Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.2% → 98.2%

Time: 16.3s

Alternatives: 18

Speedup: 1.0×

• 46.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - 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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - 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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (+ t -1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - 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 * exp((((y * log(z)) + ((t + (-1.0d0)) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t + -1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t + -1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t + -1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Final simplification 98.6%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \]
4. Add Preprocessing

Alternative 2: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+68}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow z y)))))
   (if (<= y -4.1e+33)
     t_1
     (if (<= y 2.65e+68) (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(z, y));
	double tmp;
	if (y <= -4.1e+33) {
		tmp = t_1;
	} else if (y <= 2.65e+68) {
		tmp = (x * (pow(a, (t + -1.0)) / exp(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 / (y / (z ** y))
    if (y <= (-4.1d+33)) then
        tmp = t_1
    else if (y <= 2.65d+68) then
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(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 / (y / Math.pow(z, y));
	double tmp;
	if (y <= -4.1e+33) {
		tmp = t_1;
	} else if (y <= 2.65e+68) {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(z, y))
	tmp = 0
	if y <= -4.1e+33:
		tmp = t_1
	elif y <= 2.65e+68:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (z ^ y)))
	tmp = 0.0
	if (y <= -4.1e+33)
		tmp = t_1;
	elseif (y <= 2.65e+68)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (z ^ y));
	tmp = 0.0;
	if (y <= -4.1e+33)
		tmp = t_1;
	elseif (y <= 2.65e+68)
		tmp = (x * ((a ^ (t + -1.0)) / exp(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[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+33], t$95$1, If[LessEqual[y, 2.65e+68], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999995e33 or 2.6500000000000001e68 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 84.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z}}}{y} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{y}} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \frac{e^{\log z \cdot y}}{y} \]

      3. pow-to-exp N/A

         \[\leadsto x \cdot \frac{{z}^{y}}{y} \]

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{y}{{z}^{y}}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      8. pow-lowering-pow.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 84.6%

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

   if -4.09999999999999995e33 < y < 2.6500000000000001e68

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 79.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 79.5%

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

Alternative 3: 56.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -12.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -12.2)
     t_1
     (if (<= b -2.5e-270)
       (/
        x
        (*
         y
         (+
          a
          (* b (+ a (* b (+ (* a (* b 0.16666666666666666)) (* a 0.5))))))))
       (if (<= b 2.1e-71)
         (/ (* 0.5 (* x (* b b))) y)
         (if (<= b 9.2e+24) (/ x (* y a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -12.2) {
		tmp = t_1;
	} else if (b <= -2.5e-270) {
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	} else if (b <= 2.1e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 9.2e+24) {
		tmp = x / (y * a);
	} 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 / exp(b)) / y
    if (b <= (-12.2d0)) then
        tmp = t_1
    else if (b <= (-2.5d-270)) then
        tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666d0)) + (a * 0.5d0)))))))
    else if (b <= 2.1d-71) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else if (b <= 9.2d+24) then
        tmp = x / (y * a)
    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 / Math.exp(b)) / y;
	double tmp;
	if (b <= -12.2) {
		tmp = t_1;
	} else if (b <= -2.5e-270) {
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	} else if (b <= 2.1e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 9.2e+24) {
		tmp = x / (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -12.2:
		tmp = t_1
	elif b <= -2.5e-270:
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))))
	elif b <= 2.1e-71:
		tmp = (0.5 * (x * (b * b))) / y
	elif b <= 9.2e+24:
		tmp = x / (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -12.2)
		tmp = t_1;
	elseif (b <= -2.5e-270)
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(a * Float64(b * 0.16666666666666666)) + Float64(a * 0.5))))))));
	elseif (b <= 2.1e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	elseif (b <= 9.2e+24)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -12.2)
		tmp = t_1;
	elseif (b <= -2.5e-270)
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	elseif (b <= 2.1e-71)
		tmp = (0.5 * (x * (b * b))) / y;
	elseif (b <= 9.2e+24)
		tmp = x / (y * a);
	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[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -12.2], t$95$1, If[LessEqual[b, -2.5e-270], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(a * N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9.2e+24], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -12.199999999999999 or 9.1999999999999996e24 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 78.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 78.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

   if -12.199999999999999 < b < -2.4999999999999999e-270

   1. Initial program 97.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 70.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 70.9%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 45.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 45.2%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)}\right)\right)\right)\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(a \cdot b\right)\right), \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{1}{6}\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{1}{6}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{6} \cdot b\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 45.2%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 45.2%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}} \]

   if -2.4999999999999999e-270 < b < 2.1000000000000001e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if 2.1000000000000001e-71 < b < 9.1999999999999996e24

