Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 93.3%

Time: 17.4s

Alternatives: 19

Speedup: 1.5×

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: 66.6% 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: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 1.45 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1700000.0) (not (<= z 1.45e+15)))
   (+ (/ (* (/ y (- b y)) x) z) (/ (- t a) (- b y)))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1700000.0) || !(z <= 1.45e+15)) {
		tmp = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1700000.0d0)) .or. (.not. (z <= 1.45d+15))) then
        tmp = (((y / (b - y)) * x) / z) + ((t - a) / (b - y))
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1700000.0) || !(z <= 1.45e+15)) {
		tmp = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1700000.0) or not (z <= 1.45e+15):
		tmp = (((y / (b - y)) * x) / z) + ((t - a) / (b - y))
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1700000.0) || !(z <= 1.45e+15))
		tmp = Float64(Float64(Float64(Float64(y / Float64(b - y)) * x) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1700000.0) || ~((z <= 1.45e+15)))
		tmp = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1700000.0], N[Not[LessEqual[z, 1.45e+15]], $MachinePrecision]], N[(N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e6 or 1.45e15 < z

   1. Initial program 48.6%

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

   2. Taylor expanded in z around -inf 67.7%

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

      1. +-commutative 67.7%

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

      2. associate--l+ 67.7%

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

   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 80.7%

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

      1. times-frac 98.6%

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

   7. Simplified 98.6%

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

      1. associate-*r/ 98.6%

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

   9. Applied egg-rr 98.6%

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

   if -1.7e6 < z < 1.45e15

   1. Initial program 89.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 1.45 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} + \frac{y}{b - y} \cdot \frac{x}{z}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{y \cdot x + z \cdot t}{t_2}\\ \mathbf{if}\;z \leq -0.35:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{t_2}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_2}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot x}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (- t a) (- b y)) (* (/ y (- b y)) (/ x z))))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* y x) (* z t)) t_2)))
   (if (<= z -0.35)
     t_1
     (if (<= z -1.6e-284)
       t_3
       (if (<= z 9e-267)
         (/ (- (* y x) (* z a)) t_2)
         (if (<= z 5.6e-83)
           t_3
           (if (<= z 1.35e-29)
             (/ (* z (- t a)) t_2)
             (if (<= z 1.1e-22) (/ (* y x) t_2) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) + ((y / (b - y)) * (x / z));
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + (z * t)) / t_2;
	double tmp;
	if (z <= -0.35) {
		tmp = t_1;
	} else if (z <= -1.6e-284) {
		tmp = t_3;
	} else if (z <= 9e-267) {
		tmp = ((y * x) - (z * a)) / t_2;
	} else if (z <= 5.6e-83) {
		tmp = t_3;
	} else if (z <= 1.35e-29) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.1e-22) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) + ((y / (b - y)) * (x / z))
    t_2 = y + (z * (b - y))
    t_3 = ((y * x) + (z * t)) / t_2
    if (z <= (-0.35d0)) then
        tmp = t_1
    else if (z <= (-1.6d-284)) then
        tmp = t_3
    else if (z <= 9d-267) then
        tmp = ((y * x) - (z * a)) / t_2
    else if (z <= 5.6d-83) then
        tmp = t_3
    else if (z <= 1.35d-29) then
        tmp = (z * (t - a)) / t_2
    else if (z <= 1.1d-22) then
        tmp = (y * x) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) + ((y / (b - y)) * (x / z));
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + (z * t)) / t_2;
	double tmp;
	if (z <= -0.35) {
		tmp = t_1;
	} else if (z <= -1.6e-284) {
		tmp = t_3;
	} else if (z <= 9e-267) {
		tmp = ((y * x) - (z * a)) / t_2;
	} else if (z <= 5.6e-83) {
		tmp = t_3;
	} else if (z <= 1.35e-29) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.1e-22) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) + ((y / (b - y)) * (x / z))
	t_2 = y + (z * (b - y))
	t_3 = ((y * x) + (z * t)) / t_2
	tmp = 0
	if z <= -0.35:
		tmp = t_1
	elif z <= -1.6e-284:
		tmp = t_3
	elif z <= 9e-267:
		tmp = ((y * x) - (z * a)) / t_2
	elif z <= 5.6e-83:
		tmp = t_3
	elif z <= 1.35e-29:
		tmp = (z * (t - a)) / t_2
	elif z <= 1.1e-22:
		tmp = (y * x) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / Float64(b - y)) * Float64(x / z)))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_2)
	tmp = 0.0
	if (z <= -0.35)
		tmp = t_1;
	elseif (z <= -1.6e-284)
		tmp = t_3;
	elseif (z <= 9e-267)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / t_2);
	elseif (z <= 5.6e-83)
		tmp = t_3;
	elseif (z <= 1.35e-29)
		tmp = Float64(Float64(z * Float64(t - a)) / t_2);
	elseif (z <= 1.1e-22)
		tmp = Float64(Float64(y * x) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) + ((y / (b - y)) * (x / z));
	t_2 = y + (z * (b - y));
	t_3 = ((y * x) + (z * t)) / t_2;
	tmp = 0.0;
	if (z <= -0.35)
		tmp = t_1;
	elseif (z <= -1.6e-284)
		tmp = t_3;
	elseif (z <= 9e-267)
		tmp = ((y * x) - (z * a)) / t_2;
	elseif (z <= 5.6e-83)
		tmp = t_3;
	elseif (z <= 1.35e-29)
		tmp = (z * (t - a)) / t_2;
	elseif (z <= 1.1e-22)
		tmp = (y * x) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -0.35], t$95$1, If[LessEqual[z, -1.6e-284], t$95$3, If[LessEqual[z, 9e-267], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 5.6e-83], t$95$3, If[LessEqual[z, 1.35e-29], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.1e-22], N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.34999999999999998 or 1.1e-22 < z

   1. Initial program 50.2%

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

   2. Taylor expanded in z around -inf 68.7%

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

      1. +-commutative 68.7%

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

      2. associate--l+ 68.7%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. times-frac 98.6%

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

   7. Simplified 98.6%

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

   if -0.34999999999999998 < z < -1.60000000000000012e-284 or 8.9999999999999999e-267 < z < 5.6000000000000002e-83

