Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.2% → 90.0%

Time: 16.9s

Alternatives: 18

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3800000000000 \lor \neg \left(z \leq 1.45 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}} - \left(\frac{y}{z} \cdot \frac{x}{y - b} + \frac{t - a}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3800000000000.0) (not (<= z 1.45e+31)))
     (-
      (* y (/ (- a t) (* z (pow (- b y) 2.0))))
      (+ (* (/ y z) (/ x (- y b))) (/ (- t a) (- y b))))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3800000000000.0) || !(z <= 1.45e+31)) {
		tmp = (y * ((a - t) / (z * pow((b - y), 2.0)))) - (((y / z) * (x / (y - b))) + ((t - a) / (y - b)));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-3800000000000.0d0)) .or. (.not. (z <= 1.45d+31))) then
        tmp = (y * ((a - t) / (z * ((b - y) ** 2.0d0)))) - (((y / z) * (x / (y - b))) + ((t - a) / (y - b)))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3800000000000.0) || !(z <= 1.45e+31)) {
		tmp = (y * ((a - t) / (z * Math.pow((b - y), 2.0)))) - (((y / z) * (x / (y - b))) + ((t - a) / (y - b)));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -3800000000000.0) or not (z <= 1.45e+31):
		tmp = (y * ((a - t) / (z * math.pow((b - y), 2.0)))) - (((y / z) * (x / (y - b))) + ((t - a) / (y - b)))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -3800000000000.0) || !(z <= 1.45e+31))
		tmp = Float64(Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))) - Float64(Float64(Float64(y / z) * Float64(x / Float64(y - b))) + Float64(Float64(t - a) / Float64(y - b))));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -3800000000000.0) || ~((z <= 1.45e+31)))
		tmp = (y * ((a - t) / (z * ((b - y) ^ 2.0)))) - (((y / z) * (x / (y - b))) + ((t - a) / (y - b)));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3800000000000.0], N[Not[LessEqual[z, 1.45e+31]], $MachinePrecision]], N[(N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e12 or 1.45e31 < z

