified 44.7%

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

   if -1.69999999999999996e-105 < y < 2.59999999999999995e48

   1. Initial program 79.2%

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

   3. Taylor expanded in y around 0 58.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-105}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -145000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e+111)
     t_1
     (if (<= y -145000.0)
       (/ (- a t) y)
       (if (<= y 2.4e+45) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e+111) {
		tmp = t_1;
	} else if (y <= -145000.0) {
		tmp = (a - t) / y;
	} else if (y <= 2.4e+45) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.8d+111)) then
        tmp = t_1
    else if (y <= (-145000.0d0)) then
        tmp = (a - t) / y
    else if (y <= 2.4d+45) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e+111) {
		tmp = t_1;
	} else if (y <= -145000.0) {
		tmp = (a - t) / y;
	} else if (y <= 2.4e+45) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7.8e+111:
		tmp = t_1
	elif y <= -145000.0:
		tmp = (a - t) / y
	elif y <= 2.4e+45:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.8e+111)
		tmp = t_1;
	elseif (y <= -145000.0)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 2.4e+45)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7.8e+111)
		tmp = t_1;
	elseif (y <= -145000.0)
		tmp = (a - t) / y;
	elseif (y <= 2.4e+45)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+111], t$95$1, If[LessEqual[y, -145000.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.4e+45], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.79999999999999958e111 or 2.39999999999999989e45 < y

   1. Initial program 43.3%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

   5. Simplified 52.1%

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

   if -7.79999999999999958e111 < y < -145000

   1. Initial program 64.6%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in z around inf 49.3%

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

      1. div-sub 49.3%

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

      2. *-commutative 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in b around 0 41.4%

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

      1. associate-*r/ 41.4%

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

      2. mul-1-neg 41.4%

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

   9. Simplified 41.4%

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

   if -145000 < y < 2.39999999999999989e45

   1. Initial program 78.0%

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

   3. Taylor expanded in y around 0 55.0%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -145000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-208}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.32e+48)
   x
   (if (<= y -2.7e-208) (- (/ a b)) (if (<= y 8.4e+37) (/ t b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.32e+48) {
		tmp = x;
	} else if (y <= -2.7e-208) {
		tmp = -(a / b);
	} else if (y <= 8.4e+37) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.32d+48)) then
        tmp = x
    else if (y <= (-2.7d-208)) then
        tmp = -(a / b)
    else if (y <= 8.4d+37) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.32e+48) {
		tmp = x;
	} else if (y <= -2.7e-208) {
		tmp = -(a / b);
	} else if (y <= 8.4e+37) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.32e+48:
		tmp = x
	elif y <= -2.7e-208:
		tmp = -(a / b)
	elif y <= 8.4e+37:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.32e+48)
		tmp = x;
	elseif (y <= -2.7e-208)
		tmp = Float64(-Float64(a / b));
	elseif (y <= 8.4e+37)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.32e+48)
		tmp = x;
	elseif (y <= -2.7e-208)
		tmp = -(a / b);
	elseif (y <= 8.4e+37)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.32e+48], x, If[LessEqual[y, -2.7e-208], (-N[(a / b), $MachinePrecision]), If[LessEqual[y, 8.4e+37], N[(t / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e48 or 8.4000000000000004e37 < y

   1. Initial program 44.3%

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

   3. Taylor expanded in z around 0 37.6%

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

   if -1.32e48 < y < -2.7e-208

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 36.5%

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

      1. mul-1-neg 36.5%

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

      2. distribute-lft-neg-out 36.5%

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

      3. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in y around 0 30.4%

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

      1. associate-*r/ 30.4%

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

      2. mul-1-neg 30.4%

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

   8. Simplified 30.4%

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

   if -2.7e-208 < y < 8.4000000000000004e37

   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. Taylor expanded in x around inf 60.1%

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

   4. Taylor expanded in b around inf 55.2%

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

   5. Taylor expanded in t around inf 41.0%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-208}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-160} \lor \neg \left(z \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e-160) (not (<= z 2e-47))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-160) || !(z <= 2e-47)) {
		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 <= (-1.6d-160)) .or. (.not. (z <= 2d-47))) 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 <= -1.6e-160) || !(z <= 2e-47)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e-160) or not (z <= 2e-47):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e-160) || !(z <= 2e-47))
		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 <= -1.6e-160) || ~((z <= 2e-47)))
		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, -1.6e-160], N[Not[LessEqual[z, 2e-47]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000004e-160 or 1.9999999999999999e-47 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in z around inf 75.7%

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

   if -1.60000000000000004e-160 < z < 1.9999999999999999e-47

   1. Initial program 86.3%

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

   3. Taylor expanded in z around 0 51.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-160} \lor \neg \left(z \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+108} \lor \neg \left(y \leq 3.7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e+108) (not (<= y 3.7e+37))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+108) || !(y <= 3.7e+37)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (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 ((y <= (-8.2d+108)) .or. (.not. (y <= 3.7d+37))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (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 ((y <= -8.2e+108) || !(y <= 3.7e+37)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e+108) or not (y <= 3.7e+37):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e+108) || !(y <= 3.7e+37))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e+108) || ~((y <= 3.7e+37)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e+108], N[Not[LessEqual[y, 3.7e+37]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e108 or 3.6999999999999999e37 < y

   1. Initial program 43.9%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   if -8.1999999999999998e108 < y < 3.6999999999999999e37

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf 64.1%

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

   4. Taylor expanded in z around inf 54.3%

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

      1. div-sub 55.0%

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

      2. *-commutative 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in t around inf 39.1%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+108} \lor \neg \left(y \leq 3.7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+45} \lor \neg \left(y \leq 1.55 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.1e+45) (not (<= y 1.55e+45))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e+45) || !(y <= 1.55e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.1d+45)) .or. (.not. (y <= 1.55d+45))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e+45) || !(y <= 1.55e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.1e+45) or not (y <= 1.55e+45):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.1e+45) || !(y <= 1.55e+45))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.1e+45) || ~((y <= 1.55e+45)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.1e+45], N[Not[LessEqual[y, 1.55e+45]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0999999999999997e45 or 1.54999999999999994e45 < y

   1. Initial program 43.9%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

   5. Simplified 47.6%

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

   if -5.0999999999999997e45 < y < 1.54999999999999994e45

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 52.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+45} \lor \neg \left(y \leq 1.55 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.22e-29) x (if (<= y 5.8e+37) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.22e-29) {
		tmp = x;
	} else if (y <= 5.8e+37) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.22d-29)) then
        tmp = x
    else if (y <= 5.8d+37) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.22e-29) {
		tmp = x;
	} else if (y <= 5.8e+37) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.22e-29:
		tmp = x
	elif y <= 5.8e+37:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.22e-29)
		tmp = x;
	elseif (y <= 5.8e+37)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.22e-29)
		tmp = x;
	elseif (y <= 5.8e+37)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.22e-29], x, If[LessEqual[y, 5.8e+37], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999996e-29 or 5.79999999999999957e37 < y

   1. Initial program 49.7%

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

   3. Taylor expanded in z around 0 34.7%

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

   if -1.21999999999999996e-29 < y < 5.79999999999999957e37

   1. Initial program 79.5%

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

   3. Taylor expanded in x around inf 62.7%

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

   4. Taylor expanded in b around inf 55.2%

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

   5. Taylor expanded in t around inf 36.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.3%

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

3. Taylor expanded in z around 0 21.0%

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

4. Final simplification 21.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.8% 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 2024079 
(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)))))