   1. Initial program 90.2%

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

   2. Taylor expanded in a around 0 75.1%

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

   if -1.60000000000000012e-284 < z < 8.9999999999999999e-267

   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 t around 0 79.6%

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

      1. *-commutative 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   if 5.6000000000000002e-83 < z < 1.35000000000000011e-29

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 82.0%

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

   if 1.35000000000000011e-29 < z < 1.1e-22

   1. Initial program 76.5%

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

   2. Taylor expanded in x around inf 76.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.35:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{b - y} \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{b - y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{b - y} \cdot x}{z} + \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{y \cdot x + z \cdot t}{t_2}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{t_2}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-27}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_2}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot x}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* (/ y (- b y)) x) z) (/ (- t a) (- b y))))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* y x) (* z t)) t_2)))
   (if (<= z -2.8e-5)
     t_1
     (if (<= z -1.6e-284)
       t_3
       (if (<= z 7.2e-267)
         (/ (- (* y x) (* z a)) t_2)
         (if (<= z 8.5e-82)
           t_3
           (if (<= z 6e-27)
             (/ (* z (- t a)) t_2)
             (if (<= z 1.5e-22) (/ (* y x) t_2) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + (z * t)) / t_2;
	double tmp;
	if (z <= -2.8e-5) {
		tmp = t_1;
	} else if (z <= -1.6e-284) {
		tmp = t_3;
	} else if (z <= 7.2e-267) {
		tmp = ((y * x) - (z * a)) / t_2;
	} else if (z <= 8.5e-82) {
		tmp = t_3;
	} else if (z <= 6e-27) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.5e-22) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (((y / (b - y)) * x) / z) + ((t - a) / (b - y))
    t_2 = y + (z * (b - y))
    t_3 = ((y * x) + (z * t)) / t_2
    if (z <= (-2.8d-5)) then
        tmp = t_1
    else if (z <= (-1.6d-284)) then
        tmp = t_3
    else if (z <= 7.2d-267) then
        tmp = ((y * x) - (z * a)) / t_2
    else if (z <= 8.5d-82) then
        tmp = t_3
    else if (z <= 6d-27) then
        tmp = (z * (t - a)) / t_2
    else if (z <= 1.5d-22) then
        tmp = (y * x) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + (z * t)) / t_2;
	double tmp;
	if (z <= -2.8e-5) {
		tmp = t_1;
	} else if (z <= -1.6e-284) {
		tmp = t_3;
	} else if (z <= 7.2e-267) {
		tmp = ((y * x) - (z * a)) / t_2;
	} else if (z <= 8.5e-82) {
		tmp = t_3;
	} else if (z <= 6e-27) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.5e-22) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((y / (b - y)) * x) / z) + ((t - a) / (b - y))
	t_2 = y + (z * (b - y))
	t_3 = ((y * x) + (z * t)) / t_2
	tmp = 0
	if z <= -2.8e-5:
		tmp = t_1
	elif z <= -1.6e-284:
		tmp = t_3
	elif z <= 7.2e-267:
		tmp = ((y * x) - (z * a)) / t_2
	elif z <= 8.5e-82:
		tmp = t_3
	elif z <= 6e-27:
		tmp = (z * (t - a)) / t_2
	elif z <= 1.5e-22:
		tmp = (y * x) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(y / Float64(b - y)) * x) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_2)
	tmp = 0.0
	if (z <= -2.8e-5)
		tmp = t_1;
	elseif (z <= -1.6e-284)
		tmp = t_3;
	elseif (z <= 7.2e-267)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / t_2);
	elseif (z <= 8.5e-82)
		tmp = t_3;
	elseif (z <= 6e-27)
		tmp = Float64(Float64(z * Float64(t - a)) / t_2);
	elseif (z <= 1.5e-22)
		tmp = Float64(Float64(y * x) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((y / (b - y)) * x) / z) + ((t - a) / (b - y));
	t_2 = y + (z * (b - y));
	t_3 = ((y * x) + (z * t)) / t_2;
	tmp = 0.0;
	if (z <= -2.8e-5)
		tmp = t_1;
	elseif (z <= -1.6e-284)
		tmp = t_3;
	elseif (z <= 7.2e-267)
		tmp = ((y * x) - (z * a)) / t_2;
	elseif (z <= 8.5e-82)
		tmp = t_3;
	elseif (z <= 6e-27)
		tmp = (z * (t - a)) / t_2;
	elseif (z <= 1.5e-22)
		tmp = (y * x) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -2.8e-5], t$95$1, If[LessEqual[z, -1.6e-284], t$95$3, If[LessEqual[z, 7.2e-267], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 8.5e-82], t$95$3, If[LessEqual[z, 6e-27], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.5e-22], N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.79999999999999996e-5 or 1.5e-22 < z

   1. Initial program 50.2%

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

   2. Taylor expanded in z around -inf 68.7%

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

      1. +-commutative 68.7%

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

      2. associate--l+ 68.7%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. times-frac 98.6%

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

   7. Simplified 98.6%

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

      1. associate-*r/ 98.6%

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

   9. Applied egg-rr 98.6%

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

   if -2.79999999999999996e-5 < z < -1.60000000000000012e-284 or 7.2000000000000002e-267 < z < 8.4999999999999997e-82

   1. Initial program 90.2%

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

   2. Taylor expanded in a around 0 75.1%

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

   if -1.60000000000000012e-284 < z < 7.2000000000000002e-267

   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 t around 0 79.6%

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

      1. *-commutative 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   if 8.4999999999999997e-82 < z < 6.0000000000000002e-27