   1. Initial program 98.5%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 60.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 54.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 54.7%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 39.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 39.2%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 45.8%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 62.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ t_2 := \frac{x}{y \cdot a}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(\frac{b \cdot \left(x \cdot 0.5\right)}{y \cdot a} - t\_2\right) + t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))) (t_2 (/ x (* y a))))
   (if (<= t -1.65e+32)
     t_1
     (if (<= t -1.1e-173)
       (+ (* b (- (/ (* b (* x 0.5)) (* y a)) t_2)) t_2)
       (if (<= t 2.2e+60) (/ (/ x (exp b)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double t_2 = x / (y * a);
	double tmp;
	if (t <= -1.65e+32) {
		tmp = t_1;
	} else if (t <= -1.1e-173) {
		tmp = (b * (((b * (x * 0.5)) / (y * a)) - t_2)) + t_2;
	} else if (t <= 2.2e+60) {
		tmp = (x / exp(b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    t_2 = x / (y * a)
    if (t <= (-1.65d+32)) then
        tmp = t_1
    else if (t <= (-1.1d-173)) then
        tmp = (b * (((b * (x * 0.5d0)) / (y * a)) - t_2)) + t_2
    else if (t <= 2.2d+60) then
        tmp = (x / exp(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 * (Math.pow(a, t) / y);
	double t_2 = x / (y * a);
	double tmp;
	if (t <= -1.65e+32) {
		tmp = t_1;
	} else if (t <= -1.1e-173) {
		tmp = (b * (((b * (x * 0.5)) / (y * a)) - t_2)) + t_2;
	} else if (t <= 2.2e+60) {
		tmp = (x / Math.exp(b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	t_2 = x / (y * a)
	tmp = 0
	if t <= -1.65e+32:
		tmp = t_1
	elif t <= -1.1e-173:
		tmp = (b * (((b * (x * 0.5)) / (y * a)) - t_2)) + t_2
	elif t <= 2.2e+60:
		tmp = (x / math.exp(b)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	t_2 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (t <= -1.65e+32)
		tmp = t_1;
	elseif (t <= -1.1e-173)
		tmp = Float64(Float64(b * Float64(Float64(Float64(b * Float64(x * 0.5)) / Float64(y * a)) - t_2)) + t_2);
	elseif (t <= 2.2e+60)
		tmp = Float64(Float64(x / exp(b)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	t_2 = x / (y * a);
	tmp = 0.0;
	if (t <= -1.65e+32)
		tmp = t_1;
	elseif (t <= -1.1e-173)
		tmp = (b * (((b * (x * 0.5)) / (y * a)) - t_2)) + t_2;
	elseif (t <= 2.2e+60)
		tmp = (x / exp(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[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+32], t$95$1, If[LessEqual[t, -1.1e-173], N[(N[(b * N[(N[(N[(b * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 2.2e+60], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6500000000000001e32 or 2.19999999999999996e60 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot \log a\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\log a \cdot t\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log a, t\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 81.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), t\right)\right)\right), y\right) \]

   5. Simplified 81.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot t}}{y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot t}}{y} \cdot \color{blue}{x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{e^{\log a \cdot t}}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(e^{\log a \cdot t}\right), y\right), x\right) \]

      5. exp-to-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({a}^{t}\right), y\right), x\right) \]

      6. pow-lowering-pow.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), y\right), x\right) \]

   7. Applied egg-rr 81.4%

      \[\leadsto \color{blue}{\frac{{a}^{t}}{y} \cdot x} \]

   if -1.6500000000000001e32 < t < -1.1e-173

   1. Initial program 94.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 63.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 70.6%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 77.7%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{a \cdot y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a \cdot y}\right)\right) - \frac{x}{a \cdot y}\right)\right)}\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot y\right)\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a \cdot y}\right)\right) - \frac{x}{a \cdot y}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, y\right)\right), \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a \cdot y}\right)\right) - \frac{x}{a \cdot y}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, y\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a \cdot y}\right)\right) - \frac{x}{a \cdot y}\right)}\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, y\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a \cdot y}\right)\right)\right), \color{blue}{\left(\frac{x}{a \cdot y}\right)}\right)\right)\right) \]

   13. Simplified 57.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y} + b \cdot \left(\frac{b \cdot \left(x \cdot 0.5\right)}{a \cdot y} - \frac{x}{a \cdot y}\right)} \]

   if -1.1e-173 < t < 2.19999999999999996e60

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 59.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 59.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      2. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 59.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 59.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(\frac{b \cdot \left(x \cdot 0.5\right)}{y \cdot a} - \frac{x}{y \cdot a}\right) + \frac{x}{y \cdot a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.36e+41)
     t_1
     (if (<= t 1.55e+59) (/ x (* y (* a (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -1.36e+41) {
		tmp = t_1;
	} else if (t <= 1.55e+59) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    if (t <= (-1.36d+41)) then
        tmp = t_1
    else if (t <= 1.55d+59) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -1.36e+41) {
		tmp = t_1;
	} else if (t <= 1.55e+59) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -1.36e+41:
		tmp = t_1
	elif t <= 1.55e+59:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -1.36e+41)
		tmp = t_1;
	elseif (t <= 1.55e+59)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -1.36e+41)
		tmp = t_1;
	elseif (t <= 1.55e+59)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+41], t$95$1, If[LessEqual[t, 1.55e+59], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35999999999999995e41 or 1.55000000000000007e59 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot \log a\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\log a \cdot t\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log a, t\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 81.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), t\right)\right)\right), y\right) \]

   5. Simplified 81.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot t}}{y}} \]

      2. *-commutative N/A

         \[\leadsto \frac{e^{\log a \cdot t}}{y} \cdot \color{blue}{x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{e^{\log a \cdot t}}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(e^{\log a \cdot t}\right), y\right), x\right) \]

      5. exp-to-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({a}^{t}\right), y\right), x\right) \]

      6. pow-lowering-pow.f64 81.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), y\right), x\right) \]

   7. Applied egg-rr 81.0%

      \[\leadsto \color{blue}{\frac{{a}^{t}}{y} \cdot x} \]

