Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.1% → 87.4%

Time: 17.9s

Alternatives: 16

Speedup: 1.3×

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: 66.1% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+44}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1e+44)
     (- t_1 (/ x z))
     (if (<= z -3.05e-238)
       (/ (+ (* x y) (* z (- t a))) (+ (* y (- 1.0 z)) (* z b)))
       (if (<= z 6.7e-9)
         (- x (/ (* z (- a t)) (+ y (* z (- b y)))))
         (+
          t_1
          (/
           (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y)))
           z)))))))

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 <= -1e+44) {
		tmp = t_1 - (x / z);
	} else if (z <= -3.05e-238) {
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 6.7e-9) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else {
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1d+44)) then
        tmp = t_1 - (x / z)
    else if (z <= (-3.05d-238)) then
        tmp = ((x * y) + (z * (t - a))) / ((y * (1.0d0 - z)) + (z * b))
    else if (z <= 6.7d-9) then
        tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
    else
        tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (((b - y) ** 2.0d0) / y))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1e+44) {
		tmp = t_1 - (x / z);
	} else if (z <= -3.05e-238) {
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 6.7e-9) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else {
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1e+44:
		tmp = t_1 - (x / z)
	elif z <= -3.05e-238:
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b))
	elif z <= 6.7e-9:
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
	else:
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z)
	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 <= -1e+44)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= -3.05e-238)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(Float64(y * Float64(1.0 - z)) + Float64(z * b)));
	elseif (z <= 6.7e-9)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z));
	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 <= -1e+44)
		tmp = t_1 - (x / z);
	elseif (z <= -3.05e-238)
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	elseif (z <= 6.7e-9)
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	else
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z);
	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, -1e+44], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.05e-238], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.7e-9], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0000000000000001e44

   1. Initial program 47.7%

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

   2. Taylor expanded in z around -inf 62.8%

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

      1. +-commutative 62.8%

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

      2. associate--l+ 62.8%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in x around inf 79.3%

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

   6. Taylor expanded in y around inf 89.3%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

   8. Simplified 89.3%

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

   if -1.0000000000000001e44 < z < -3.05e-238

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 94.9%

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

   if -3.05e-238 < z < 6.69999999999999961e-9

   1. Initial program 79.6%

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

   2. Taylor expanded in x around inf 79.6%

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

   3. Taylor expanded in z around 0 90.9%

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

   if 6.69999999999999961e-9 < z

   1. Initial program 44.7%

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

   2. Taylor expanded in z around -inf 60.9%

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

      1. +-commutative 60.9%

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

      2. associate--l+ 60.9%

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

   4. Simplified 94.1%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+44}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \]

Alternative 2: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot y + t_3}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{y}{\frac{t_1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (- (/ (- t a) (- b y)) (/ x z)))
        (t_3 (* z (- t a))))
   (if (<= z -1.3e+49)
     t_2
     (if (<= z 1.36e-263)
       (/ (+ (* x y) t_3) (+ (* y (- 1.0 z)) (* z b)))
       (if (<= z 3.35e+50) (+ (/ t_3 t_1) (/ y (/ t_1 x))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -1.3e+49) {
		tmp = t_2;
	} else if (z <= 1.36e-263) {
		tmp = ((x * y) + t_3) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 3.35e+50) {
		tmp = (t_3 / t_1) + (y / (t_1 / x));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = ((t - a) / (b - y)) - (x / z)
    t_3 = z * (t - a)
    if (z <= (-1.3d+49)) then
        tmp = t_2
    else if (z <= 1.36d-263) then
        tmp = ((x * y) + t_3) / ((y * (1.0d0 - z)) + (z * b))
    else if (z <= 3.35d+50) then
        tmp = (t_3 / t_1) + (y / (t_1 / x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -1.3e+49) {
		tmp = t_2;
	} else if (z <= 1.36e-263) {
		tmp = ((x * y) + t_3) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 3.35e+50) {
		tmp = (t_3 / t_1) + (y / (t_1 / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((t - a) / (b - y)) - (x / z)
	t_3 = z * (t - a)
	tmp = 0
	if z <= -1.3e+49:
		tmp = t_2
	elif z <= 1.36e-263:
		tmp = ((x * y) + t_3) / ((y * (1.0 - z)) + (z * b))
	elif z <= 3.35e+50:
		tmp = (t_3 / t_1) + (y / (t_1 / x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	t_3 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -1.3e+49)
		tmp = t_2;
	elseif (z <= 1.36e-263)
		tmp = Float64(Float64(Float64(x * y) + t_3) / Float64(Float64(y * Float64(1.0 - z)) + Float64(z * b)));
	elseif (z <= 3.35e+50)
		tmp = Float64(Float64(t_3 / t_1) + Float64(y / Float64(t_1 / x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((t - a) / (b - y)) - (x / z);
	t_3 = z * (t - a);
	tmp = 0.0;
	if (z <= -1.3e+49)
		tmp = t_2;
	elseif (z <= 1.36e-263)
		tmp = ((x * y) + t_3) / ((y * (1.0 - z)) + (z * b));
	elseif (z <= 3.35e+50)
		tmp = (t_3 / t_1) + (y / (t_1 / x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+49], t$95$2, If[LessEqual[z, 1.36e-263], N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e+50], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.29999999999999994e49 or 3.3499999999999999e50 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around -inf 62.2%

