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

Percentage Accurate: 98.4% → 98.4%

Time: 16.5s

Alternatives: 20

Speedup: 1.0×

• 47.0% 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: 98.4% 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: 98.4% 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 99.3%

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

3. Final simplification 99.3%

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

Alternative 2: 82.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{z}^{y}}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow z y) y))))
   (if (<= y -1.2e+55)
     t_1
     (if (<= y 8.5e+17) (/ (* (pow a (+ t -1.0)) (/ 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(z, y) / y);
	double tmp;
	if (y <= -1.2e+55) {
		tmp = t_1;
	} else if (y <= 8.5e+17) {
		tmp = (pow(a, (t + -1.0)) * (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) :: tmp
    t_1 = x * ((z ** y) / y)
    if (y <= (-1.2d+55)) then
        tmp = t_1
    else if (y <= 8.5d+17) then
        tmp = ((a ** (t + (-1.0d0))) * (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(z, y) / y);
	double tmp;
	if (y <= -1.2e+55) {
		tmp = t_1;
	} else if (y <= 8.5e+17) {
		tmp = (Math.pow(a, (t + -1.0)) * (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(z, y) / y)
	tmp = 0
	if y <= -1.2e+55:
		tmp = t_1
	elif y <= 8.5e+17:
		tmp = (math.pow(a, (t + -1.0)) * (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((z ^ y) / y))
	tmp = 0.0
	if (y <= -1.2e+55)
		tmp = t_1;
	elseif (y <= 8.5e+17)
		tmp = Float64(Float64((a ^ Float64(t + -1.0)) * 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 * ((z ^ y) / y);
	tmp = 0.0;
	if (y <= -1.2e+55)
		tmp = t_1;
	elseif (y <= 8.5e+17)
		tmp = ((a ^ (t + -1.0)) * (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[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+55], t$95$1, If[LessEqual[y, 8.5e+17], N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e55 or 8.5e17 < 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 82.4%

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

   5. Simplified 82.4%

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

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

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

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

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

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

      7. pow-lowering-pow.f64 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -1.2e55 < y < 8.5e17

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 79.9%

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

   5. Simplified 79.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.45e+56)
     t_1
     (if (<= t 0.00055) (/ (* x (pow z y)) (* a (* y (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 <= -1.45e+56) {
		tmp = t_1;
	} else if (t <= 0.00055) {
		tmp = (x * pow(z, y)) / (a * (y * 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 <= (-1.45d+56)) then
        tmp = t_1
    else if (t <= 0.00055d0) then
        tmp = (x * (z ** y)) / (a * (y * 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 <= -1.45e+56) {
		tmp = t_1;
	} else if (t <= 0.00055) {
		tmp = (x * Math.pow(z, y)) / (a * (y * 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 <= -1.45e+56:
		tmp = t_1
	elif t <= 0.00055:
		tmp = (x * math.pow(z, y)) / (a * (y * 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 <= -1.45e+56)
		tmp = t_1;
	elseif (t <= 0.00055)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * 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 <= -1.45e+56)
		tmp = t_1;
	elseif (t <= 0.00055)
		tmp = (x * (z ^ y)) / (a * (y * 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, -1.45e+56], t$95$1, If[LessEqual[t, 0.00055], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45000000000000004e56 or 5.50000000000000033e-4 < 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 83.7%

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

   5. Simplified 83.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -1.45000000000000004e56 < t < 5.50000000000000033e-4

   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 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