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 82.0%

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

   if 6.0000000000000002e-27 < z < 1.5e-22

   1. Initial program 76.5%

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

   2. Taylor expanded in x around inf 76.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-27}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{b - y} \cdot x}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x}{1 - z}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t_1}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+62}:\\ \;\;\;\;t_3 + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{elif}\;y \leq 10^{+219}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{t_1}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ x (- 1.0 z)))
        (t_3 (/ (- t a) (- b y))))
   (if (<= y -3.05e+122)
     t_2
     (if (<= y -5e-6)
       (/ (+ (* y x) (* z t)) t_1)
       (if (<= y 5.9e+62)
         (+ t_3 (/ (/ y (/ b x)) z))
         (if (<= y 1e+219)
           (/ (- (* y x) (* z a)) t_1)
           (if (<= y 3.3e+255) t_3 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 = x / (1.0 - z);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (y <= -3.05e+122) {
		tmp = t_2;
	} else if (y <= -5e-6) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else if (y <= 5.9e+62) {
		tmp = t_3 + ((y / (b / x)) / z);
	} else if (y <= 1e+219) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (y <= 3.3e+255) {
		tmp = t_3;
	} 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 = x / (1.0d0 - z)
    t_3 = (t - a) / (b - y)
    if (y <= (-3.05d+122)) then
        tmp = t_2
    else if (y <= (-5d-6)) then
        tmp = ((y * x) + (z * t)) / t_1
    else if (y <= 5.9d+62) then
        tmp = t_3 + ((y / (b / x)) / z)
    else if (y <= 1d+219) then
        tmp = ((y * x) - (z * a)) / t_1
    else if (y <= 3.3d+255) then
        tmp = t_3
    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 = x / (1.0 - z);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (y <= -3.05e+122) {
		tmp = t_2;
	} else if (y <= -5e-6) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else if (y <= 5.9e+62) {
		tmp = t_3 + ((y / (b / x)) / z);
	} else if (y <= 1e+219) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (y <= 3.3e+255) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x / (1.0 - z)
	t_3 = (t - a) / (b - y)
	tmp = 0
	if y <= -3.05e+122:
		tmp = t_2
	elif y <= -5e-6:
		tmp = ((y * x) + (z * t)) / t_1
	elif y <= 5.9e+62:
		tmp = t_3 + ((y / (b / x)) / z)
	elif y <= 1e+219:
		tmp = ((y * x) - (z * a)) / t_1
	elif y <= 3.3e+255:
		tmp = t_3
	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(x / Float64(1.0 - z))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (y <= -3.05e+122)
		tmp = t_2;
	elseif (y <= -5e-6)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / t_1);
	elseif (y <= 5.9e+62)
		tmp = Float64(t_3 + Float64(Float64(y / Float64(b / x)) / z));
	elseif (y <= 1e+219)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / t_1);
	elseif (y <= 3.3e+255)
		tmp = t_3;
	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 = x / (1.0 - z);
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (y <= -3.05e+122)
		tmp = t_2;
	elseif (y <= -5e-6)
		tmp = ((y * x) + (z * t)) / t_1;
	elseif (y <= 5.9e+62)
		tmp = t_3 + ((y / (b / x)) / z);
	elseif (y <= 1e+219)
		tmp = ((y * x) - (z * a)) / t_1;
	elseif (y <= 3.3e+255)
		tmp = t_3;
	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[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.05e+122], t$95$2, If[LessEqual[y, -5e-6], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5.9e+62], N[(t$95$3 + N[(N[(y / N[(b / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+219], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.3e+255], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.0499999999999999e122 or 3.29999999999999982e255 < y

   1. Initial program 29.7%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   4. Simplified 70.3%

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

   if -3.0499999999999999e122 < y < -5.00000000000000041e-6

   1. Initial program 82.5%

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

   2. Taylor expanded in a around 0 76.1%

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

   if -5.00000000000000041e-6 < y < 5.9000000000000003e62

   1. Initial program 78.5%

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

   2. Taylor expanded in z around -inf 68.5%

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

      1. +-commutative 68.5%

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

      2. associate--l+ 68.5%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around inf 76.2%

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

      1. times-frac 71.5%

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

   7. Simplified 71.5%

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

      1. associate-*r/ 75.0%

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

   9. Applied egg-rr 75.0%

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

   10. Taylor expanded in y around 0 75.2%

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

       1. associate-/l* 72.4%

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

   12. Simplified 72.4%

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

   if 5.9000000000000003e62 < y < 9.99999999999999965e218

   1. Initial program 78.5%

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

   2. Taylor expanded in t around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. *-commutative 69.8%

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

   4. Simplified 69.8%

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

   if 9.99999999999999965e218 < y < 3.29999999999999982e255

   1. Initial program 29.4%

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

   2. Taylor expanded in z around inf 86.1%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+62}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{elif}\;y \leq 10^{+219}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 5: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.65e+117)
     t_1
     (if (<= y -3.4e-6)
       (/ (+ (* y x) (* z t)) (+ y (* z (- b y))))
       (if (<= y 1.4e+79) (+ (/ (- t a) (- b y)) (/ (/ y (/ b x)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.65e+117) {
		tmp = t_1;
	} else if (y <= -3.4e-6) {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 1.4e+79) {
		tmp = ((t - a) / (b - y)) + ((y / (b / x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.65d+117)) then
        tmp = t_1
    else if (y <= (-3.4d-6)) then
        tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
    else if (y <= 1.4d+79) then
        tmp = ((t - a) / (b - y)) + ((y / (b / x)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.65e+117) {
		tmp = t_1;
	} else if (y <= -3.4e-6) {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 1.4e+79) {
		tmp = ((t - a) / (b - y)) + ((y / (b / x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.65e+117:
		tmp = t_1
	elif y <= -3.4e-6:
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
	elif y <= 1.4e+79:
		tmp = ((t - a) / (b - y)) + ((y / (b / x)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.65e+117)
		tmp = t_1;
	elseif (y <= -3.4e-6)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 1.4e+79)
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / Float64(b / x)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.65e+117)
		tmp = t_1;
	elseif (y <= -3.4e-6)
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	elseif (y <= 1.4e+79)
		tmp = ((t - a) / (b - y)) + ((y / (b / x)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+117], t$95$1, If[LessEqual[y, -3.4e-6], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+79], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(b / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e117 or 1.4000000000000001e79 < y

   1. Initial program 46.8%

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

   2. Taylor expanded in y around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

   4. Simplified 62.8%

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

   if -1.6499999999999999e117 < y < -3.40000000000000006e-6

   1. Initial program 82.5%

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

   2. Taylor expanded in a around 0 76.1%

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

   if -3.40000000000000006e-6 < y < 1.4000000000000001e79

   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 z around -inf 68.5%

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

      1. +-commutative 68.5%

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

      2. associate--l+ 68.5%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around inf 76.0%