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

      1. +-commutative 62.2%

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

      2. associate--l+ 62.2%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in x around inf 77.2%

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

   6. Taylor expanded in y around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

   if -1.29999999999999994e49 < z < 1.3599999999999999e-263

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 93.7%

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

   if 1.3599999999999999e-263 < z < 3.3499999999999999e50

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf 75.5%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. associate-/l* 87.3%

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

      2. +-commutative 87.3%

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

      3. *-commutative 87.3%

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

      4. *-commutative 87.3%

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

      5. +-commutative 87.3%

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

      6. fma-def 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around 0 87.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 3: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{t_2}\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{t_2}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -5.8e+42)
     t_1
     (if (<= z -8e-236)
       (/ (+ (* x y) (* z (- t a))) t_2)
       (if (<= z 3800000000000.0)
         (- x (/ (* z (- a t)) t_2))
         (if (<= z 1.65e+61)
           (+ (/ t (- b y)) (* (/ x z) (/ y (- 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)) - (x / z);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -5.8e+42) {
		tmp = t_1;
	} else if (z <= -8e-236) {
		tmp = ((x * y) + (z * (t - a))) / t_2;
	} else if (z <= 3800000000000.0) {
		tmp = x - ((z * (a - t)) / t_2);
	} else if (z <= 1.65e+61) {
		tmp = (t / (b - y)) + ((x / z) * (y / (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) :: t_2
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    t_2 = y + (z * (b - y))
    if (z <= (-5.8d+42)) then
        tmp = t_1
    else if (z <= (-8d-236)) then
        tmp = ((x * y) + (z * (t - a))) / t_2
    else if (z <= 3800000000000.0d0) then
        tmp = x - ((z * (a - t)) / t_2)
    else if (z <= 1.65d+61) then
        tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -5.8e+42) {
		tmp = t_1;
	} else if (z <= -8e-236) {
		tmp = ((x * y) + (z * (t - a))) / t_2;
	} else if (z <= 3800000000000.0) {
		tmp = x - ((z * (a - t)) / t_2);
	} else if (z <= 1.65e+61) {
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -5.8e+42:
		tmp = t_1
	elif z <= -8e-236:
		tmp = ((x * y) + (z * (t - a))) / t_2
	elif z <= 3800000000000.0:
		tmp = x - ((z * (a - t)) / t_2)
	elif z <= 1.65e+61:
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -5.8e+42)
		tmp = t_1;
	elseif (z <= -8e-236)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_2);
	elseif (z <= 3800000000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / t_2));
	elseif (z <= 1.65e+61)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / 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)) - (x / z);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -5.8e+42)
		tmp = t_1;
	elseif (z <= -8e-236)
		tmp = ((x * y) + (z * (t - a))) / t_2;
	elseif (z <= 3800000000000.0)
		tmp = x - ((z * (a - t)) / t_2);
	elseif (z <= 1.65e+61)
		tmp = (t / (b - y)) + ((x / z) * (y / (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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+42], t$95$1, If[LessEqual[z, -8e-236], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 3800000000000.0], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+61], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.79999999999999961e42 or 1.6499999999999999e61 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around -inf 62.2%

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

      1. +-commutative 62.2%

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

      2. associate--l+ 62.2%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in x around inf 77.2%