   1. Initial program 37.7%

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

   3. Taylor expanded in z around inf 61.7%

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

      1. associate--r+ 61.7%

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

      2. +-commutative 61.7%

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

      3. associate--l+ 61.7%

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

      4. *-commutative 61.7%

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

      5. times-frac 69.0%

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

      6. div-sub 69.0%

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

      7. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

   if -3.8e12 < z < 1.45e31

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 94.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3800000000000 \lor \neg \left(z \leq 1.45 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}} - \left(\frac{y}{z} \cdot \frac{x}{y - b} + \frac{t - a}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{z}{y} \cdot \frac{a - t}{z + -1}\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-93}:\\ \;\;\;\;\left(\frac{t}{b} + \frac{y \cdot x}{z \cdot b}\right) - \frac{a}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (* (/ z y) (/ (- a t) (+ z -1.0))))))
   (if (<= y -1.42e-98)
     t_1
     (if (<= y 7.6e-93)
       (- (+ (/ t b) (/ (* y x) (* z b))) (/ a b))
       (if (<= y 1.15e+42)
         (/ (+ (* y x) (* z t)) (+ y (* z (- b y))))
         (if (<= y 1.7e+108) (/ (- 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)) + ((z / y) * ((a - t) / (z + -1.0)));
	double tmp;
	if (y <= -1.42e-98) {
		tmp = t_1;
	} else if (y <= 7.6e-93) {
		tmp = ((t / b) + ((y * x) / (z * b))) - (a / b);
	} else if (y <= 1.15e+42) {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 1.7e+108) {
		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)) + ((z / y) * ((a - t) / (z + (-1.0d0))))
    if (y <= (-1.42d-98)) then
        tmp = t_1
    else if (y <= 7.6d-93) then
        tmp = ((t / b) + ((y * x) / (z * b))) - (a / b)
    else if (y <= 1.15d+42) then
        tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
    else if (y <= 1.7d+108) 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)) + ((z / y) * ((a - t) / (z + -1.0)));
	double tmp;
	if (y <= -1.42e-98) {
		tmp = t_1;
	} else if (y <= 7.6e-93) {
		tmp = ((t / b) + ((y * x) / (z * b))) - (a / b);
	} else if (y <= 1.15e+42) {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 1.7e+108) {
		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)) + ((z / y) * ((a - t) / (z + -1.0)))
	tmp = 0
	if y <= -1.42e-98:
		tmp = t_1
	elif y <= 7.6e-93:
		tmp = ((t / b) + ((y * x) / (z * b))) - (a / b)
	elif y <= 1.15e+42:
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
	elif y <= 1.7e+108:
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(z / y) * Float64(Float64(a - t) / Float64(z + -1.0))))
	tmp = 0.0
	if (y <= -1.42e-98)
		tmp = t_1;
	elseif (y <= 7.6e-93)
		tmp = Float64(Float64(Float64(t / b) + Float64(Float64(y * x) / Float64(z * b))) - Float64(a / b));
	elseif (y <= 1.15e+42)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 1.7e+108)
		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)) + ((z / y) * ((a - t) / (z + -1.0)));
	tmp = 0.0;
	if (y <= -1.42e-98)
		tmp = t_1;
	elseif (y <= 7.6e-93)
		tmp = ((t / b) + ((y * x) / (z * b))) - (a / b);
	elseif (y <= 1.15e+42)
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	elseif (y <= 1.7e+108)
		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[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(z / y), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e-98], t$95$1, If[LessEqual[y, 7.6e-93], N[(N[(N[(t / b), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+42], 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, 1.7e+108], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.41999999999999999e-98 or 1.69999999999999998e108 < y

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. mul-1-neg 11.3%

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

      2. unsub-neg 11.3%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in x around 0 67.8%

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

      1. times-frac 85.4%

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

   8. Simplified 85.4%

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

   if -1.41999999999999999e-98 < y < 7.5999999999999998e-93

   1. Initial program 82.9%

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

   3. Taylor expanded in x around inf 72.0%

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

   4. Taylor expanded in b around inf 66.2%

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

      1. associate-/l* 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in x around 0 83.1%

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

   if 7.5999999999999998e-93 < y < 1.15e42

   1. Initial program 82.9%

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

   3. Taylor expanded in a around 0 78.7%

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

   if 1.15e42 < y < 1.69999999999999998e108

   1. Initial program 32.6%

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

   3. Taylor expanded in z around inf 70.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \frac{a - t}{z + -1}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-93}:\\ \;\;\;\;\left(\frac{t}{b} + \frac{y \cdot x}{z \cdot b}\right) - \frac{a}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \frac{a - t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+23} \lor \neg \left(z \leq 4.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3e+23) (not (<= z 4.5e+40)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3e+23) || !(z <= 4.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-3d+23)) .or. (.not. (z <= 4.5d+40))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3e+23) || !(z <= 4.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -3e+23) or not (z <= 4.5e+40):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -3e+23) || !(z <= 4.5e+40))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -3e+23) || ~((z <= 4.5e+40)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3e+23], N[Not[LessEqual[z, 4.5e+40]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e23 or 4.50000000000000032e40 < z