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

      1. times-frac 71.4%

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

   7. Simplified 71.4%

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

      1. associate-*r/ 74.8%

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

   9. Applied egg-rr 74.8%

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

   10. Taylor expanded in y around 0 75.0%

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

       1. associate-/l* 72.3%

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

   12. Simplified 72.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 6: 42.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-233}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.7 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)) (t_3 (/ x (- 1.0 z))))
   (if (<= y -2.4e-6)
     t_3
     (if (<= y -2.7e-216)
       t_1
       (if (<= y -8.3e-286)
         t_2
         (if (<= y 1.35e-233)
           (/ t b)
           (if (<= y 1.4e-29)
             t_2
             (if (<= y 8.7e+64) t_1 (if (<= y 6.8e+68) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.4e-6) {
		tmp = t_3;
	} else if (y <= -2.7e-216) {
		tmp = t_1;
	} else if (y <= -8.3e-286) {
		tmp = t_2;
	} else if (y <= 1.35e-233) {
		tmp = t / b;
	} else if (y <= 1.4e-29) {
		tmp = t_2;
	} else if (y <= 8.7e+64) {
		tmp = t_1;
	} else if (y <= 6.8e+68) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = -a / b
    t_3 = x / (1.0d0 - z)
    if (y <= (-2.4d-6)) then
        tmp = t_3
    else if (y <= (-2.7d-216)) then
        tmp = t_1
    else if (y <= (-8.3d-286)) then
        tmp = t_2
    else if (y <= 1.35d-233) then
        tmp = t / b
    else if (y <= 1.4d-29) then
        tmp = t_2
    else if (y <= 8.7d+64) then
        tmp = t_1
    else if (y <= 6.8d+68) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.4e-6) {
		tmp = t_3;
	} else if (y <= -2.7e-216) {
		tmp = t_1;
	} else if (y <= -8.3e-286) {
		tmp = t_2;
	} else if (y <= 1.35e-233) {
		tmp = t / b;
	} else if (y <= 1.4e-29) {
		tmp = t_2;
	} else if (y <= 8.7e+64) {
		tmp = t_1;
	} else if (y <= 6.8e+68) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	t_3 = x / (1.0 - z)
	tmp = 0
	if y <= -2.4e-6:
		tmp = t_3
	elif y <= -2.7e-216:
		tmp = t_1
	elif y <= -8.3e-286:
		tmp = t_2
	elif y <= 1.35e-233:
		tmp = t / b
	elif y <= 1.4e-29:
		tmp = t_2
	elif y <= 8.7e+64:
		tmp = t_1
	elif y <= 6.8e+68:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.4e-6)
		tmp = t_3;
	elseif (y <= -2.7e-216)
		tmp = t_1;
	elseif (y <= -8.3e-286)
		tmp = t_2;
	elseif (y <= 1.35e-233)
		tmp = Float64(t / b);
	elseif (y <= 1.4e-29)
		tmp = t_2;
	elseif (y <= 8.7e+64)
		tmp = t_1;
	elseif (y <= 6.8e+68)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.4e-6)
		tmp = t_3;
	elseif (y <= -2.7e-216)
		tmp = t_1;
	elseif (y <= -8.3e-286)
		tmp = t_2;
	elseif (y <= 1.35e-233)
		tmp = t / b;
	elseif (y <= 1.4e-29)
		tmp = t_2;
	elseif (y <= 8.7e+64)
		tmp = t_1;
	elseif (y <= 6.8e+68)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-6], t$95$3, If[LessEqual[y, -2.7e-216], t$95$1, If[LessEqual[y, -8.3e-286], t$95$2, If[LessEqual[y, 1.35e-233], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.4e-29], t$95$2, If[LessEqual[y, 8.7e+64], t$95$1, If[LessEqual[y, 6.8e+68], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3999999999999999e-6 or 6.8000000000000003e68 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   4. Simplified 60.9%

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

   if -2.3999999999999999e-6 < y < -2.6999999999999999e-216 or 1.4000000000000001e-29 < y < 8.70000000000000038e64

   1. Initial program 74.0%

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

   2. Taylor expanded in z around -inf 66.6%

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

      1. +-commutative 66.6%

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

      2. associate--l+ 66.6%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in x around inf 69.8%

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

      1. times-frac 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in t around inf 41.8%

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

   if -2.6999999999999999e-216 < y < -8.30000000000000022e-286 or 1.35e-233 < y < 1.4000000000000001e-29 or 8.70000000000000038e64 < y < 6.8000000000000003e68

   1. Initial program 79.3%

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

   2. Taylor expanded in b around inf 49.0%

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

   3. Taylor expanded in a around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. mul-1-neg 52.1%

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

   5. Simplified 52.1%

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

   if -8.30000000000000022e-286 < y < 1.35e-233

   1. Initial program 92.4%

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

   2. Taylor expanded in b around inf 85.3%

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

   3. Taylor expanded in t around inf 53.8%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-216}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-286}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-233}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 8.7 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 7: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -16.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;t_1 + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+75} \lor \neg \left(y \leq 8 \cdot 10^{+220}\right) \land y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -16.5)
     t_2
     (if (<= y -1.45e-207)
       (+ t_1 (* (/ y z) (/ x b)))
       (if (<= y 2.05e-160)
         (/ (- (+ t (/ (* y x) z)) a) b)
         (if (or (<= y 1.25e+75) (and (not (<= y 8e+220)) (<= y 3.3e+255)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -16.5) {
		tmp = t_2;
	} else if (y <= -1.45e-207) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (y <= 2.05e-160) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if ((y <= 1.25e+75) || (!(y <= 8e+220) && (y <= 3.3e+255))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-16.5d0)) then
        tmp = t_2
    else if (y <= (-1.45d-207)) then
        tmp = t_1 + ((y / z) * (x / b))
    else if (y <= 2.05d-160) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if ((y <= 1.25d+75) .or. (.not. (y <= 8d+220)) .and. (y <= 3.3d+255)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -16.5) {
		tmp = t_2;
	} else if (y <= -1.45e-207) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (y <= 2.05e-160) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if ((y <= 1.25e+75) || (!(y <= 8e+220) && (y <= 3.3e+255))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -16.5:
		tmp = t_2
	elif y <= -1.45e-207:
		tmp = t_1 + ((y / z) * (x / b))
	elif y <= 2.05e-160:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif (y <= 1.25e+75) or (not (y <= 8e+220) and (y <= 3.3e+255)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -16.5)
		tmp = t_2;
	elseif (y <= -1.45e-207)
		tmp = Float64(t_1 + Float64(Float64(y / z) * Float64(x / b)));
	elseif (y <= 2.05e-160)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif ((y <= 1.25e+75) || (!(y <= 8e+220) && (y <= 3.3e+255)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -16.5)
		tmp = t_2;
	elseif (y <= -1.45e-207)
		tmp = t_1 + ((y / z) * (x / b));
	elseif (y <= 2.05e-160)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif ((y <= 1.25e+75) || (~((y <= 8e+220)) && (y <= 3.3e+255)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -16.5], t$95$2, If[LessEqual[y, -1.45e-207], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-160], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 1.25e+75], And[N[Not[LessEqual[y, 8e+220]], $MachinePrecision], LessEqual[y, 3.3e+255]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -16.5 or 1.2500000000000001e75 < y < 8e220 or 3.29999999999999982e255 < y