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

   6. Taylor expanded in y around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

   if -5.79999999999999961e42 < z < -8.0000000000000004e-236

   1. Initial program 94.9%

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

   if -8.0000000000000004e-236 < z < 3.8e12

   1. Initial program 78.9%

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

   2. Taylor expanded in x around inf 78.9%

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

   3. Taylor expanded in z around 0 89.9%

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

   if 3.8e12 < z < 1.6499999999999999e61

   1. Initial program 74.4%

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

   2. Taylor expanded in z around -inf 60.2%

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

      1. +-commutative 60.2%

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

      2. associate--l+ 60.2%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x around inf 74.2%

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

   6. Taylor expanded in a around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. times-frac 95.4%

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

      3. *-commutative 95.4%

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

   8. Simplified 95.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3800000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-237}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_2}\\ \mathbf{elif}\;z \leq 960000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{t_2}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -2.4e+46)
     t_1
     (if (<= z -2.7e-237)
       (/ (+ (* x y) (- (* z t) (* z a))) t_2)
       (if (<= z 960000000000.0)
         (- x (/ (* z (- a t)) t_2))
         (if (<= z 1.06e+65)
           (+ (/ t (- b y)) (* (/ x z) (/ y (- 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)) - (x / z);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -2.4e+46) {
		tmp = t_1;
	} else if (z <= -2.7e-237) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_2;
	} else if (z <= 960000000000.0) {
		tmp = x - ((z * (a - t)) / t_2);
	} else if (z <= 1.06e+65) {
		tmp = (t / (b - y)) + ((x / z) * (y / (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) :: t_2
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    t_2 = y + (z * (b - y))
    if (z <= (-2.4d+46)) then
        tmp = t_1
    else if (z <= (-2.7d-237)) then
        tmp = ((x * y) + ((z * t) - (z * a))) / t_2
    else if (z <= 960000000000.0d0) then
        tmp = x - ((z * (a - t)) / t_2)
    else if (z <= 1.06d+65) then
        tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -2.4e+46) {
		tmp = t_1;
	} else if (z <= -2.7e-237) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_2;
	} else if (z <= 960000000000.0) {
		tmp = x - ((z * (a - t)) / t_2);
	} else if (z <= 1.06e+65) {
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -2.4e+46:
		tmp = t_1
	elif z <= -2.7e-237:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_2
	elif z <= 960000000000.0:
		tmp = x - ((z * (a - t)) / t_2)
	elif z <= 1.06e+65:
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -2.4e+46)
		tmp = t_1;
	elseif (z <= -2.7e-237)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_2);
	elseif (z <= 960000000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / t_2));
	elseif (z <= 1.06e+65)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / 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)) - (x / z);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -2.4e+46)
		tmp = t_1;
	elseif (z <= -2.7e-237)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_2;
	elseif (z <= 960000000000.0)
		tmp = x - ((z * (a - t)) / t_2);
	elseif (z <= 1.06e+65)
		tmp = (t / (b - y)) + ((x / z) * (y / (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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+46], t$95$1, If[LessEqual[z, -2.7e-237], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 960000000000.0], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+65], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000008e46 or 1.06e65 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around -inf 62.2%

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

      1. +-commutative 62.2%

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

      2. associate--l+ 62.2%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in x around inf 77.2%

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

   6. Taylor expanded in y around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

   if -2.40000000000000008e46 < z < -2.69999999999999984e-237

   1. Initial program 94.9%

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

      1. sub-neg 94.9%

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

      2. distribute-lft-in 94.9%

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

   3. Applied egg-rr 94.9%

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

   if -2.69999999999999984e-237 < z < 9.6e11

   1. Initial program 78.9%

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

   2. Taylor expanded in x around inf 78.9%

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

   3. Taylor expanded in z around 0 89.9%

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

   if 9.6e11 < z < 1.06e65

   1. Initial program 74.4%

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

   2. Taylor expanded in z around -inf 60.2%

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

      1. +-commutative 60.2%

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

      2. associate--l+ 60.2%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x around inf 74.2%