   1. Initial program 37.9%

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

   3. Taylor expanded in z around inf 81.5%

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

   if -3.0000000000000001e23 < z < 4.50000000000000032e40

   1. Initial program 89.9%

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

   3. Taylor expanded in x around inf 92.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+23} \lor \neg \left(z \leq 4.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.0085:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-280}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} + \left(x - \frac{a}{y}\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-188}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.0085)
     t_1
     (if (<= z -8.4e-280)
       (+ x (* z (+ (/ t y) (- x (/ a y)))))
       (if (<= z 5e-188)
         (/ (* y x) (+ y (* z (- b y))))
         (if (<= z 3.6e-18) (/ (+ (* z (- t a)) (* y x)) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.0085) {
		tmp = t_1;
	} else if (z <= -8.4e-280) {
		tmp = x + (z * ((t / y) + (x - (a / y))));
	} else if (z <= 5e-188) {
		tmp = (y * x) / (y + (z * (b - y)));
	} else if (z <= 3.6e-18) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.0085d0)) then
        tmp = t_1
    else if (z <= (-8.4d-280)) then
        tmp = x + (z * ((t / y) + (x - (a / y))))
    else if (z <= 5d-188) then
        tmp = (y * x) / (y + (z * (b - y)))
    else if (z <= 3.6d-18) then
        tmp = ((z * (t - a)) + (y * x)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.0085) {
		tmp = t_1;
	} else if (z <= -8.4e-280) {
		tmp = x + (z * ((t / y) + (x - (a / y))));
	} else if (z <= 5e-188) {
		tmp = (y * x) / (y + (z * (b - y)));
	} else if (z <= 3.6e-18) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.0085:
		tmp = t_1
	elif z <= -8.4e-280:
		tmp = x + (z * ((t / y) + (x - (a / y))))
	elif z <= 5e-188:
		tmp = (y * x) / (y + (z * (b - y)))
	elif z <= 3.6e-18:
		tmp = ((z * (t - a)) + (y * x)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.0085)
		tmp = t_1;
	elseif (z <= -8.4e-280)
		tmp = Float64(x + Float64(z * Float64(Float64(t / y) + Float64(x - Float64(a / y)))));
	elseif (z <= 5e-188)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 3.6e-18)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.0085)
		tmp = t_1;
	elseif (z <= -8.4e-280)
		tmp = x + (z * ((t / y) + (x - (a / y))));
	elseif (z <= 5e-188)
		tmp = (y * x) / (y + (z * (b - y)));
	elseif (z <= 3.6e-18)
		tmp = ((z * (t - a)) + (y * x)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0085], t$95$1, If[LessEqual[z, -8.4e-280], N[(x + N[(z * N[(N[(t / y), $MachinePrecision] + N[(x - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-188], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-18], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0085000000000000006 or 3.6000000000000001e-18 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in z around inf 76.1%

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

   if -0.0085000000000000006 < z < -8.40000000000000003e-280

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in z around 0 69.6%

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

   if -8.40000000000000003e-280 < z < 5.0000000000000001e-188

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 82.8%

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

      1. *-commutative 60.4%

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

   5. Simplified 82.8%

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

   if 5.0000000000000001e-188 < z < 3.6000000000000001e-18

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 71.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0085:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-280}:\\ \;\;\;\;x + z \cdot \left(\frac{t}{y} + \left(x - \frac{a}{y}\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-188}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -4.2e+52)
     t_1
     (if (<= y -1.2e-12)
       (/ (- a t) y)
       (if (<= y -1.9e-94)
         t_1
         (if (<= y 5.5e-89)
           (/ (- t a) b)
           (if (<= y 6.2) (/ t (- 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 <= -4.2e+52) {
		tmp = t_1;
	} else if (y <= -1.2e-12) {
		tmp = (a - t) / y;
	} else if (y <= -1.9e-94) {
		tmp = t_1;
	} else if (y <= 5.5e-89) {
		tmp = (t - a) / b;
	} else if (y <= 6.2) {
		tmp = t / (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 <= (-4.2d+52)) then
        tmp = t_1
    else if (y <= (-1.2d-12)) then
        tmp = (a - t) / y
    else if (y <= (-1.9d-94)) then
        tmp = t_1
    else if (y <= 5.5d-89) then
        tmp = (t - a) / b
    else if (y <= 6.2d0) then
        tmp = t / (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 <= -4.2e+52) {
		tmp = t_1;
	} else if (y <= -1.2e-12) {
		tmp = (a - t) / y;
	} else if (y <= -1.9e-94) {
		tmp = t_1;
	} else if (y <= 5.5e-89) {
		tmp = (t - a) / b;
	} else if (y <= 6.2) {
		tmp = t / (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 <= -4.2e+52:
		tmp = t_1
	elif y <= -1.2e-12:
		tmp = (a - t) / y
	elif y <= -1.9e-94:
		tmp = t_1
	elif y <= 5.5e-89:
		tmp = (t - a) / b
	elif y <= 6.2:
		tmp = t / (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 <= -4.2e+52)
		tmp = t_1;
	elseif (y <= -1.2e-12)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= -1.9e-94)
		tmp = t_1;
	elseif (y <= 5.5e-89)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 6.2)
		tmp = Float64(t / 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 <= -4.2e+52)
		tmp = t_1;
	elseif (y <= -1.2e-12)
		tmp = (a - t) / y;
	elseif (y <= -1.9e-94)
		tmp = t_1;
	elseif (y <= 5.5e-89)
		tmp = (t - a) / b;
	elseif (y <= 6.2)
		tmp = t / (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, -4.2e+52], t$95$1, If[LessEqual[y, -1.2e-12], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.9e-94], t$95$1, If[LessEqual[y, 5.5e-89], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.2], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e52 or -1.19999999999999994e-12 < y < -1.9e-94 or 6.20000000000000018 < y