   1. Initial program 57.2%

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

   2. Taylor expanded in y around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

   4. Simplified 65.2%

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

   if -16.5 < y < -1.45000000000000006e-207

   1. Initial program 80.4%

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

   2. Taylor expanded in z around -inf 69.2%

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

      1. +-commutative 69.2%

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

      2. associate--l+ 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in b around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. times-frac 76.9%

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

   7. Simplified 76.9%

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

   if -1.45000000000000006e-207 < y < 2.05000000000000001e-160

   1. Initial program 84.7%

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

   2. Taylor expanded in z around -inf 70.0%

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

      1. +-commutative 70.0%

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

      2. associate--l+ 70.0%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. times-frac 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in b around inf 80.5%

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

   if 2.05000000000000001e-160 < y < 1.2500000000000001e75 or 8e220 < y < 3.29999999999999982e255

   1. Initial program 65.3%

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

   2. Taylor expanded in z around inf 69.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16.5:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+75} \lor \neg \left(y \leq 8 \cdot 10^{+220}\right) \land y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 8: 56.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 23000000:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+220} \lor \neg \left(y \leq 3.3 \cdot 10^{+255}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5500.0)
     t_1
     (if (<= y 23000000.0)
       (/ (- (+ t (/ (* y x) z)) a) b)
       (if (<= y 6.4e+69)
         (/ (* z (- t a)) (+ y (* z (- b y))))
         (if (or (<= y 7.4e+220) (not (<= y 3.3e+255)))
           t_1
           (/ (- t a) (- b y))))))))

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 <= -5500.0) {
		tmp = t_1;
	} else if (y <= 23000000.0) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (y <= 6.4e+69) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if ((y <= 7.4e+220) || !(y <= 3.3e+255)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-5500.0d0)) then
        tmp = t_1
    else if (y <= 23000000.0d0) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (y <= 6.4d+69) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if ((y <= 7.4d+220) .or. (.not. (y <= 3.3d+255))) then
        tmp = t_1
    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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5500.0) {
		tmp = t_1;
	} else if (y <= 23000000.0) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (y <= 6.4e+69) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if ((y <= 7.4e+220) || !(y <= 3.3e+255)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -5500.0:
		tmp = t_1
	elif y <= 23000000.0:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif y <= 6.4e+69:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif (y <= 7.4e+220) or not (y <= 3.3e+255):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5500.0)
		tmp = t_1;
	elseif (y <= 23000000.0)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (y <= 6.4e+69)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif ((y <= 7.4e+220) || !(y <= 3.3e+255))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5500.0)
		tmp = t_1;
	elseif (y <= 23000000.0)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (y <= 6.4e+69)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif ((y <= 7.4e+220) || ~((y <= 3.3e+255)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	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, -5500.0], t$95$1, If[LessEqual[y, 23000000.0], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.4e+69], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.4e+220], N[Not[LessEqual[y, 3.3e+255]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5500 or 6.3999999999999997e69 < y < 7.4e220 or 3.29999999999999982e255 < y

   1. Initial program 56.7%

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

   2. Taylor expanded in y around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   4. Simplified 65.9%

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

   if -5500 < y < 2.3e7

   1. Initial program 80.2%

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

   2. Taylor expanded in z around -inf 69.9%

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

      1. +-commutative 69.9%

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

      2. associate--l+ 69.9%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in x around inf 78.5%

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

      1. times-frac 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in b around inf 73.2%

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

   if 2.3e7 < y < 6.3999999999999997e69

   1. Initial program 72.0%

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

   2. Taylor expanded in x around 0 62.5%

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

   if 7.4e220 < y < 3.29999999999999982e255

   1. Initial program 29.4%

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

   2. Taylor expanded in z around inf 86.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5500:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 23000000:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+220} \lor \neg \left(y \leq 3.3 \cdot 10^{+255}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -27.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+77}:\\ \;\;\;\;t_1 + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+220} \lor \neg \left(y \leq 3.3 \cdot 10^{+255}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -27.5)
     t_2
     (if (<= y 1.06e+77)
       (+ t_1 (/ (/ y (/ b x)) z))
       (if (or (<= y 8e+220) (not (<= y 3.3e+255))) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -27.5) {
		tmp = t_2;
	} else if (y <= 1.06e+77) {
		tmp = t_1 + ((y / (b / x)) / z);
	} else if ((y <= 8e+220) || !(y <= 3.3e+255)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-27.5d0)) then
        tmp = t_2
    else if (y <= 1.06d+77) then
        tmp = t_1 + ((y / (b / x)) / z)
    else if ((y <= 8d+220) .or. (.not. (y <= 3.3d+255))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -27.5) {
		tmp = t_2;
	} else if (y <= 1.06e+77) {
		tmp = t_1 + ((y / (b / x)) / z);
	} else if ((y <= 8e+220) || !(y <= 3.3e+255)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -27.5:
		tmp = t_2
	elif y <= 1.06e+77:
		tmp = t_1 + ((y / (b / x)) / z)
	elif (y <= 8e+220) or not (y <= 3.3e+255):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -27.5)
		tmp = t_2;
	elseif (y <= 1.06e+77)
		tmp = Float64(t_1 + Float64(Float64(y / Float64(b / x)) / z));
	elseif ((y <= 8e+220) || !(y <= 3.3e+255))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -27.5)
		tmp = t_2;
	elseif (y <= 1.06e+77)
		tmp = t_1 + ((y / (b / x)) / z);
	elseif ((y <= 8e+220) || ~((y <= 3.3e+255)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -27.5], t$95$2, If[LessEqual[y, 1.06e+77], N[(t$95$1 + N[(N[(y / N[(b / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8e+220], N[Not[LessEqual[y, 3.3e+255]], $MachinePrecision]], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -27.5 or 1.06000000000000003e77 < y < 8e220 or 3.29999999999999982e255 < y