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

   6. Taylor expanded in a around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. times-frac 95.4%

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

      3. *-commutative 95.4%

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

   8. Simplified 95.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-237}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 960000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 960000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -6.2e+50)
     t_1
     (if (<= z -6.4e-239)
       (/ (+ (* x y) (* z (- t a))) (+ (* y (- 1.0 z)) (* z b)))
       (if (<= z 960000000000.0)
         (- x (/ (* z (- a t)) (+ y (* z (- b y)))))
         (if (<= z 1.8e+53)
           (+ (/ t (- b y)) (* (/ x z) (/ y (- 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)) - (x / z);
	double tmp;
	if (z <= -6.2e+50) {
		tmp = t_1;
	} else if (z <= -6.4e-239) {
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 960000000000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else if (z <= 1.8e+53) {
		tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z)
    if (z <= (-6.2d+50)) then
        tmp = t_1
    else if (z <= (-6.4d-239)) then
        tmp = ((x * y) + (z * (t - a))) / ((y * (1.0d0 - z)) + (z * b))
    else if (z <= 960000000000.0d0) then
        tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
    else if (z <= 1.8d+53) then
        tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z);
	double tmp;
	if (z <= -6.2e+50) {
		tmp = t_1;
	} else if (z <= -6.4e-239) {
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	} else if (z <= 960000000000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else if (z <= 1.8e+53) {
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -6.2e+50:
		tmp = t_1
	elif z <= -6.4e-239:
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b))
	elif z <= 960000000000.0:
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
	elif z <= 1.8e+53:
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -6.2e+50)
		tmp = t_1;
	elseif (z <= -6.4e-239)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(Float64(y * Float64(1.0 - z)) + Float64(z * b)));
	elseif (z <= 960000000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 1.8e+53)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / 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)) - (x / z);
	tmp = 0.0;
	if (z <= -6.2e+50)
		tmp = t_1;
	elseif (z <= -6.4e-239)
		tmp = ((x * y) + (z * (t - a))) / ((y * (1.0 - z)) + (z * b));
	elseif (z <= 960000000000.0)
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	elseif (z <= 1.8e+53)
		tmp = (t / (b - y)) + ((x / z) * (y / (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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+50], t$95$1, If[LessEqual[z, -6.4e-239], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 960000000000.0], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+53], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.20000000000000006e50 or 1.8e53 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around -inf 62.2%

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

      1. +-commutative 62.2%

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

      2. associate--l+ 62.2%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in x around inf 77.2%

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

   6. Taylor expanded in y around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

   if -6.20000000000000006e50 < z < -6.3999999999999998e-239

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 94.9%

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

   if -6.3999999999999998e-239 < z < 9.6e11

   1. Initial program 78.9%

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

   2. Taylor expanded in x around inf 78.9%

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

   3. Taylor expanded in z around 0 89.9%

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

   if 9.6e11 < z < 1.8e53

   1. Initial program 74.4%

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

   2. Taylor expanded in z around -inf 60.2%

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

      1. +-commutative 60.2%

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

      2. associate--l+ 60.2%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x around inf 74.2%

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

   6. Taylor expanded in a around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. times-frac 95.4%

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

      3. *-commutative 95.4%

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

   8. Simplified 95.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \mathbf{elif}\;z \leq 960000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -8e-22)
     t_1
     (if (<= z 2.25e-23)
       (+ x (/ (- t a) (/ y z)))
       (if (<= z 5.8e+53) (+ (/ t (- b y)) (* (/ x z) (/ y (- 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)) - (x / z);
	double tmp;
	if (z <= -8e-22) {
		tmp = t_1;
	} else if (z <= 2.25e-23) {
		tmp = x + ((t - a) / (y / z));
	} else if (z <= 5.8e+53) {
		tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z)
    if (z <= (-8d-22)) then
        tmp = t_1
    else if (z <= 2.25d-23) then
        tmp = x + ((t - a) / (y / z))
    else if (z <= 5.8d+53) then
        tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z);
	double tmp;
	if (z <= -8e-22) {
		tmp = t_1;
	} else if (z <= 2.25e-23) {
		tmp = x + ((t - a) / (y / z));
	} else if (z <= 5.8e+53) {
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -8e-22:
		tmp = t_1
	elif z <= 2.25e-23:
		tmp = x + ((t - a) / (y / z))
	elif z <= 5.8e+53:
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -8e-22)
		tmp = t_1;
	elseif (z <= 2.25e-23)
		tmp = Float64(x + Float64(Float64(t - a) / Float64(y / z)));
	elseif (z <= 5.8e+53)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / 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)) - (x / z);
	tmp = 0.0;
	if (z <= -8e-22)
		tmp = t_1;
	elseif (z <= 2.25e-23)
		tmp = x + ((t - a) / (y / z));
	elseif (z <= 5.8e+53)
		tmp = (t / (b - y)) + ((x / z) * (y / (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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-22], t$95$1, If[LessEqual[z, 2.25e-23], N[(x + N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+53], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000004e-22 or 5.8000000000000004e53 < z