   if -1.35999999999999995e41 < t < 1.55000000000000007e59

   1. Initial program 97.6%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 69.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 73.9%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 74.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 + b \cdot 0.5\\ t_2 := x \cdot \left(b \cdot t\_1\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \frac{\frac{x \cdot \left(y \cdot \left(b \cdot -0.16666666666666666\right)\right) + y \cdot \left(x \cdot 0.5\right)}{y}}{y} - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq -0.0026:\\ \;\;\;\;\frac{\left(x \cdot \left(x \cdot x\right) + t\_2 \cdot \left(b \cdot \left(t\_2 \cdot \left(x \cdot t\_1\right)\right)\right)\right) \cdot \frac{1}{y}}{x \cdot x}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ -1.0 (* b 0.5))) (t_2 (* x (* b t_1))))
   (if (<= b -2.75e+69)
     (+
      (/ x y)
      (*
       b
       (-
        (*
         b
         (/
          (/ (+ (* x (* y (* b -0.16666666666666666))) (* y (* x 0.5))) y)
          y))
        (/ x y))))
     (if (<= b -0.0026)
       (/
        (* (+ (* x (* x x)) (* t_2 (* b (* t_2 (* x t_1))))) (/ 1.0 y))
        (* x x))
       (if (<= b -2e-270)
         (/
          x
          (*
           y
           (+
            a
            (* b (+ a (* b (+ (* a (* b 0.16666666666666666)) (* a 0.5))))))))
         (if (<= b 1.75e-71)
           (/ (* 0.5 (* x (* b b))) y)
           (/
            x
            (*
             y
             (*
              a
              (+
               1.0
               (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 + (b * 0.5);
	double t_2 = x * (b * t_1);
	double tmp;
	if (b <= -2.75e+69) {
		tmp = (x / y) + (b * ((b * ((((x * (y * (b * -0.16666666666666666))) + (y * (x * 0.5))) / y) / y)) - (x / y)));
	} else if (b <= -0.0026) {
		tmp = (((x * (x * x)) + (t_2 * (b * (t_2 * (x * t_1))))) * (1.0 / y)) / (x * x);
	} else if (b <= -2e-270) {
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-1.0d0) + (b * 0.5d0)
    t_2 = x * (b * t_1)
    if (b <= (-2.75d+69)) then
        tmp = (x / y) + (b * ((b * ((((x * (y * (b * (-0.16666666666666666d0)))) + (y * (x * 0.5d0))) / y) / y)) - (x / y)))
    else if (b <= (-0.0026d0)) then
        tmp = (((x * (x * x)) + (t_2 * (b * (t_2 * (x * t_1))))) * (1.0d0 / y)) / (x * x)
    else if (b <= (-2d-270)) then
        tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666d0)) + (a * 0.5d0)))))))
    else if (b <= 1.75d-71) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else
        tmp = x / (y * (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 = -1.0 + (b * 0.5);
	double t_2 = x * (b * t_1);
	double tmp;
	if (b <= -2.75e+69) {
		tmp = (x / y) + (b * ((b * ((((x * (y * (b * -0.16666666666666666))) + (y * (x * 0.5))) / y) / y)) - (x / y)));
	} else if (b <= -0.0026) {
		tmp = (((x * (x * x)) + (t_2 * (b * (t_2 * (x * t_1))))) * (1.0 / y)) / (x * x);
	} else if (b <= -2e-270) {
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -1.0 + (b * 0.5)
	t_2 = x * (b * t_1)
	tmp = 0
	if b <= -2.75e+69:
		tmp = (x / y) + (b * ((b * ((((x * (y * (b * -0.16666666666666666))) + (y * (x * 0.5))) / y) / y)) - (x / y)))
	elif b <= -0.0026:
		tmp = (((x * (x * x)) + (t_2 * (b * (t_2 * (x * t_1))))) * (1.0 / y)) / (x * x)
	elif b <= -2e-270:
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))))
	elif b <= 1.75e-71:
		tmp = (0.5 * (x * (b * b))) / y
	else:
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-1.0 + Float64(b * 0.5))
	t_2 = Float64(x * Float64(b * t_1))
	tmp = 0.0
	if (b <= -2.75e+69)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(Float64(x * Float64(y * Float64(b * -0.16666666666666666))) + Float64(y * Float64(x * 0.5))) / y) / y)) - Float64(x / y))));
	elseif (b <= -0.0026)
		tmp = Float64(Float64(Float64(Float64(x * Float64(x * x)) + Float64(t_2 * Float64(b * Float64(t_2 * Float64(x * t_1))))) * Float64(1.0 / y)) / Float64(x * x));
	elseif (b <= -2e-270)
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(a * Float64(b * 0.16666666666666666)) + Float64(a * 0.5))))))));
	elseif (b <= 1.75e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -1.0 + (b * 0.5);
	t_2 = x * (b * t_1);
	tmp = 0.0;
	if (b <= -2.75e+69)
		tmp = (x / y) + (b * ((b * ((((x * (y * (b * -0.16666666666666666))) + (y * (x * 0.5))) / y) / y)) - (x / y)));
	elseif (b <= -0.0026)
		tmp = (((x * (x * x)) + (t_2 * (b * (t_2 * (x * t_1))))) * (1.0 / y)) / (x * x);
	elseif (b <= -2e-270)
		tmp = x / (y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5)))))));
	elseif (b <= 1.75e-71)
		tmp = (0.5 * (x * (b * b))) / y;
	else
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+69], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(N[(x * N[(y * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -0.0026], N[(N[(N[(N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(b * N[(t$95$2 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-270], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(a * N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.75000000000000001e69

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \color{blue}{-1 \cdot \frac{x}{y}}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) - \color{blue}{\frac{x}{y}}\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

   8. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{x}{y} + b \cdot \left(b \cdot \left(\frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y} + \frac{x \cdot 0.5}{y}\right) - \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. frac-add N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y \cdot y}\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      2. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y}}{y}\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\left(\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y}\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \left(x \cdot \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      11. *-lowering-*.f64 79.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), y\right), y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

   10. Applied egg-rr 79.6%

       \[\leadsto \frac{x}{y} + b \cdot \left(b \cdot \color{blue}{\frac{\frac{x \cdot \left(\left(b \cdot -0.16666666666666666\right) \cdot y\right) + y \cdot \left(x \cdot 0.5\right)}{y}}{y}} - \frac{x}{y}\right) \]

   if -2.75000000000000001e69 < b < -0.0025999999999999999

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 77.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 15.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 15.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]
   9. Step-by-step derivation

      1. div-inv N/A

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

      2. flip3-+ N/A

         \[\leadsto \frac{{x}^{3} + {\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)}^{3}}{x \cdot x + \left(\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) - x \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)\right)} \cdot \frac{\color{blue}{1}}{y} \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left({x}^{3} + {\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)}^{3}\right) \cdot \frac{1}{y}}{\color{blue}{x \cdot x + \left(\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) - x \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)\right)}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left({x}^{3} + {\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)}^{3}\right) \cdot \frac{1}{y}\right), \color{blue}{\left(x \cdot x + \left(\left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right) - x \cdot \left(b \cdot \left(x \cdot \left(b \cdot \frac{1}{2} + -1\right)\right)\right)\right)\right)}\right) \]