   1. Initial program 57.2%

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

   2. Taylor expanded in y around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

   4. Simplified 65.2%

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

   if -27.5 < y < 1.06000000000000003e77

   1. Initial program 79.1%

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

   2. Taylor expanded in z around -inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate--l+ 68.9%

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

   4. Simplified 69.0%

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

   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. Step-by-step derivation

      1. times-frac 71.8%

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

   7. Simplified 71.8%

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

      1. associate-*r/ 75.2%

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

   9. Applied egg-rr 75.2%

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

   10. Taylor expanded in y around 0 74.8%

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

       1. associate-/l* 72.1%

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

   12. Simplified 72.1%

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

   if 8e220 < y < 3.29999999999999982e255

   1. Initial program 29.4%

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

   2. Taylor expanded in z around inf 86.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27.5:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+77}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b}{x}}}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+220} \lor \neg \left(y \leq 3.3 \cdot 10^{+255}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 58.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -460000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+74} \lor \neg \left(y \leq 7.9 \cdot 10^{+220}\right) \land y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -460000000.0)
     t_1
     (if (<= y 2.55e-160)
       (/ (- (+ t (/ (* y x) z)) a) b)
       (if (or (<= y 1.55e+74) (and (not (<= y 7.9e+220)) (<= y 3.3e+255)))
         (/ (- t a) (- b y))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -460000000.0) {
		tmp = t_1;
	} else if (y <= 2.55e-160) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if ((y <= 1.55e+74) || (!(y <= 7.9e+220) && (y <= 3.3e+255))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-460000000.0d0)) then
        tmp = t_1
    else if (y <= 2.55d-160) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if ((y <= 1.55d+74) .or. (.not. (y <= 7.9d+220)) .and. (y <= 3.3d+255)) then
        tmp = (t - a) / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -460000000.0) {
		tmp = t_1;
	} else if (y <= 2.55e-160) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if ((y <= 1.55e+74) || (!(y <= 7.9e+220) && (y <= 3.3e+255))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -460000000.0:
		tmp = t_1
	elif y <= 2.55e-160:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif (y <= 1.55e+74) or (not (y <= 7.9e+220) and (y <= 3.3e+255)):
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -460000000.0)
		tmp = t_1;
	elseif (y <= 2.55e-160)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif ((y <= 1.55e+74) || (!(y <= 7.9e+220) && (y <= 3.3e+255)))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -460000000.0)
		tmp = t_1;
	elseif (y <= 2.55e-160)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif ((y <= 1.55e+74) || (~((y <= 7.9e+220)) && (y <= 3.3e+255)))
		tmp = (t - a) / (b - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -460000000.0], t$95$1, If[LessEqual[y, 2.55e-160], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 1.55e+74], And[N[Not[LessEqual[y, 7.9e+220]], $MachinePrecision], LessEqual[y, 3.3e+255]]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6e8 or 1.55000000000000011e74 < y < 7.8999999999999996e220 or 3.29999999999999982e255 < y

   1. Initial program 56.7%

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

   2. Taylor expanded in y around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   4. Simplified 65.9%

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

   if -4.6e8 < y < 2.55e-160

   1. Initial program 83.0%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 69.0%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in x around inf 78.0%

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

      1. times-frac 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in b around inf 74.0%

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

   if 2.55e-160 < y < 1.55000000000000011e74 or 7.8999999999999996e220 < y < 3.29999999999999982e255

   1. Initial program 65.3%

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

   2. Taylor expanded in z around inf 69.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -460000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+74} \lor \neg \left(y \leq 7.9 \cdot 10^{+220}\right) \land y \leq 3.3 \cdot 10^{+255}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 64.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{\frac{z}{x}}}{b}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{-125}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.2e+195)
     t_1
     (if (<= z -4.7e+108)
       (/ (+ (- t a) (/ y (/ z x))) b)
       (if (or (<= z -4.2e-50) (not (<= z 1.7e-125)))
         t_1
         (+ x (/ t (/ 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 <= -2.2e+195) {
		tmp = t_1;
	} else if (z <= -4.7e+108) {
		tmp = ((t - a) + (y / (z / x))) / b;
	} else if ((z <= -4.2e-50) || !(z <= 1.7e-125)) {
		tmp = t_1;
	} else {
		tmp = x + (t / (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 <= (-2.2d+195)) then
        tmp = t_1
    else if (z <= (-4.7d+108)) then
        tmp = ((t - a) + (y / (z / x))) / b
    else if ((z <= (-4.2d-50)) .or. (.not. (z <= 1.7d-125))) then
        tmp = t_1
    else
        tmp = x + (t / (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 <= -2.2e+195) {
		tmp = t_1;
	} else if (z <= -4.7e+108) {
		tmp = ((t - a) + (y / (z / x))) / b;
	} else if ((z <= -4.2e-50) || !(z <= 1.7e-125)) {
		tmp = t_1;
	} else {
		tmp = x + (t / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.2e+195:
		tmp = t_1
	elif z <= -4.7e+108:
		tmp = ((t - a) + (y / (z / x))) / b
	elif (z <= -4.2e-50) or not (z <= 1.7e-125):
		tmp = t_1
	else:
		tmp = x + (t / (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 <= -2.2e+195)
		tmp = t_1;
	elseif (z <= -4.7e+108)
		tmp = Float64(Float64(Float64(t - a) + Float64(y / Float64(z / x))) / b);
	elseif ((z <= -4.2e-50) || !(z <= 1.7e-125))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t / Float64(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 <= -2.2e+195)
		tmp = t_1;
	elseif (z <= -4.7e+108)
		tmp = ((t - a) + (y / (z / x))) / b;
	elseif ((z <= -4.2e-50) || ~((z <= 1.7e-125)))
		tmp = t_1;
	else
		tmp = x + (t / (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, -2.2e+195], t$95$1, If[LessEqual[z, -4.7e+108], N[(N[(N[(t - a), $MachinePrecision] + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[z, -4.2e-50], N[Not[LessEqual[z, 1.7e-125]], $MachinePrecision]], t$95$1, N[(x + N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e195 or -4.6999999999999996e108 < z < -4.2000000000000002e-50 or 1.69999999999999988e-125 < z