   1. Initial program 44.7%

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

   2. Taylor expanded in z around -inf 62.0%

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

      1. +-commutative 62.0%

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

      2. associate--l+ 62.0%

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

   4. Simplified 87.3%

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

   5. Taylor expanded in x around inf 76.9%

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

   6. Taylor expanded in y around inf 88.3%

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

      1. associate-*r/ 88.3%

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

      2. neg-mul-1 88.3%

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

   8. Simplified 88.3%

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

   if -8.0000000000000004e-22 < z < 2.24999999999999987e-23

   1. Initial program 86.0%

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

   2. Taylor expanded in x around inf 86.0%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. associate-/l* 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around 0 71.1%

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

   if 2.24999999999999987e-23 < z < 5.8000000000000004e53

   1. Initial program 73.4%

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

   2. Taylor expanded in z around -inf 56.0%

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

      1. +-commutative 56.0%

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

      2. associate--l+ 56.0%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in x around inf 73.2%

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

   6. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. times-frac 86.5%

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

      3. *-commutative 86.5%

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

   8. Simplified 86.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-22}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 7: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4100000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -10500000000000.0)
     t_1
     (if (<= z 4100000000000.0)
       (- x (/ (* z (- a t)) (+ y (* z (- b y)))))
       (if (<= z 3.3e+63) (+ (/ t (- b y)) (* (/ x z) (/ y (- 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)) - (x / z);
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_1;
	} else if (z <= 4100000000000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else if (z <= 3.3e+63) {
		tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z)
    if (z <= (-10500000000000.0d0)) then
        tmp = t_1
    else if (z <= 4100000000000.0d0) then
        tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
    else if (z <= 3.3d+63) then
        tmp = (t / (b - y)) + ((x / z) * (y / (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)) - (x / z);
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_1;
	} else if (z <= 4100000000000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else if (z <= 3.3e+63) {
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -10500000000000.0:
		tmp = t_1
	elif z <= 4100000000000.0:
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
	elif z <= 3.3e+63:
		tmp = (t / (b - y)) + ((x / z) * (y / (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -10500000000000.0)
		tmp = t_1;
	elseif (z <= 4100000000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 3.3e+63)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / 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)) - (x / z);
	tmp = 0.0;
	if (z <= -10500000000000.0)
		tmp = t_1;
	elseif (z <= 4100000000000.0)
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	elseif (z <= 3.3e+63)
		tmp = (t / (b - y)) + ((x / z) * (y / (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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10500000000000.0], t$95$1, If[LessEqual[z, 4100000000000.0], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+63], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e13 or 3.3000000000000002e63 < z

   1. Initial program 42.6%

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

   2. Taylor expanded in z around -inf 62.4%

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

      1. +-commutative 62.4%

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

      2. associate--l+ 62.4%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in x around inf 76.9%

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

   6. Taylor expanded in y around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. neg-mul-1 89.7%

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

   8. Simplified 89.7%

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

   if -1.05e13 < z < 4.1e12

   1. Initial program 86.0%

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

   2. Taylor expanded in x around inf 86.0%

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

   3. Taylor expanded in z around 0 84.9%

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

   if 4.1e12 < z < 3.3000000000000002e63

   1. Initial program 74.4%

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

   2. Taylor expanded in z around -inf 60.2%

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

      1. +-commutative 60.2%

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

      2. associate--l+ 60.2%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in x around inf 74.2%