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

   5. Simplified 58.1%

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

   if -4.2e52 < y < -1.19999999999999994e-12

   1. Initial program 54.5%

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

   3. Taylor expanded in y around inf 36.9%

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

      1. mul-1-neg 10.7%

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

      2. unsub-neg 10.7%

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

   5. Simplified 36.9%

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

   6. Taylor expanded in z around inf 54.8%

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

      1. mul-1-neg 54.8%

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

   8. Simplified 54.8%

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

   if -1.9e-94 < y < 5.50000000000000012e-89

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0 71.8%

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

   if 5.50000000000000012e-89 < y < 6.20000000000000018

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 43.6%

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

      1. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in z around inf 42.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+25} \lor \neg \left(z \leq 2.9 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e+25) (not (<= z 2.9e+28)))
   (/ (- 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 <= -3.2e+25) || !(z <= 2.9e+28)) {
		tmp = (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 <= (-3.2d+25)) .or. (.not. (z <= 2.9d+28))) then
        tmp = (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 <= -3.2e+25) || !(z <= 2.9e+28)) {
		tmp = (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 <= -3.2e+25) or not (z <= 2.9e+28):
		tmp = (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 <= -3.2e+25) || !(z <= 2.9e+28))
		tmp = 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 <= -3.2e+25) || ~((z <= 2.9e+28)))
		tmp = (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, -3.2e+25], N[Not[LessEqual[z, 2.9e+28]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999999e25 or 2.9000000000000001e28 < z

   1. Initial program 39.4%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -3.1999999999999999e25 < z < 2.9000000000000001e28

   1. Initial program 90.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+25} \lor \neg \left(z \leq 2.9 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.066:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+210} \lor \neg \left(z \leq 1.35 \cdot 10^{+264}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.05e-14)
     t_1
     (if (<= z 0.066)
       (+ x (* z x))
       (if (or (<= z 4.9e+210) (not (<= z 1.35e+264))) 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 <= -1.05e-14) {
		tmp = t_1;
	} else if (z <= 0.066) {
		tmp = x + (z * x);
	} else if ((z <= 4.9e+210) || !(z <= 1.35e+264)) {
		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 <= (-1.05d-14)) then
        tmp = t_1
    else if (z <= 0.066d0) then
        tmp = x + (z * x)
    else if ((z <= 4.9d+210) .or. (.not. (z <= 1.35d+264))) 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 <= -1.05e-14) {
		tmp = t_1;
	} else if (z <= 0.066) {
		tmp = x + (z * x);
	} else if ((z <= 4.9e+210) || !(z <= 1.35e+264)) {
		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 <= -1.05e-14:
		tmp = t_1
	elif z <= 0.066:
		tmp = x + (z * x)
	elif (z <= 4.9e+210) or not (z <= 1.35e+264):
		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 <= -1.05e-14)
		tmp = t_1;
	elseif (z <= 0.066)
		tmp = Float64(x + Float64(z * x));
	elseif ((z <= 4.9e+210) || !(z <= 1.35e+264))
		tmp = t_1;
	else
		tmp = Float64(a / Float64(-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 <= -1.05e-14)
		tmp = t_1;
	elseif (z <= 0.066)
		tmp = x + (z * x);
	elseif ((z <= 4.9e+210) || ~((z <= 1.35e+264)))
		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, -1.05e-14], t$95$1, If[LessEqual[z, 0.066], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.9e+210], N[Not[LessEqual[z, 1.35e+264]], $MachinePrecision]], t$95$1, N[(a / (-b)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e-14 or 0.066000000000000003 < z < 4.90000000000000007e210 or 1.3500000000000001e264 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in t around inf 25.3%