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

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

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

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

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

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

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

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

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

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

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

      6. exp-lowering-exp.f64 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\\ t_2 := x + b \cdot \left(x - t\_1\right)\\ t_3 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-45}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.52 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(b \cdot \left(b \cdot \left(\frac{-0.16666666666666666 + \frac{0.5}{b}}{\frac{y}{x}} + \frac{\frac{x}{b} - x}{y \cdot \left(b \cdot b\right)}\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.75:\\ \;\;\;\;\frac{\frac{1}{y} \cdot \left(\left(x + b \cdot \left(t\_1 - x\right)\right) \cdot t\_2\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b (+ 0.5 (* b -0.16666666666666666)))))
        (t_2 (+ x (* b (- x t_1))))
        (t_3 (/ (/ x (exp b)) y)))
   (if (<= b -1.55e-45)
     t_3
     (if (<= b -1.52e-251)
       (/ x (* y a))
       (if (<= b 7.3e-211)
         (*
          b
          (*
           b
           (*
            b
            (+
             (/ (+ -0.16666666666666666 (/ 0.5 b)) (/ y x))
             (/ (- (/ x b) x) (* y (* b b)))))))
         (if (<= b 1.75)
           (/ (* (/ 1.0 y) (* (+ x (* b (- t_1 x))) t_2)) t_2)
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = x + (b * (x - t_1));
	double t_3 = (x / exp(b)) / y;
	double tmp;
	if (b <= -1.55e-45) {
		tmp = t_3;
	} else if (b <= -1.52e-251) {
		tmp = x / (y * a);
	} else if (b <= 7.3e-211) {
		tmp = b * (b * (b * (((-0.16666666666666666 + (0.5 / b)) / (y / x)) + (((x / b) - x) / (y * (b * b))))));
	} else if (b <= 1.75) {
		tmp = ((1.0 / y) * ((x + (b * (t_1 - x))) * t_2)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (b * (0.5d0 + (b * (-0.16666666666666666d0))))
    t_2 = x + (b * (x - t_1))
    t_3 = (x / exp(b)) / y
    if (b <= (-1.55d-45)) then
        tmp = t_3
    else if (b <= (-1.52d-251)) then
        tmp = x / (y * a)
    else if (b <= 7.3d-211) then
        tmp = b * (b * (b * ((((-0.16666666666666666d0) + (0.5d0 / b)) / (y / x)) + (((x / b) - x) / (y * (b * b))))))
    else if (b <= 1.75d0) then
        tmp = ((1.0d0 / y) * ((x + (b * (t_1 - x))) * t_2)) / t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.5 + (b * -0.16666666666666666)));
	double t_2 = x + (b * (x - t_1));
	double t_3 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -1.55e-45) {
		tmp = t_3;
	} else if (b <= -1.52e-251) {
		tmp = x / (y * a);
	} else if (b <= 7.3e-211) {
		tmp = b * (b * (b * (((-0.16666666666666666 + (0.5 / b)) / (y / x)) + (((x / b) - x) / (y * (b * b))))));
	} else if (b <= 1.75) {
		tmp = ((1.0 / y) * ((x + (b * (t_1 - x))) * t_2)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * (0.5 + (b * -0.16666666666666666)))
	t_2 = x + (b * (x - t_1))
	t_3 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -1.55e-45:
		tmp = t_3
	elif b <= -1.52e-251:
		tmp = x / (y * a)
	elif b <= 7.3e-211:
		tmp = b * (b * (b * (((-0.16666666666666666 + (0.5 / b)) / (y / x)) + (((x / b) - x) / (y * (b * b))))))
	elif b <= 1.75:
		tmp = ((1.0 / y) * ((x + (b * (t_1 - x))) * t_2)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))
	t_2 = Float64(x + Float64(b * Float64(x - t_1)))
	t_3 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -1.55e-45)
		tmp = t_3;
	elseif (b <= -1.52e-251)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 7.3e-211)
		tmp = Float64(b * Float64(b * Float64(b * Float64(Float64(Float64(-0.16666666666666666 + Float64(0.5 / b)) / Float64(y / x)) + Float64(Float64(Float64(x / b) - x) / Float64(y * Float64(b * b)))))));
	elseif (b <= 1.75)
		tmp = Float64(Float64(Float64(1.0 / y) * Float64(Float64(x + Float64(b * Float64(t_1 - x))) * t_2)) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * (0.5 + (b * -0.16666666666666666)));
	t_2 = x + (b * (x - t_1));
	t_3 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -1.55e-45)
		tmp = t_3;
	elseif (b <= -1.52e-251)
		tmp = x / (y * a);
	elseif (b <= 7.3e-211)
		tmp = b * (b * (b * (((-0.16666666666666666 + (0.5 / b)) / (y / x)) + (((x / b) - x) / (y * (b * b))))));
	elseif (b <= 1.75)
		tmp = ((1.0 / y) * ((x + (b * (t_1 - x))) * t_2)) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(x - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.55e-45], t$95$3, If[LessEqual[b, -1.52e-251], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.3e-211], N[(b * N[(b * N[(b * N[(N[(N[(-0.16666666666666666 + N[(0.5 / b), $MachinePrecision]), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / b), $MachinePrecision] - x), $MachinePrecision] / N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75], N[(N[(N[(1.0 / y), $MachinePrecision] * N[(N[(x + N[(b * N[(t$95$1 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55e-45 or 1.75 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 72.2%