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

   6. Taylor expanded in a around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. times-frac 95.4%

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

      3. *-commutative 95.4%

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

   8. Simplified 95.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 4100000000000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 8: 31.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+252}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-281}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.2e+252)
   x
   (if (<= y -1.9e+58)
     (/ (- x) z)
     (if (<= y -3.6e-30)
       x
       (if (<= y -1.02e-281)
         (/ t b)
         (if (<= y 5.9e-285) (/ (- a) b) (if (<= y 9e-18) (/ t b) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.2e+252) {
		tmp = x;
	} else if (y <= -1.9e+58) {
		tmp = -x / z;
	} else if (y <= -3.6e-30) {
		tmp = x;
	} else if (y <= -1.02e-281) {
		tmp = t / b;
	} else if (y <= 5.9e-285) {
		tmp = -a / b;
	} else if (y <= 9e-18) {
		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 <= (-1.2d+252)) then
        tmp = x
    else if (y <= (-1.9d+58)) then
        tmp = -x / z
    else if (y <= (-3.6d-30)) then
        tmp = x
    else if (y <= (-1.02d-281)) then
        tmp = t / b
    else if (y <= 5.9d-285) then
        tmp = -a / b
    else if (y <= 9d-18) 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 <= -1.2e+252) {
		tmp = x;
	} else if (y <= -1.9e+58) {
		tmp = -x / z;
	} else if (y <= -3.6e-30) {
		tmp = x;
	} else if (y <= -1.02e-281) {
		tmp = t / b;
	} else if (y <= 5.9e-285) {
		tmp = -a / b;
	} else if (y <= 9e-18) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.2e+252:
		tmp = x
	elif y <= -1.9e+58:
		tmp = -x / z
	elif y <= -3.6e-30:
		tmp = x
	elif y <= -1.02e-281:
		tmp = t / b
	elif y <= 5.9e-285:
		tmp = -a / b
	elif y <= 9e-18:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.2e+252)
		tmp = x;
	elseif (y <= -1.9e+58)
		tmp = Float64(Float64(-x) / z);
	elseif (y <= -3.6e-30)
		tmp = x;
	elseif (y <= -1.02e-281)
		tmp = Float64(t / b);
	elseif (y <= 5.9e-285)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 9e-18)
		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 <= -1.2e+252)
		tmp = x;
	elseif (y <= -1.9e+58)
		tmp = -x / z;
	elseif (y <= -3.6e-30)
		tmp = x;
	elseif (y <= -1.02e-281)
		tmp = t / b;
	elseif (y <= 5.9e-285)
		tmp = -a / b;
	elseif (y <= 9e-18)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.2e+252], x, If[LessEqual[y, -1.9e+58], N[((-x) / z), $MachinePrecision], If[LessEqual[y, -3.6e-30], x, If[LessEqual[y, -1.02e-281], N[(t / b), $MachinePrecision], If[LessEqual[y, 5.9e-285], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 9e-18], N[(t / b), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e252 or -1.8999999999999999e58 < y < -3.6000000000000003e-30 or 8.99999999999999987e-18 < y

   1. Initial program 57.0%

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

   2. Taylor expanded in z around 0 49.5%

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

   if -1.2e252 < y < -1.8999999999999999e58

   1. Initial program 46.7%

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

   2. Taylor expanded in y around inf 43.8%

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

      1. +-commutative 43.8%

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

      2. mul-1-neg 43.8%

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

      3. unsub-neg 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in z around inf 33.8%

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

      1. associate-*r/ 33.8%

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

      2. mul-1-neg 33.8%

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

   7. Simplified 33.8%

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

   if -3.6000000000000003e-30 < y < -1.01999999999999996e-281 or 5.89999999999999963e-285 < y < 8.99999999999999987e-18

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 83.5%

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

   3. Taylor expanded in y around 0 62.5%

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

   4. Taylor expanded in t around inf 47.3%

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

   if -1.01999999999999996e-281 < y < 5.89999999999999963e-285

   1. Initial program 83.1%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-lft-neg-out 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. neg-mul-1 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+252}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-281}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-22} \lor \neg \left(z \leq 2.7 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e-22) (not (<= z 2.7e-23)))
   (- (/ (- t a) (- b y)) (/ x z))
   (+ x (/ (- t a) (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e-22) || !(z <= 2.7e-23)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8d-22)) .or. (.not. (z <= 2.7d-23))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = x + ((t - a) / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e-22) || !(z <= 2.7e-23)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8e-22) or not (z <= 2.7e-23):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = x + ((t - a) / (y / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8e-22) || !(z <= 2.7e-23))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(x + Float64(Float64(t - a) / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8e-22) || ~((z <= 2.7e-23)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = x + ((t - a) / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8e-22], N[Not[LessEqual[z, 2.7e-23]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000004e-22 or 2.69999999999999985e-23 < z

   1. Initial program 48.7%

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

   2. Taylor expanded in z around -inf 61.1%

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

      1. +-commutative 61.1%

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

      2. associate--l+ 61.1%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in x around inf 76.3%

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

   6. Taylor expanded in y around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. neg-mul-1 84.7%

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

   8. Simplified 84.7%

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

   if -8.0000000000000004e-22 < z < 2.69999999999999985e-23

   1. Initial program 86.0%

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

   2. Taylor expanded in x around inf 86.0%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. associate-/l* 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around 0 71.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-22} \lor \neg \left(z \leq 2.7 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \]