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

      1. *-commutative 25.3%

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

   5. Simplified 25.3%

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

   6. Taylor expanded in z around inf 43.7%

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

   if -1.0499999999999999e-14 < z < 0.066000000000000003

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. mul-1-neg 15.5%

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

      2. unsub-neg 15.5%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in z around 0 57.6%

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

   if 4.90000000000000007e210 < z < 1.3500000000000001e264

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 16.7%

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

   4. Taylor expanded in b around inf 55.0%

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

      1. associate-/l* 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in a around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

   9. Simplified 68.4%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 0.066:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+210} \lor \neg \left(z \leq 1.35 \cdot 10^{+264}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+23} \lor \neg \left(z \leq 2.25 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.08e+23) (not (<= z 2.25e+16)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.08e+23) || !(z <= 2.25e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.08d+23)) .or. (.not. (z <= 2.25d+16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.08e+23) || !(z <= 2.25e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.08e+23) or not (z <= 2.25e+16):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.08e+23) || !(z <= 2.25e+16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.08e+23) || ~((z <= 2.25e+16)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.08e+23], N[Not[LessEqual[z, 2.25e+16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0800000000000001e23 or 2.25e16 < z

   1. Initial program 39.4%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -1.0800000000000001e23 < z < 2.25e16

   1. Initial program 90.9%

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

   3. Taylor expanded in a around 0 81.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+23} \lor \neg \left(z \leq 2.25 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20 \lor \neg \left(z \leq 4.8 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -20.0) (not (<= z 4.8e-18)))
   (/ (- t a) (- b y))
   (/ (* 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 <= -20.0) || !(z <= 4.8e-18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (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 <= (-20.0d0)) .or. (.not. (z <= 4.8d-18))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (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 <= -20.0) || !(z <= 4.8e-18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (y * x) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -20.0) or not (z <= 4.8e-18):
		tmp = (t - a) / (b - y)
	else:
		tmp = (y * x) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -20.0) || !(z <= 4.8e-18))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(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 <= -20.0) || ~((z <= 4.8e-18)))
		tmp = (t - a) / (b - y);
	else
		tmp = (y * x) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -20.0], N[Not[LessEqual[z, 4.8e-18]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -20 or 4.79999999999999988e-18 < z

   1. Initial program 44.1%

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

   3. Taylor expanded in z around inf 76.6%

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

   if -20 < z < 4.79999999999999988e-18

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 52.2%

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

   5. Simplified 64.6%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20 \lor \neg \left(z \leq 4.8 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{-14} \lor \neg \left(z \leq 2.1 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.14e-14) (not (<= z 2.1e-18)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.14e-14) || !(z <= 2.1e-18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.14d-14)) .or. (.not. (z <= 2.1d-18))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.14e-14) || !(z <= 2.1e-18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.14e-14) or not (z <= 2.1e-18):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.14e-14) || !(z <= 2.1e-18))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.14e-14) || ~((z <= 2.1e-18)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.14e-14], N[Not[LessEqual[z, 2.1e-18]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1400000000000001e-14 or 2.1e-18 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in z around inf 74.1%