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

   5. Simplified 72.2%

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

      1. sub0-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. rec-exp N/A

         \[\leadsto \frac{x \cdot \frac{1}{e^{b}}}{y} \]

      3. div-inv N/A

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

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

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

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

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

      6. exp-lowering-exp.f64 72.2%

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

   7. Applied egg-rr 72.2%

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

   if -1.55e-45 < b < -1.52e-251

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 69.8%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 48.3%

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

   11. Simplified 48.3%

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

   if -1.52e-251 < b < 7.29999999999999968e-211

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 10.3%

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

   5. Simplified 10.3%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 10.3%

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

   8. Simplified 10.3%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{{b}^{3} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \left(b \cdot {b}^{2}\right) \cdot \left(-1 \cdot \color{blue}{\frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto b \cdot \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{\left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(b \cdot b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

       8. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right) + \color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}}\right)\right)\right) \]

       9. associate-+r+ N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \frac{1}{2} \cdot \frac{x}{b \cdot y}\right) + \frac{x}{{b}^{3} \cdot y}\right) + \color{blue}{-1} \cdot \frac{x}{{b}^{2} \cdot y}\right)\right)\right) \]

   11. Simplified 0.0%

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

       1. associate-*l* N/A

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

       2. *-commutative N/A

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

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

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

   13. Applied egg-rr 54.5%

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

   if 7.29999999999999968e-211 < b < 1.75

   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. 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 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 25.2%

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

   8. Simplified 25.2%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. *-lowering-*.f64 25.2%

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

   10. Applied egg-rr 25.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}} \]
   11. Step-by-step derivation

       1. associate-/r/ N/A

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

       2. flip-+ N/A

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

       3. associate-*r/ N/A

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

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

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

   12. Applied egg-rr 51.6%

       \[\leadsto \color{blue}{\frac{\frac{1}{y} \cdot \left(\left(x + b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)\right) \cdot \left(x - b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)\right)\right)}{x - b \cdot \left(x \cdot \left(\left(0.5 + b \cdot -0.16666666666666666\right) \cdot b\right) - x\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -1.52 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(b \cdot \left(b \cdot \left(\frac{-0.16666666666666666 + \frac{0.5}{b}}{\frac{y}{x}} + \frac{\frac{x}{b} - x}{y \cdot \left(b \cdot b\right)}\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.75:\\ \;\;\;\;\frac{\frac{1}{y} \cdot \left(\left(x + b \cdot \left(x \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)\right) \cdot \left(x + b \cdot \left(x - x \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)\right)\right)}{x + b \cdot \left(x - x \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.65e+56)
   (* x (/ (pow a t) y))
   (if (<= t 1.65e-159)
     (/ (/ x (* a (exp b))) y)
     (if (<= t 5.9e-21)
       (* x (/ (pow z y) y))
       (/ (* x (pow a (+ t -1.0))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+56) {
		tmp = x * (pow(a, t) / y);
	} else if (t <= 1.65e-159) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 5.9e-21) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.65d+56)) then
        tmp = x * ((a ** t) / y)
    else if (t <= 1.65d-159) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 5.9d-21) then
        tmp = x * ((z ** y) / y)
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+56) {
		tmp = x * (Math.pow(a, t) / y);
	} else if (t <= 1.65e-159) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 5.9e-21) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.65e+56:
		tmp = x * (math.pow(a, t) / y)
	elif t <= 1.65e-159:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 5.9e-21:
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.65e+56)
		tmp = Float64(x * Float64((a ^ t) / y));
	elseif (t <= 1.65e-159)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 5.9e-21)
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.65e+56)
		tmp = x * ((a ^ t) / y);
	elseif (t <= 1.65e-159)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 5.9e-21)
		tmp = x * ((z ^ y) / y);
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.65e+56], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-159], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 5.9e-21], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65000000000000001e56