Alternative 10: 42.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -8.2e-32)
     t_1
     (if (<= y -5.2e-280)
       (/ t b)
       (if (<= y 5.8e-287) (/ (- a) b) (if (<= y 2.25e-20) (/ t 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 <= -8.2e-32) {
		tmp = t_1;
	} else if (y <= -5.2e-280) {
		tmp = t / b;
	} else if (y <= 5.8e-287) {
		tmp = -a / b;
	} else if (y <= 2.25e-20) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-8.2d-32)) then
        tmp = t_1
    else if (y <= (-5.2d-280)) then
        tmp = t / b
    else if (y <= 5.8d-287) then
        tmp = -a / b
    else if (y <= 2.25d-20) then
        tmp = t / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -8.2e-32) {
		tmp = t_1;
	} else if (y <= -5.2e-280) {
		tmp = t / b;
	} else if (y <= 5.8e-287) {
		tmp = -a / b;
	} else if (y <= 2.25e-20) {
		tmp = t / 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 <= -8.2e-32:
		tmp = t_1
	elif y <= -5.2e-280:
		tmp = t / b
	elif y <= 5.8e-287:
		tmp = -a / b
	elif y <= 2.25e-20:
		tmp = t / 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 <= -8.2e-32)
		tmp = t_1;
	elseif (y <= -5.2e-280)
		tmp = Float64(t / b);
	elseif (y <= 5.8e-287)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.25e-20)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -8.2e-32)
		tmp = t_1;
	elseif (y <= -5.2e-280)
		tmp = t / b;
	elseif (y <= 5.8e-287)
		tmp = -a / b;
	elseif (y <= 2.25e-20)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-32], t$95$1, If[LessEqual[y, -5.2e-280], N[(t / b), $MachinePrecision], If[LessEqual[y, 5.8e-287], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.25e-20], N[(t / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999995e-32 or 2.2500000000000001e-20 < y

   1. Initial program 54.9%

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

   2. Taylor expanded in y around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   if -8.1999999999999995e-32 < y < -5.2e-280 or 5.7999999999999996e-287 < y < 2.2500000000000001e-20

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 83.5%

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

   3. Taylor expanded in y around 0 62.5%

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

   4. Taylor expanded in t around inf 47.3%

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

   if -5.2e-280 < y < 5.7999999999999996e-287

   1. Initial program 83.1%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-lft-neg-out 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. neg-mul-1 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-23} \lor \neg \left(z \leq 2.45 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.2e-23) (not (<= z 2.45e-23)))
   (/ (- t a) (- b y))
   (+ x (/ (- t a) (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.2e-23) || !(z <= 2.45e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.2d-23)) .or. (.not. (z <= 2.45d-23))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((t - a) / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.2e-23) || !(z <= 2.45e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.2e-23) or not (z <= 2.45e-23):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((t - a) / (y / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.2e-23) || !(z <= 2.45e-23))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(t - a) / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.2e-23) || ~((z <= 2.45e-23)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((t - a) / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.2e-23], N[Not[LessEqual[z, 2.45e-23]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000059e-23 or 2.4499999999999999e-23 < z

   1. Initial program 48.7%

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

   2. Taylor expanded in z around inf 77.9%

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

   if -8.20000000000000059e-23 < z < 2.4499999999999999e-23

   1. Initial program 86.0%

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

   2. Taylor expanded in x around inf 86.0%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. associate-/l* 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around 0 71.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-23} \lor \neg \left(z \leq 2.45 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \]

Alternative 12: 35.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-282}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.8e-31)
   x
   (if (<= y -6.6e-282)
     (/ t b)
     (if (<= y 1.85e-285) (/ (- a) b) (if (<= y 2.7e-20) (/ t b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e-31) {
		tmp = x;
	} else if (y <= -6.6e-282) {
		tmp = t / b;
	} else if (y <= 1.85e-285) {
		tmp = -a / b;
	} else if (y <= 2.7e-20) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.8d-31)) then
        tmp = x
    else if (y <= (-6.6d-282)) then
        tmp = t / b
    else if (y <= 1.85d-285) then
        tmp = -a / b
    else if (y <= 2.7d-20) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e-31) {
		tmp = x;
	} else if (y <= -6.6e-282) {
		tmp = t / b;
	} else if (y <= 1.85e-285) {
		tmp = -a / b;
	} else if (y <= 2.7e-20) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.8e-31:
		tmp = x
	elif y <= -6.6e-282:
		tmp = t / b
	elif y <= 1.85e-285:
		tmp = -a / b
	elif y <= 2.7e-20:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.8e-31)
		tmp = x;
	elseif (y <= -6.6e-282)
		tmp = Float64(t / b);
	elseif (y <= 1.85e-285)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.7e-20)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.8e-31)
		tmp = x;
	elseif (y <= -6.6e-282)
		tmp = t / b;
	elseif (y <= 1.85e-285)
		tmp = -a / b;
	elseif (y <= 2.7e-20)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.8e-31], x, If[LessEqual[y, -6.6e-282], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.85e-285], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.7e-20], N[(t / b), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8000000000000002e-31 or 2.7e-20 < y