   10. Applied egg-rr 28.2%

       \[\leadsto \color{blue}{\frac{\left(x \cdot \left(x \cdot x\right) + \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right)\right) \cdot \left(b \cdot \left(\left(x \cdot \left(b \cdot 0.5 + -1\right)\right) \cdot \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right)\right)\right)\right)\right) \cdot \frac{1}{y}}{x \cdot x + \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right)\right) \cdot \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right) - x\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(1, y\right)\right), \color{blue}{\left({x}^{2}\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(1, y\right)\right), \left(x \cdot \color{blue}{x}\right)\right) \]

       2. *-lowering-*.f64 50.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right), b\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right) \]

   13. Simplified 50.3%

       \[\leadsto \frac{\left(x \cdot \left(x \cdot x\right) + \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right)\right) \cdot \left(b \cdot \left(\left(x \cdot \left(b \cdot 0.5 + -1\right)\right) \cdot \left(x \cdot \left(\left(b \cdot 0.5 + -1\right) \cdot b\right)\right)\right)\right)\right) \cdot \frac{1}{y}}{\color{blue}{x \cdot x}} \]

   if -0.0025999999999999999 < b < -2.0000000000000001e-270

   1. Initial program 97.0%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 76.2%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 70.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 70.5%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 45.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 45.8%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)}\right)\right)\right)\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(a \cdot b\right)\right), \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{1}{6}\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{1}{6}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{6} \cdot b\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 45.8%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 45.8%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}} \]

   if -2.0000000000000001e-270 < b < 1.75e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if 1.75e-71 < b

   1. Initial program 99.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 50.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 68.5%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot b\right)}\right)\right)\right)\right)\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot b\right)}\right)\right)\right)\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 63.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 63.7%

       \[\leadsto \frac{x}{y \cdot \left(a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \frac{\frac{x \cdot \left(y \cdot \left(b \cdot -0.16666666666666666\right)\right) + y \cdot \left(x \cdot 0.5\right)}{y}}{y} - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq -0.0026:\\ \;\;\;\;\frac{\left(x \cdot \left(x \cdot x\right) + \left(x \cdot \left(b \cdot \left(-1 + b \cdot 0.5\right)\right)\right) \cdot \left(b \cdot \left(\left(x \cdot \left(b \cdot \left(-1 + b \cdot 0.5\right)\right)\right) \cdot \left(x \cdot \left(-1 + b \cdot 0.5\right)\right)\right)\right)\right) \cdot \frac{1}{y}}{x \cdot x}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+115)
   (+ (/ x y) (* -0.16666666666666666 (/ (* x (* b (* b b))) y)))
   (if (<= b -4.5e-270)
     (/ x (* y (* a (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
     (if (<= b 1.75e-71)
       (/ (* 0.5 (* x (* b b))) y)
       (/
        x
        (*
         y
         (*
          a
          (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -4.5e-270) {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 (b <= (-6.8d+115)) then
        tmp = (x / y) + ((-0.16666666666666666d0) * ((x * (b * (b * b))) / y))
    else if (b <= (-4.5d-270)) then
        tmp = x / (y * (a * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else if (b <= 1.75d-71) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else
        tmp = x / (y * (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -4.5e-270) {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+115:
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y))
	elif b <= -4.5e-270:
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))))
	elif b <= 1.75e-71:
		tmp = (0.5 * (x * (b * b))) / y
	else:
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+115)
		tmp = Float64(Float64(x / y) + Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y)));
	elseif (b <= -4.5e-270)
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	elseif (b <= 1.75e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+115)
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	elseif (b <= -4.5e-270)
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	elseif (b <= 1.75e-71)
		tmp = (0.5 * (x * (b * b))) / y;
	else
		tmp = x / (y * (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+115], N[(N[(x / y), $MachinePrecision] + N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-270], N[(x / N[(y * N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.8000000000000001e115

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 89.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \color{blue}{-1 \cdot \frac{x}{y}}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) - \color{blue}{\frac{x}{y}}\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x}{y} + b \cdot \left(b \cdot \left(\frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y} + \frac{x \cdot 0.5}{y}\right) - \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\left(\frac{x \cdot \left(b \cdot \frac{-1}{6}\right)}{y} + \frac{x \cdot \frac{1}{2}}{y}\right) \cdot b\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      2. frac-add N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y \cdot y} \cdot b\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b}{y \cdot y}\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 70.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

   10. Applied egg-rr 70.6%

       \[\leadsto \frac{x}{y} + b \cdot \left(\color{blue}{\frac{\left(x \cdot \left(\left(b \cdot -0.16666666666666666\right) \cdot y\right) + y \cdot \left(x \cdot 0.5\right)\right) \cdot b}{y \cdot y}} - \frac{x}{y}\right) \]

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left(\frac{{b}^{3} \cdot x}{y}\right)}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left({b}^{3} \cdot x\right), \color{blue}{y}\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left(x \cdot {b}^{3}\right), y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3}\right)\right), y\right)\right)\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot {b}^{2}\right)\right), y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right), y\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 89.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right)\right)\right) \]

   13. Simplified 89.4%

       \[\leadsto \frac{x}{y} + \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -6.8000000000000001e115 < b < -4.49999999999999998e-270

   1. Initial program 97.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 68.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 52.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 52.9%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(1 + \frac{1}{2} \cdot b\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{2} \cdot b\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 40.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 40.0%

       \[\leadsto \frac{x}{y \cdot \left(a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}\right)} \]

   if -4.49999999999999998e-270 < b < 1.75e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if 1.75e-71 < b