   1. Initial program 61.2%

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

   2. Taylor expanded in z around inf 74.7%

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

   if -2.2e195 < z < -4.6999999999999996e108

   1. Initial program 35.2%

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

   2. Taylor expanded in z around -inf 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 80.4%

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

   5. Taylor expanded in x around inf 41.9%

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

      1. times-frac 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in b around inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. associate-/l* 67.5%

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

   10. Simplified 67.5%

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

   if -4.2000000000000002e-50 < z < 1.69999999999999988e-125

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 54.3%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+195}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{\frac{z}{x}}}{b}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{y}{z}}\\ \end{array} \]

Alternative 12: 36.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -0.0012 \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.1e+165)
   (/ t b)
   (if (<= z -3.8e+24)
     (/ (- x) z)
     (if (or (<= z -0.0012) (not (<= z 1.1e+28))) (/ (- a) b) (+ x (* z x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e+165) {
		tmp = t / b;
	} else if (z <= -3.8e+24) {
		tmp = -x / z;
	} else if ((z <= -0.0012) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.1d+165)) then
        tmp = t / b
    else if (z <= (-3.8d+24)) then
        tmp = -x / z
    else if ((z <= (-0.0012d0)) .or. (.not. (z <= 1.1d+28))) then
        tmp = -a / b
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e+165) {
		tmp = t / b;
	} else if (z <= -3.8e+24) {
		tmp = -x / z;
	} else if ((z <= -0.0012) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.1e+165:
		tmp = t / b
	elif z <= -3.8e+24:
		tmp = -x / z
	elif (z <= -0.0012) or not (z <= 1.1e+28):
		tmp = -a / b
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.1e+165)
		tmp = Float64(t / b);
	elseif (z <= -3.8e+24)
		tmp = Float64(Float64(-x) / z);
	elseif ((z <= -0.0012) || !(z <= 1.1e+28))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.1e+165)
		tmp = t / b;
	elseif (z <= -3.8e+24)
		tmp = -x / z;
	elseif ((z <= -0.0012) || ~((z <= 1.1e+28)))
		tmp = -a / b;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.1e+165], N[(t / b), $MachinePrecision], If[LessEqual[z, -3.8e+24], N[((-x) / z), $MachinePrecision], If[Or[LessEqual[z, -0.0012], N[Not[LessEqual[z, 1.1e+28]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1000000000000003e165

   1. Initial program 41.0%

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

   2. Taylor expanded in b around inf 37.0%

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

   3. Taylor expanded in t around inf 36.9%

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

   if -4.1000000000000003e165 < z < -3.80000000000000015e24

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

   4. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

      1. associate-*r/ 31.7%

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

      2. mul-1-neg 31.7%

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

   7. Simplified 31.7%

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

   if -3.80000000000000015e24 < z < -0.00119999999999999989 or 1.09999999999999993e28 < z

   1. Initial program 45.8%

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

   2. Taylor expanded in b around inf 33.8%

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

   3. Taylor expanded in a around inf 41.2%

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

      1. associate-*r/ 41.2%

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

      2. mul-1-neg 41.2%

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

   5. Simplified 41.2%

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

   if -0.00119999999999999989 < z < 1.09999999999999993e28

   1. Initial program 89.6%

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

   2. Taylor expanded in y around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in z around 0 50.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -0.0012 \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 13: 43.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -7600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+79} \lor \neg \left(z \leq 4.6 \cdot 10^{+186}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -7600000000000.0)
     t_1
     (if (<= z 5.8e-18)
       (+ x (* z x))
       (if (or (<= z 2.75e+79) (not (<= z 4.6e+186))) t_1 (/ (- a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -7600000000000.0) {
		tmp = t_1;
	} else if (z <= 5.8e-18) {
		tmp = x + (z * x);
	} else if ((z <= 2.75e+79) || !(z <= 4.6e+186)) {
		tmp = t_1;
	} else {
		tmp = -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) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-7600000000000.0d0)) then
        tmp = t_1
    else if (z <= 5.8d-18) then
        tmp = x + (z * x)
    else if ((z <= 2.75d+79) .or. (.not. (z <= 4.6d+186))) then
        tmp = t_1
    else
        tmp = -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 t_1 = t / (b - y);
	double tmp;
	if (z <= -7600000000000.0) {
		tmp = t_1;
	} else if (z <= 5.8e-18) {
		tmp = x + (z * x);
	} else if ((z <= 2.75e+79) || !(z <= 4.6e+186)) {
		tmp = t_1;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -7600000000000.0:
		tmp = t_1
	elif z <= 5.8e-18:
		tmp = x + (z * x)
	elif (z <= 2.75e+79) or not (z <= 4.6e+186):
		tmp = t_1
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -7600000000000.0)
		tmp = t_1;
	elseif (z <= 5.8e-18)
		tmp = Float64(x + Float64(z * x));
	elseif ((z <= 2.75e+79) || !(z <= 4.6e+186))
		tmp = t_1;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -7600000000000.0)
		tmp = t_1;
	elseif (z <= 5.8e-18)
		tmp = x + (z * x);
	elseif ((z <= 2.75e+79) || ~((z <= 4.6e+186)))
		tmp = t_1;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7600000000000.0], t$95$1, If[LessEqual[z, 5.8e-18], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.75e+79], N[Not[LessEqual[z, 4.6e+186]], $MachinePrecision]], t$95$1, N[((-a) / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6e12 or 5.8e-18 < z < 2.75000000000000003e79 or 4.60000000000000027e186 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in z around -inf 71.7%

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

      1. +-commutative 71.7%

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

      2. associate--l+ 71.7%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in x around inf 81.9%

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

      1. times-frac 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in t around inf 44.1%