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

   if -1.1400000000000001e-14 < z < 2.1e-18

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 68.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{-14} \lor \neg \left(z \leq 2.1 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+90)
   (/ t (- y))
   (if (<= z -1.22e-14)
     (/ t b)
     (if (<= z 440000000.0) (+ x (* z x)) (/ a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.6e+90) {
		tmp = t / -y;
	} else if (z <= -1.22e-14) {
		tmp = t / b;
	} else if (z <= 440000000.0) {
		tmp = x + (z * x);
	} 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) :: tmp
    if (z <= (-3.6d+90)) then
        tmp = t / -y
    else if (z <= (-1.22d-14)) then
        tmp = t / b
    else if (z <= 440000000.0d0) then
        tmp = x + (z * x)
    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 tmp;
	if (z <= -3.6e+90) {
		tmp = t / -y;
	} else if (z <= -1.22e-14) {
		tmp = t / b;
	} else if (z <= 440000000.0) {
		tmp = x + (z * x);
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.6e+90:
		tmp = t / -y
	elif z <= -1.22e-14:
		tmp = t / b
	elif z <= 440000000.0:
		tmp = x + (z * x)
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.6e+90)
		tmp = Float64(t / Float64(-y));
	elseif (z <= -1.22e-14)
		tmp = Float64(t / b);
	elseif (z <= 440000000.0)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.6e+90)
		tmp = t / -y;
	elseif (z <= -1.22e-14)
		tmp = t / b;
	elseif (z <= 440000000.0)
		tmp = x + (z * x);
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.6e+90], N[(t / (-y)), $MachinePrecision], If[LessEqual[z, -1.22e-14], N[(t / b), $MachinePrecision], If[LessEqual[z, 440000000.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(a / (-b)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e90

   1. Initial program 27.8%

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

   3. Taylor expanded in t around inf 16.9%

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

      1. *-commutative 16.9%

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

   5. Simplified 16.9%

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

   6. Taylor expanded in y around inf 13.5%

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

      1. mul-1-neg 13.5%

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

      2. unsub-neg 13.5%

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

   8. Simplified 13.5%

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

   9. Taylor expanded in z around inf 30.6%

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

       1. associate-*r/ 30.6%

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

       2. neg-mul-1 30.6%

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

   11. Simplified 30.6%

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

   if -3.6e90 < z < -1.21999999999999994e-14

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf 38.2%

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

      1. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 38.0%

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

   if -1.21999999999999994e-14 < z < 4.4e8

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 15.4%

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

      2. unsub-neg 15.4%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in x around inf 50.7%

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

      1. *-commutative 50.7%

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

   8. Simplified 50.7%

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

   9. Taylor expanded in z around 0 57.1%

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

   if 4.4e8 < z

   1. Initial program 50.8%

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

   3. Taylor expanded in x around inf 44.4%

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

   4. Taylor expanded in b around inf 46.3%

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

      1. associate-/l* 43.6%

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

   6. Simplified 43.6%

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

   7. Taylor expanded in a around inf 35.3%

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

      1. associate-*r/ 35.3%

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

      2. neg-mul-1 35.3%

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

   9. Simplified 35.3%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.8:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.45e-94)
     t_1
     (if (<= y 4.8e-89) (/ (- t a) b) (if (<= y 6.8) (/ t (- 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 <= -1.45e-94) {
		tmp = t_1;
	} else if (y <= 4.8e-89) {
		tmp = (t - a) / b;
	} else if (y <= 6.8) {
		tmp = t / (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 <= (-1.45d-94)) then
        tmp = t_1
    else if (y <= 4.8d-89) then
        tmp = (t - a) / b
    else if (y <= 6.8d0) then
        tmp = t / (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 <= -1.45e-94) {
		tmp = t_1;
	} else if (y <= 4.8e-89) {
		tmp = (t - a) / b;
	} else if (y <= 6.8) {
		tmp = t / (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 <= -1.45e-94:
		tmp = t_1
	elif y <= 4.8e-89:
		tmp = (t - a) / b
	elif y <= 6.8:
		tmp = t / (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 <= -1.45e-94)
		tmp = t_1;
	elseif (y <= 4.8e-89)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 6.8)
		tmp = Float64(t / 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 <= -1.45e-94)
		tmp = t_1;
	elseif (y <= 4.8e-89)
		tmp = (t - a) / b;
	elseif (y <= 6.8)
		tmp = t / (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, -1.45e-94], t$95$1, If[LessEqual[y, 4.8e-89], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.8], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999998e-94 or 6.79999999999999982 < y