   1. Initial program 99.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 50.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 68.5%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot b\right)}\right)\right)\right)\right)\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot b\right)}\right)\right)\right)\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 63.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 63.7%

       \[\leadsto \frac{x}{y \cdot \left(a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 49.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (* a (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))
   (if (<= b -6.8e+115)
     (+ (/ x y) (* -0.16666666666666666 (/ (* x (* b (* b b))) y)))
     (if (<= b -3e-270)
       t_1
       (if (<= b 1.75e-71) (/ (* 0.5 (* x (* b b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -3e-270) {
		tmp = t_1;
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * 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 / (y * (a * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    if (b <= (-6.8d+115)) then
        tmp = (x / y) + ((-0.16666666666666666d0) * ((x * (b * (b * b))) / y))
    else if (b <= (-3d-270)) then
        tmp = t_1
    else if (b <= 1.75d-71) then
        tmp = (0.5d0 * (x * (b * 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 / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -3e-270) {
		tmp = t_1;
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))))
	tmp = 0
	if b <= -6.8e+115:
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y))
	elif b <= -3e-270:
		tmp = t_1
	elif b <= 1.75e-71:
		tmp = (0.5 * (x * (b * b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))))
	tmp = 0.0
	if (b <= -6.8e+115)
		tmp = Float64(Float64(x / y) + Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y)));
	elseif (b <= -3e-270)
		tmp = t_1;
	elseif (b <= 1.75e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * (a * (1.0 + (b * (1.0 + (b * 0.5))))));
	tmp = 0.0;
	if (b <= -6.8e+115)
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	elseif (b <= -3e-270)
		tmp = t_1;
	elseif (b <= 1.75e-71)
		tmp = (0.5 * (x * (b * 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[(y * N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+115], N[(N[(x / y), $MachinePrecision] + N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-270], t$95$1, If[LessEqual[b, 1.75e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000001e115

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 89.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \color{blue}{-1 \cdot \frac{x}{y}}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) - \color{blue}{\frac{x}{y}}\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x}{y} + b \cdot \left(b \cdot \left(\frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y} + \frac{x \cdot 0.5}{y}\right) - \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\left(\frac{x \cdot \left(b \cdot \frac{-1}{6}\right)}{y} + \frac{x \cdot \frac{1}{2}}{y}\right) \cdot b\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      2. frac-add N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y \cdot y} \cdot b\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b}{y \cdot y}\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 70.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

   10. Applied egg-rr 70.6%

       \[\leadsto \frac{x}{y} + b \cdot \left(\color{blue}{\frac{\left(x \cdot \left(\left(b \cdot -0.16666666666666666\right) \cdot y\right) + y \cdot \left(x \cdot 0.5\right)\right) \cdot b}{y \cdot y}} - \frac{x}{y}\right) \]

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left(\frac{{b}^{3} \cdot x}{y}\right)}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left({b}^{3} \cdot x\right), \color{blue}{y}\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left(x \cdot {b}^{3}\right), y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3}\right)\right), y\right)\right)\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot {b}^{2}\right)\right), y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right), y\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 89.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right)\right)\right) \]

   13. Simplified 89.4%

       \[\leadsto \frac{x}{y} + \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -6.8000000000000001e115 < b < -3.00000000000000013e-270 or 1.75e-71 < b

   1. Initial program 98.8%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 59.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.1%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 60.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 60.2%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(1 + \frac{1}{2} \cdot b\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{2} \cdot b\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 48.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 48.3%

       \[\leadsto \frac{x}{y \cdot \left(a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}\right)} \]

   if -3.00000000000000013e-270 < b < 1.75e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.6% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+115)
   (+ (/ x y) (* -0.16666666666666666 (/ (* x (* b (* b b))) y)))
   (if (<= b -1.65e-270)
     (/ x (* y a))
     (if (<= b 1.75e-71)
       (/ (* 0.5 (* x (* b b))) y)
       (/ x (* a (* y (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -1.65e-270) {
		tmp = x / (y * a);
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + 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 (b <= (-6.8d+115)) then
        tmp = (x / y) + ((-0.16666666666666666d0) * ((x * (b * (b * b))) / y))
    else if (b <= (-1.65d-270)) then
        tmp = x / (y * a)
    else if (b <= 1.75d-71) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else
        tmp = x / (a * (y * (1.0d0 + 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 (b <= -6.8e+115) {
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	} else if (b <= -1.65e-270) {
		tmp = x / (y * a);
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+115:
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y))
	elif b <= -1.65e-270:
		tmp = x / (y * a)
	elif b <= 1.75e-71:
		tmp = (0.5 * (x * (b * b))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+115)
		tmp = Float64(Float64(x / y) + Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y)));
	elseif (b <= -1.65e-270)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.75e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+115)
		tmp = (x / y) + (-0.16666666666666666 * ((x * (b * (b * b))) / y));
	elseif (b <= -1.65e-270)
		tmp = x / (y * a);
	elseif (b <= 1.75e-71)
		tmp = (0.5 * (x * (b * b))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+115], N[(N[(x / y), $MachinePrecision] + N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.65e-270], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.8000000000000001e115

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 89.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{x}{y} + b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right)}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \color{blue}{-1 \cdot \frac{x}{y}}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right) - \color{blue}{\frac{x}{y}}\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \frac{b \cdot x}{y} + \frac{1}{2} \cdot \frac{x}{y}\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x}{y} + b \cdot \left(b \cdot \left(\frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y} + \frac{x \cdot 0.5}{y}\right) - \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\left(\frac{x \cdot \left(b \cdot \frac{-1}{6}\right)}{y} + \frac{x \cdot \frac{1}{2}}{y}\right) \cdot b\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      2. frac-add N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)}{y \cdot y} \cdot b\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b}{y \cdot y}\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right) \cdot b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(\color{blue}{x}, y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y + y \cdot \left(x \cdot \frac{1}{2}\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(b \cdot \frac{-1}{6}\right)\right) \cdot y\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \frac{-1}{6}\right) \cdot y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \left(y \cdot \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \left(x \cdot \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \left(y \cdot y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 70.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{-1}{6}\right), y\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \frac{1}{2}\right)\right)\right), b\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(x, y\right)\right)\right)\right) \]

   10. Applied egg-rr 70.6%

       \[\leadsto \frac{x}{y} + b \cdot \left(\color{blue}{\frac{\left(x \cdot \left(\left(b \cdot -0.16666666666666666\right) \cdot y\right) + y \cdot \left(x \cdot 0.5\right)\right) \cdot b}{y \cdot y}} - \frac{x}{y}\right) \]

   11. Taylor expanded in b around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left(\frac{{b}^{3} \cdot x}{y}\right)}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left({b}^{3} \cdot x\right), \color{blue}{y}\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\left(x \cdot {b}^{3}\right), y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3}\right)\right), y\right)\right)\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot {b}^{2}\right)\right), y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right), y\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 89.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right)\right)\right) \]