   1. Initial program 54.9%

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

   2. Taylor expanded in z around 0 42.3%

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

   if -6.8000000000000002e-31 < y < -6.6e-282 or 1.8499999999999999e-285 < y < 2.7e-20

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 83.5%

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

   3. Taylor expanded in y around 0 62.5%

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

   4. Taylor expanded in t around inf 47.3%

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

   if -6.6e-282 < y < 1.8499999999999999e-285

   1. Initial program 83.1%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-lft-neg-out 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. neg-mul-1 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-282}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -620000000000 \lor \neg \left(y \leq 5.2 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -620000000000.0) (not (<= y 5.2e+45)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -620000000000.0) || !(y <= 5.2e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (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 <= (-620000000000.0d0)) .or. (.not. (y <= 5.2d+45))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (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 <= -620000000000.0) || !(y <= 5.2e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -620000000000.0) or not (y <= 5.2e+45):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -620000000000.0) || !(y <= 5.2e+45))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -620000000000.0) || ~((y <= 5.2e+45)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -620000000000.0], N[Not[LessEqual[y, 5.2e+45]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e11 or 5.20000000000000014e45 < y

   1. Initial program 52.2%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

   4. Simplified 60.3%

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

   if -6.2e11 < y < 5.20000000000000014e45

   1. Initial program 81.2%

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

   2. Taylor expanded in z around inf 74.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -620000000000 \lor \neg \left(y \leq 5.2 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 14: 54.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-29} \lor \neg \left(y \leq 4.5 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e-29) (not (<= y 4.5e-18))) (/ 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 <= -2e-29) || !(y <= 4.5e-18)) {
		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 <= (-2d-29)) .or. (.not. (y <= 4.5d-18))) 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 <= -2e-29) || !(y <= 4.5e-18)) {
		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 <= -2e-29) or not (y <= 4.5e-18):
		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 <= -2e-29) || !(y <= 4.5e-18))
		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 <= -2e-29) || ~((y <= 4.5e-18)))
		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, -2e-29], N[Not[LessEqual[y, 4.5e-18]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999989e-29 or 4.49999999999999994e-18 < y

   1. Initial program 54.9%

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

   2. Taylor expanded in y around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   if -1.99999999999999989e-29 < y < 4.49999999999999994e-18

   1. Initial program 83.5%

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

   2. Taylor expanded in y around 0 67.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-29} \lor \neg \left(y \leq 4.5 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 34.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e-29) x (if (<= y 7.6e-18) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e-29) {
		tmp = x;
	} else if (y <= 7.6e-18) {
		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 <= (-1.5d-29)) then
        tmp = x
    else if (y <= 7.6d-18) 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 <= -1.5e-29) {
		tmp = x;
	} else if (y <= 7.6e-18) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.5e-29:
		tmp = x
	elif y <= 7.6e-18:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e-29)
		tmp = x;
	elseif (y <= 7.6e-18)
		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 <= -1.5e-29)
		tmp = x;
	elseif (y <= 7.6e-18)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e-29], x, If[LessEqual[y, 7.6e-18], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-29 or 7.5999999999999996e-18 < y

   1. Initial program 54.9%

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

   2. Taylor expanded in z around 0 42.3%

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

   if -1.5000000000000001e-29 < y < 7.5999999999999996e-18

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 83.5%

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

   3. Taylor expanded in y around 0 65.6%

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

   4. Taylor expanded in t around inf 45.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 25.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.5%

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

2. Taylor expanded in z around 0 27.5%

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

3. Final simplification 27.5%

   \[\leadsto x \]

Developer target: 73.0% 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 2023200 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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