   1. Initial program 57.1%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   if -1.44999999999999998e-94 < y < 4.80000000000000032e-89

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0 71.8%

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

   if 4.80000000000000032e-89 < y < 6.79999999999999982

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 43.6%

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

      1. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in z around inf 42.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.8:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -6e+121)
     t_1
     (if (<= z -1e-14) (/ t b) (if (<= z 1.4e-17) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -6e+121) {
		tmp = t_1;
	} else if (z <= -1e-14) {
		tmp = t / b;
	} else if (z <= 1.4e-17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-6d+121)) then
        tmp = t_1
    else if (z <= (-1d-14)) then
        tmp = t / b
    else if (z <= 1.4d-17) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -6e+121) {
		tmp = t_1;
	} else if (z <= -1e-14) {
		tmp = t / b;
	} else if (z <= 1.4e-17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -6e+121:
		tmp = t_1
	elif z <= -1e-14:
		tmp = t / b
	elif z <= 1.4e-17:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -6e+121)
		tmp = t_1;
	elseif (z <= -1e-14)
		tmp = Float64(t / b);
	elseif (z <= 1.4e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -6e+121)
		tmp = t_1;
	elseif (z <= -1e-14)
		tmp = t / b;
	elseif (z <= 1.4e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -6e+121], t$95$1, If[LessEqual[z, -1e-14], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.4e-17], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000005e121 or 1.3999999999999999e-17 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in x around inf 40.0%

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

   4. Taylor expanded in b around inf 37.4%

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

      1. associate-/l* 34.2%

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

   6. Simplified 34.2%

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

   7. Taylor expanded in a around inf 31.9%

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

      1. associate-*r/ 31.9%

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

      2. neg-mul-1 31.9%

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

   9. Simplified 31.9%

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

   if -6.0000000000000005e121 < z < -9.99999999999999999e-15

   1. Initial program 55.1%

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

   3. Taylor expanded in t around inf 33.7%

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

      1. *-commutative 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in y around 0 30.5%

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

   if -9.99999999999999999e-15 < z < 1.3999999999999999e-17

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 59.8%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+121}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq -9.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.1e+91)
   (/ t (- y))
   (if (<= z -9.7e-14) (/ t b) (if (<= z 3.4e-17) x (/ a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e+91) {
		tmp = t / -y;
	} else if (z <= -9.7e-14) {
		tmp = t / b;
	} else if (z <= 3.4e-17) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-2.1d+91)) then
        tmp = t / -y
    else if (z <= (-9.7d-14)) then
        tmp = t / b
    else if (z <= 3.4d-17) then
        tmp = x
    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 tmp;
	if (z <= -2.1e+91) {
		tmp = t / -y;
	} else if (z <= -9.7e-14) {
		tmp = t / b;
	} else if (z <= 3.4e-17) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.1e+91:
		tmp = t / -y
	elif z <= -9.7e-14:
		tmp = t / b
	elif z <= 3.4e-17:
		tmp = x
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.1e+91)
		tmp = Float64(t / Float64(-y));
	elseif (z <= -9.7e-14)
		tmp = Float64(t / b);
	elseif (z <= 3.4e-17)
		tmp = x;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.1e+91)
		tmp = t / -y;
	elseif (z <= -9.7e-14)
		tmp = t / b;
	elseif (z <= 3.4e-17)
		tmp = x;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.1e+91], N[(t / (-y)), $MachinePrecision], If[LessEqual[z, -9.7e-14], N[(t / b), $MachinePrecision], If[LessEqual[z, 3.4e-17], x, N[(a / (-b)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000008e91