   13. Simplified 89.4%

       \[\leadsto \frac{x}{y} + \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -6.8000000000000001e115 < b < -1.65000000000000009e-270

   1. Initial program 97.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 68.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 52.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 52.9%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 39.5%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

   if -1.65000000000000009e-270 < b < 1.75e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if 1.75e-71 < b

   1. Initial program 99.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 50.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 68.5%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y + a \cdot \left(b \cdot y\right)\right)}\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       3. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(b + 1\right) \cdot \color{blue}{y}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b + 1\right), \color{blue}{y}\right)\right)\right) \]

       5. +-lowering-+.f64 40.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), y\right)\right)\right) \]

   13. Simplified 40.6%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} + -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.9% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{\left(b \cdot b\right) \cdot -0.5}{0 - y}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.3e+117)
   (* x (/ (* (* b b) -0.5) (- 0.0 y)))
   (if (<= b -3.7e-270)
     (/ x (* y a))
     (if (<= b 1.75e-71)
       (/ (* 0.5 (* x (* b b))) y)
       (/ x (* a (* y (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e+117) {
		tmp = x * (((b * b) * -0.5) / (0.0 - y));
	} else if (b <= -3.7e-270) {
		tmp = x / (y * a);
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + 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 (b <= (-1.3d+117)) then
        tmp = x * (((b * b) * (-0.5d0)) / (0.0d0 - y))
    else if (b <= (-3.7d-270)) then
        tmp = x / (y * a)
    else if (b <= 1.75d-71) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else
        tmp = x / (a * (y * (1.0d0 + 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 (b <= -1.3e+117) {
		tmp = x * (((b * b) * -0.5) / (0.0 - y));
	} else if (b <= -3.7e-270) {
		tmp = x / (y * a);
	} else if (b <= 1.75e-71) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.3e+117:
		tmp = x * (((b * b) * -0.5) / (0.0 - y))
	elif b <= -3.7e-270:
		tmp = x / (y * a)
	elif b <= 1.75e-71:
		tmp = (0.5 * (x * (b * b))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.3e+117)
		tmp = Float64(x * Float64(Float64(Float64(b * b) * -0.5) / Float64(0.0 - y)));
	elseif (b <= -3.7e-270)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.75e-71)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.3e+117)
		tmp = x * (((b * b) * -0.5) / (0.0 - y));
	elseif (b <= -3.7e-270)
		tmp = x / (y * a);
	elseif (b <= 1.75e-71)
		tmp = (0.5 * (x * (b * b))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.3e+117], N[(x * N[(N[(N[(b * b), $MachinePrecision] * -0.5), $MachinePrecision] / N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.7e-270], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-71], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.3e117

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 89.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 89.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 73.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 86.4%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1}{2} \cdot \frac{{b}^{2}}{y}\right)}\right)\right) \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \left(\frac{\frac{-1}{2} \cdot {b}^{2}}{\color{blue}{y}}\right)\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {b}^{2}\right), \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({b}^{2}\right)\right), y\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(b \cdot b\right)\right), y\right)\right)\right) \]

       5. *-lowering-*.f64 86.4%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(b, b\right)\right), y\right)\right)\right) \]

   14. Simplified 86.4%

       \[\leadsto 0 - x \cdot \color{blue}{\frac{-0.5 \cdot \left(b \cdot b\right)}{y}} \]

   if -1.3e117 < b < -3.7000000000000001e-270

   1. Initial program 97.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 68.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.9%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 53.4%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 39.1%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

   if -3.7000000000000001e-270 < b < 1.75e-71

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 17.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 17.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 17.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 17.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 17.5%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 55.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if 1.75e-71 < b

   1. Initial program 99.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 50.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 68.5%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y + a \cdot \left(b \cdot y\right)\right)}\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       3. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(b + 1\right) \cdot \color{blue}{y}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b + 1\right), \color{blue}{y}\right)\right)\right) \]

       5. +-lowering-+.f64 40.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), y\right)\right)\right) \]

   13. Simplified 40.6%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{\left(b \cdot b\right) \cdot -0.5}{0 - y}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.7% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* 0.5 (* x (* b b))) y)))
   (if (<= b -1.3e+117)
     t_1
     (if (<= b -3.6e-270)
       (/ x (* y a))
       (if (<= b 3.4e-69) t_1 (/ x (* a (* y (+ 1.0 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.5 * (x * (b * b))) / y;
	double tmp;
	if (b <= -1.3e+117) {
		tmp = t_1;
	} else if (b <= -3.6e-270) {
		tmp = x / (y * a);
	} else if (b <= 3.4e-69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + 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 = (0.5d0 * (x * (b * b))) / y
    if (b <= (-1.3d+117)) then
        tmp = t_1
    else if (b <= (-3.6d-270)) then
        tmp = x / (y * a)
    else if (b <= 3.4d-69) then
        tmp = t_1
    else
        tmp = x / (a * (y * (1.0d0 + 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 = (0.5 * (x * (b * b))) / y;
	double tmp;
	if (b <= -1.3e+117) {
		tmp = t_1;
	} else if (b <= -3.6e-270) {
		tmp = x / (y * a);
	} else if (b <= 3.4e-69) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.5 * (x * (b * b))) / y
	tmp = 0
	if b <= -1.3e+117:
		tmp = t_1
	elif b <= -3.6e-270:
		tmp = x / (y * a)
	elif b <= 3.4e-69:
		tmp = t_1
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y)
	tmp = 0.0
	if (b <= -1.3e+117)
		tmp = t_1;
	elseif (b <= -3.6e-270)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 3.4e-69)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.5 * (x * (b * b))) / y;
	tmp = 0.0;
	if (b <= -1.3e+117)
		tmp = t_1;
	elseif (b <= -3.6e-270)
		tmp = x / (y * a);
	elseif (b <= 3.4e-69)
		tmp = t_1;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.3e+117], t$95$1, If[LessEqual[b, -3.6e-270], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-69], t$95$1, N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e117 or -3.5999999999999998e-270 < b < 3.40000000000000008e-69