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

   if -7.6e12 < z < 5.8e-18

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

   4. Simplified 51.2%

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

   5. Taylor expanded in z around 0 51.8%

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

   if 2.75000000000000003e79 < z < 4.60000000000000027e186

   1. Initial program 45.6%

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

   2. Taylor expanded in b around inf 30.2%

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

   3. Taylor expanded in a around inf 42.2%

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

      1. associate-*r/ 42.2%

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

      2. mul-1-neg 42.2%

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

   5. Simplified 42.2%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600000000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+79} \lor \neg \left(z \leq 4.6 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 35.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-40} \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e+161)
   (/ t b)
   (if (<= z -2.6e+23)
     (/ (- x) z)
     (if (or (<= z -9.6e-40) (not (<= z 1.1e+28))) (/ (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+161) {
		tmp = t / b;
	} else if (z <= -2.6e+23) {
		tmp = -x / z;
	} else if ((z <= -9.6e-40) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.5d+161)) then
        tmp = t / b
    else if (z <= (-2.6d+23)) then
        tmp = -x / z
    else if ((z <= (-9.6d-40)) .or. (.not. (z <= 1.1d+28))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+161) {
		tmp = t / b;
	} else if (z <= -2.6e+23) {
		tmp = -x / z;
	} else if ((z <= -9.6e-40) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e+161:
		tmp = t / b
	elif z <= -2.6e+23:
		tmp = -x / z
	elif (z <= -9.6e-40) or not (z <= 1.1e+28):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e+161)
		tmp = Float64(t / b);
	elseif (z <= -2.6e+23)
		tmp = Float64(Float64(-x) / z);
	elseif ((z <= -9.6e-40) || !(z <= 1.1e+28))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e+161)
		tmp = t / b;
	elseif (z <= -2.6e+23)
		tmp = -x / z;
	elseif ((z <= -9.6e-40) || ~((z <= 1.1e+28)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e+161], N[(t / b), $MachinePrecision], If[LessEqual[z, -2.6e+23], N[((-x) / z), $MachinePrecision], If[Or[LessEqual[z, -9.6e-40], N[Not[LessEqual[z, 1.1e+28]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e161

   1. Initial program 41.0%

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

   2. Taylor expanded in b around inf 37.0%

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

   3. Taylor expanded in t around inf 36.9%

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

   if -6.5e161 < z < -2.59999999999999992e23

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

   4. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

      1. associate-*r/ 31.7%

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

      2. mul-1-neg 31.7%

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

   7. Simplified 31.7%

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

   if -2.59999999999999992e23 < z < -9.59999999999999965e-40 or 1.09999999999999993e28 < z

   1. Initial program 53.0%

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

   2. Taylor expanded in b around inf 36.6%

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

   3. Taylor expanded in a around inf 39.7%

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

      1. associate-*r/ 39.7%

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

      2. mul-1-neg 39.7%

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

   5. Simplified 39.7%

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

   if -9.59999999999999965e-40 < z < 1.09999999999999993e28

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 51.8%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-40} \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 66.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-50) (not (<= z 1.7e-125)))
   (/ (- t a) (- b y))
   (+ x (/ t (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-50) || !(z <= 1.7e-125)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t / (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 <= (-4.8d-50)) .or. (.not. (z <= 1.7d-125))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (t / (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 <= -4.8e-50) || !(z <= 1.7e-125)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-50) or not (z <= 1.7e-125):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (t / (y / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-50) || !(z <= 1.7e-125))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(t / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e-50) || ~((z <= 1.7e-125)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (t / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-50], N[Not[LessEqual[z, 1.7e-125]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000004e-50 or 1.69999999999999988e-125 < z

   1. Initial program 58.8%

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

   2. Taylor expanded in z around inf 71.2%

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

   if -4.80000000000000004e-50 < z < 1.69999999999999988e-125

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 54.3%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{y}{z}}\\ \end{array} \]

Alternative 16: 53.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -115000000 \lor \neg \left(y \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -115000000.0) (not (<= y 4.5e+38)))
   (/ 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 <= -115000000.0) || !(y <= 4.5e+38)) {
		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 <= (-115000000.0d0)) .or. (.not. (y <= 4.5d+38))) 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 <= -115000000.0) || !(y <= 4.5e+38)) {
		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 <= -115000000.0) or not (y <= 4.5e+38):
		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 <= -115000000.0) || !(y <= 4.5e+38))
		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 <= -115000000.0) || ~((y <= 4.5e+38)))
		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, -115000000.0], N[Not[LessEqual[y, 4.5e+38]], $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 < -1.15e8 or 4.4999999999999998e38 < y

   1. Initial program 56.8%

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

   2. Taylor expanded in y around inf 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

   4. Simplified 59.8%

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

   if -1.15e8 < y < 4.4999999999999998e38

   1. Initial program 79.3%

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

   2. Taylor expanded in y around 0 61.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -115000000 \lor \neg \left(y \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 17: 35.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-40} \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.2e-40) (not (<= z 1.1e+28))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e-40) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.2d-40)) .or. (.not. (z <= 1.1d+28))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e-40) || !(z <= 1.1e+28)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.2e-40) or not (z <= 1.1e+28):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.2e-40) || !(z <= 1.1e+28))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.2e-40) || ~((z <= 1.1e+28)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.2e-40], N[Not[LessEqual[z, 1.1e+28]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e-40 or 1.09999999999999993e28 < z

   1. Initial program 52.3%

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

   2. Taylor expanded in b around inf 34.0%

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

   3. Taylor expanded in a around inf 33.9%

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

      1. associate-*r/ 33.9%

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

      2. mul-1-neg 33.9%

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

   5. Simplified 33.9%

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

   if -9.2e-40 < z < 1.09999999999999993e28

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 51.8%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-40} \lor \neg \left(z \leq 1.1 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 37.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.2e-17) (/ t b) (if (<= z 3.5e-18) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.2e-17) {
		tmp = t / b;
	} else if (z <= 3.5e-18) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.2d-17)) then
        tmp = t / b
    else if (z <= 3.5d-18) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.2e-17) {
		tmp = t / b;
	} else if (z <= 3.5e-18) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.2e-17:
		tmp = t / b
	elif z <= 3.5e-18:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.2e-17)
		tmp = Float64(t / b);
	elseif (z <= 3.5e-18)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.2e-17)
		tmp = t / b;
	elseif (z <= 3.5e-18)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.2e-17], N[(t / b), $MachinePrecision], If[LessEqual[z, 3.5e-18], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000001e-17 or 3.4999999999999999e-18 < z

   1. Initial program 52.7%

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

   2. Taylor expanded in b around inf 33.8%

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

   3. Taylor expanded in t around inf 26.4%

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

   if -8.2000000000000001e-17 < z < 3.4999999999999999e-18

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 52.9%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 19: 25.1% 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 69.4%

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

2. Taylor expanded in z around 0 27.1%

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

3. Final simplification 27.1%

   \[\leadsto x \]

Developer target: 73.6% 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 2023192 
(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)))))