   1. Initial program 27.8%

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

   3. Taylor expanded in t around inf 16.9%

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

      1. *-commutative 16.9%

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

   5. Simplified 16.9%

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

   6. Taylor expanded in y around inf 13.5%

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

      1. mul-1-neg 13.5%

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

      2. unsub-neg 13.5%

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

   8. Simplified 13.5%

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

   9. Taylor expanded in z around inf 30.6%

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

       1. associate-*r/ 30.6%

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

       2. neg-mul-1 30.6%

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

   11. Simplified 30.6%

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

   if -2.10000000000000008e91 < z < -9.70000000000000032e-14

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf 38.2%

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

      1. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 38.0%

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

   if -9.70000000000000032e-14 < z < 3.3999999999999998e-17

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 59.8%

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

   if 3.3999999999999998e-17 < z

   1. Initial program 55.1%

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

   3. Taylor expanded in x around inf 50.9%

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

   4. Taylor expanded in b around inf 44.1%

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

      1. associate-/l* 41.7%

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

   6. Simplified 41.7%

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

   7. Taylor expanded in a around inf 32.8%

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

      1. associate-*r/ 32.8%

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

      2. neg-mul-1 32.8%

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

   9. Simplified 32.8%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq -9.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -64 \lor \neg \left(z \leq 200\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -64.0) (not (<= z 200.0))) (/ (- t a) (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -64.0) || !(z <= 200.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-64.0d0)) .or. (.not. (z <= 200.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -64.0) || !(z <= 200.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -64.0) or not (z <= 200.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -64.0) || !(z <= 200.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -64.0) || ~((z <= 200.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -64.0], N[Not[LessEqual[z, 200.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -64 or 200 < z

   1. Initial program 41.8%

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

   3. Taylor expanded in z around inf 79.1%

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

   if -64 < z < 200

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. unsub-neg 57.0%

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

   5. Simplified 57.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -64 \lor \neg \left(z \leq 200\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+192} \lor \neg \left(t \leq 1.3 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e+192) (not (<= t 1.3e+114))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e+192) || !(t <= 1.3e+114)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1d+192)) .or. (.not. (t <= 1.3d+114))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e+192) || !(t <= 1.3e+114)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e+192) or not (t <= 1.3e+114):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e+192) || !(t <= 1.3e+114))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e+192) || ~((t <= 1.3e+114)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e+192], N[Not[LessEqual[t, 1.3e+114]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000004e192 or 1.3e114 < t

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in z around inf 62.4%

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

   if -1.00000000000000004e192 < t < 1.3e114

   1. Initial program 70.2%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

   5. Simplified 47.6%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+192} \lor \neg \left(t \leq 1.3 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-13} \lor \neg \left(z \leq 1.25 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e-13) (not (<= z 1.25e-18))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-13) || !(z <= 1.25e-18)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.1d-13)) .or. (.not. (z <= 1.25d-18))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-13) || !(z <= 1.25e-18)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e-13) or not (z <= 1.25e-18):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e-13) || !(z <= 1.25e-18))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e-13) || ~((z <= 1.25e-18)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e-13], N[Not[LessEqual[z, 1.25e-18]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999989e-13 or 1.25000000000000009e-18 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf 25.5%

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

      1. *-commutative 25.5%

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

   5. Simplified 25.5%

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

   6. Taylor expanded in y around 0 24.9%

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

   if -2.09999999999999989e-13 < z < 1.25000000000000009e-18

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 59.8%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-13} \lor \neg \left(z \leq 1.25 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.9%

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

3. Taylor expanded in z around 0 28.7%

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

4. Final simplification 28.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 74.6% 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 2024077 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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