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 47.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 47.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 40.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 40.8%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 46.3%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 67.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   14. Simplified 67.2%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -1.3e117 < b < -3.5999999999999998e-270

   1. Initial program 97.9%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 68.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 67.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 67.9%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 53.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 53.4%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 39.1%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]

   if 3.40000000000000008e-69 < b

   1. Initial program 99.7%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 50.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 68.5%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y + a \cdot \left(b \cdot y\right)\right)}\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       3. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(b + 1\right) \cdot \color{blue}{y}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b + 1\right), \color{blue}{y}\right)\right)\right) \]

       5. +-lowering-+.f64 40.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), y\right)\right)\right) \]

   13. Simplified 40.6%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-69}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.8% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.32:\\ \;\;\;\;0.5 \cdot \left(b \cdot \frac{x \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.32) (* 0.5 (* b (/ (* x b) y))) (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.32) {
		tmp = 0.5 * (b * ((x * b) / y));
	} else {
		tmp = x / (a * (y * (1.0 + 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 (b <= (-1.32d0)) then
        tmp = 0.5d0 * (b * ((x * b) / y))
    else
        tmp = x / (a * (y * (1.0d0 + 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 (b <= -1.32) {
		tmp = 0.5 * (b * ((x * b) / y));
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.32:
		tmp = 0.5 * (b * ((x * b) / y))
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.32)
		tmp = Float64(0.5 * Float64(b * Float64(Float64(x * b) / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.32)
		tmp = 0.5 * (b * ((x * b) / y));
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.32], N[(0.5 * N[(b * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.32000000000000006

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 48.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 48.3%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. associate-*l* N/A

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

       4. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{y}\right) \cdot \left(b \cdot \color{blue}{b}\right) \]

       5. associate-*r* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \frac{x}{y}\right) \cdot b\right) \cdot \color{blue}{b} \]

       6. associate-*l* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left(\frac{x}{y} \cdot b\right)\right) \cdot b \]

       7. *-commutative N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left(b \cdot \frac{x}{y}\right)\right) \cdot b \]

       8. associate-/l* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{b \cdot x}{y}\right) \cdot b \]

       9. associate-*l* N/A

          \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{b \cdot x}{y} \cdot b\right)} \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{b \cdot x}{y} \cdot b\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\frac{b \cdot x}{y}\right), \color{blue}{b}\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(b \cdot x\right), y\right), b\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x \cdot b\right), y\right), b\right)\right) \]

       14. *-lowering-*.f64 46.0%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, b\right), y\right), b\right)\right) \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x \cdot b}{y} \cdot b\right)} \]

   if -1.32000000000000006 < b

   1. Initial program 98.1%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 63.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.8%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 53.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 53.0%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y + a \cdot \left(b \cdot y\right)\right)}\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(y + b \cdot y\right)}\right)\right) \]

       3. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(b + 1\right) \cdot \color{blue}{y}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b + 1\right), \color{blue}{y}\right)\right)\right) \]

       5. +-lowering-+.f64 41.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), y\right)\right)\right) \]

   13. Simplified 41.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32:\\ \;\;\;\;0.5 \cdot \left(b \cdot \frac{x \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.4% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;0.5 \cdot \left(b \cdot \frac{x \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e+119) (* 0.5 (* b (/ (* x b) y))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e+119) {
		tmp = 0.5 * (b * ((x * b) / y));
	} else {
		tmp = x / (y * a);
	}
	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 (b <= (-1.7d+119)) then
        tmp = 0.5d0 * (b * ((x * b) / y))
    else
        tmp = x / (y * a)
    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 (b <= -1.7e+119) {
		tmp = 0.5 * (b * ((x * b) / y));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e+119:
		tmp = 0.5 * (b * ((x * b) / y))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e+119)
		tmp = Float64(0.5 * Float64(b * Float64(Float64(x * b) / y)));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e+119)
		tmp = 0.5 * (b * ((x * b) / y));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e+119], N[(0.5 * N[(b * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.70000000000000007e119

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 89.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 89.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 73.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. associate-*l* N/A

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

       4. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{y}\right) \cdot \left(b \cdot \color{blue}{b}\right) \]

       5. associate-*r* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot \frac{x}{y}\right) \cdot b\right) \cdot \color{blue}{b} \]

       6. associate-*l* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left(\frac{x}{y} \cdot b\right)\right) \cdot b \]

       7. *-commutative N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left(b \cdot \frac{x}{y}\right)\right) \cdot b \]

       8. associate-/l* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{b \cdot x}{y}\right) \cdot b \]

       9. associate-*l* N/A

          \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{b \cdot x}{y} \cdot b\right)} \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{b \cdot x}{y} \cdot b\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\frac{b \cdot x}{y}\right), \color{blue}{b}\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(b \cdot x\right), y\right), b\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x \cdot b\right), y\right), b\right)\right) \]

       14. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, b\right), y\right), b\right)\right) \]

   11. Simplified 65.6%

       \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x \cdot b}{y} \cdot b\right)} \]

   if -1.70000000000000007e119 < b

   1. Initial program 98.4%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 62.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 62.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 62.6%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 55.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 55.4%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 34.5%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;0.5 \cdot \left(b \cdot \frac{x \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.8% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y} \cdot \left(0 - \left(b + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+106) (* (/ x y) (- 0.0 (+ b -1.0))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+106) {
		tmp = (x / y) * (0.0 - (b + -1.0));
	} else {
		tmp = x / (y * a);
	}
	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 (b <= (-3.5d+106)) then
        tmp = (x / y) * (0.0d0 - (b + (-1.0d0)))
    else
        tmp = x / (y * a)
    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 (b <= -3.5e+106) {
		tmp = (x / y) * (0.0 - (b + -1.0));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+106:
		tmp = (x / y) * (0.0 - (b + -1.0))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+106)
		tmp = Float64(Float64(x / y) * Float64(0.0 - Float64(b + -1.0)));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+106)
		tmp = (x / y) * (0.0 - (b + -1.0));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+106], N[(N[(x / y), $MachinePrecision] * N[(0.0 - N[(b + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.49999999999999981e106

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 84.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot \left(b \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot b\right) \cdot x + -1 \cdot x\right)\right)\right), y\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{1}{2} \cdot b\right), -1\right)\right)\right)\right), y\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

      13. *-lowering-*.f64 67.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1}{2}\right), -1\right)\right)\right)\right), y\right) \]

   8. Simplified 67.8%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{x \cdot \left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right)}{y}\right)}\right) \]

       4. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1}{y}\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(b \cdot \left(\frac{1}{2} \cdot b - 1\right)\right) - 1\right), \color{blue}{y}\right)\right)\right) \]

   11. Simplified 80.0%

       \[\leadsto \color{blue}{0 - x \cdot \frac{-1 + \left(0 - b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}} \]

   12. Taylor expanded in b around 0

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

       1. distribute-lft-out-- N/A

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

       2. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(\frac{b \cdot x}{y} - \frac{x}{y}\right)\right) \]

       3. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b \cdot x}{y} - \frac{x}{y}\right)\right) \]

       4. sub-neg N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b \cdot x}{y} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b \cdot x}{y} + -1 \cdot \frac{x}{y}\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(b \cdot \frac{x}{y} + -1 \cdot \frac{x}{y}\right)\right) \]

       7. distribute-rgt-out N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{x}{y} \cdot \left(b + -1\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{y}\right), \left(b + -1\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b + -1\right)\right)\right) \]

       10. +-lowering-+.f64 38.3%

           \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(b, -1\right)\right)\right) \]

   14. Simplified 38.3%

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

   if -3.49999999999999981e106 < b

   1. Initial program 98.3%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 62.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 63.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 63.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 55.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 55.7%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 34.9%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y} \cdot \left(0 - \left(b + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+111) (/ (* x (- 1.0 b)) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+111) {
		tmp = (x * (1.0 - b)) / y;
	} else {
		tmp = x / (y * a);
	}
	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 (b <= (-2.8d+111)) then
        tmp = (x * (1.0d0 - b)) / y
    else
        tmp = x / (y * a)
    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 (b <= -2.8e+111) {
		tmp = (x * (1.0 - b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e+111:
		tmp = (x * (1.0 - b)) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+111)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.8e+111)
		tmp = (x * (1.0 - b)) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+111], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7999999999999999e111

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 84.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + -1 \cdot \left(b \cdot x\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(-1 \cdot b\right) \cdot x\right), y\right) \]

      2. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot b + 1\right) \cdot x\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot b\right) \cdot x\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + -1 \cdot b\right), x\right), y\right) \]

      5. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right), x\right), y\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 38.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 38.3%

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

   if -2.7999999999999999e111 < b

   1. Initial program 98.3%

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

      1. associate-*l/ N/A

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

      2. exp-diff N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l/ N/A

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

      5. associate-/r/ N/A

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

      6. exp-diff N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

      9. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

      11. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      12. exp-sum N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

      15. exp-to-pow N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   3. Simplified 62.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

      3. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

      4. pow-lowering-pow.f64 63.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 63.0%

      \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 55.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   10. Simplified 55.7%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 34.9%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.7% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

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

C

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

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 * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. associate-*l/ N/A

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

   2. exp-diff N/A

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

   3. associate-*r/ N/A

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

   4. associate-*l/ N/A

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

   5. associate-/r/ N/A

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

   6. exp-diff N/A

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

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}\right)}\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{\color{blue}{b - \left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right)}}\right)\right) \]

   9. exp-diff N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{e^{b}}{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}\right)\right) \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(e^{b}\right), \color{blue}{\left(e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right)}\right)\right) \]

   11. exp-lowering-exp.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{\color{blue}{y \cdot \log z + \left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

   12. exp-sum N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(e^{y \cdot \log z} \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a}}\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{y \cdot \log z}\right), \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a}\right)}\right)\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left(e^{\log z \cdot y}\right), \left(e^{\color{blue}{\left(t - 1\right)} \cdot \log a}\right)\right)\right)\right) \]

   15. exp-to-pow N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\left({z}^{y}\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

   16. pow-lowering-pow.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), \left(e^{\color{blue}{\left(t - 1\right) \cdot \log a}}\right)\right)\right)\right) \]

3. Simplified 59.5%

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

5. Taylor expanded in t around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{a \cdot e^{b}}{{z}^{y}}\right)}\right) \]
6. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\left(a \cdot e^{b}\right), \color{blue}{\left({z}^{y}\right)}\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(e^{b}\right)\right), \left({\color{blue}{z}}^{y}\right)\right)\right) \]

   3. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \left({z}^{y}\right)\right)\right) \]

   4. pow-lowering-pow.f64 62.4%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right), \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

7. Simplified 62.4%

   \[\leadsto \frac{\frac{x}{y}}{\color{blue}{\frac{a \cdot e^{b}}{{z}^{y}}}} \]

8. Taylor expanded in y around 0

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

   3. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

   7. exp-lowering-exp.f64 60.2%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

10. Simplified 60.2%

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

11. Taylor expanded in b around 0

    \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]
12. Step-by-step derivation

13. Simplified 33.8%

    \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
14. Add Preprocessing

Alternative 17: 16.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / 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 = 1.0d0 / (y / x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

   3. --lowering--.f64 47.9%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 47.9%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, y\right) \]
7. Step-by-step derivation

8. Simplified 16.9%

   \[\leadsto \frac{\color{blue}{x}}{y} \]
9. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

   2. metadata-eval N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{x}\right)}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{x}\right)\right) \]

   5. /-lowering-/.f64 17.2%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

10. Applied egg-rr 17.2%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
11. Add Preprocessing

Alternative 18: 16.3% accurate, 105.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

   3. --lowering--.f64 47.9%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 47.9%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, y\right) \]
7. Step-by-step derivation

8. Simplified 16.9%

   \[\leadsto \frac{\color{blue}{x}}{y} \]
9. Add Preprocessing

Developer Target 1: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))