   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 87.7%

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

   5. Simplified 87.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 87.7%

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

   7. Applied egg-rr 87.7%

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

   if -1.65000000000000001e56 < t < 1.6500000000000001e-159

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. exp-lowering-exp.f64 75.9%

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

   8. Simplified 75.9%

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

   if 1.6500000000000001e-159 < t < 5.9000000000000003e-21

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 73.8%

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

   5. Simplified 73.8%

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

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

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

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

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

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

      7. pow-lowering-pow.f64 73.8%

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

   7. Applied egg-rr 73.8%

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

   if 5.9000000000000003e-21 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 78.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.75e+56)
     t_1
     (if (<= t 2.4e-153)
       (/ (/ x (* a (exp b))) y)
       (if (<= t 0.00055) (* x (/ (pow z y) 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 tmp;
	if (t <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 2.4e-153) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 0.00055) {
		tmp = x * (pow(z, y) / 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 * ((a ** t) / y)
    if (t <= (-1.75d+56)) then
        tmp = t_1
    else if (t <= 2.4d-153) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 0.00055d0) then
        tmp = x * ((z ** y) / 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 tmp;
	if (t <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 2.4e-153) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 0.00055) {
		tmp = x * (Math.pow(z, y) / y);
	} 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 <= -1.75e+56:
		tmp = t_1
	elif t <= 2.4e-153:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 0.00055:
		tmp = x * (math.pow(z, y) / y)
	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 <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 2.4e-153)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 0.00055)
		tmp = Float64(x * Float64((z ^ y) / 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);
	tmp = 0.0;
	if (t <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 2.4e-153)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 0.00055)
		tmp = x * ((z ^ y) / 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]}, If[LessEqual[t, -1.75e+56], t$95$1, If[LessEqual[t, 2.4e-153], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.00055], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e56 or 5.50000000000000033e-4 < 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 83.7%

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

   5. Simplified 83.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -1.75e56 < t < 2.4000000000000002e-153

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. exp-lowering-exp.f64 75.9%

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

   8. Simplified 75.9%

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

   if 2.4000000000000002e-153 < t < 5.50000000000000033e-4

   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 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 68.2%

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

   5. Simplified 68.2%

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

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

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

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

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

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

      7. pow-lowering-pow.f64 68.2%

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

   7. Applied egg-rr 68.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.35e+56)
     t_1
     (if (<= t 4.1e-154)
       (/ x (* a (* y (exp b))))
       (if (<= t 0.00055) (* x (/ (pow z y) 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 tmp;
	if (t <= -1.35e+56) {
		tmp = t_1;
	} else if (t <= 4.1e-154) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= 0.00055) {
		tmp = x * (pow(z, y) / 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 * ((a ** t) / y)
    if (t <= (-1.35d+56)) then
        tmp = t_1
    else if (t <= 4.1d-154) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= 0.00055d0) then
        tmp = x * ((z ** y) / 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 tmp;
	if (t <= -1.35e+56) {
		tmp = t_1;
	} else if (t <= 4.1e-154) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= 0.00055) {
		tmp = x * (Math.pow(z, y) / y);
	} 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 <= -1.35e+56:
		tmp = t_1
	elif t <= 4.1e-154:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= 0.00055:
		tmp = x * (math.pow(z, y) / y)
	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 <= -1.35e+56)
		tmp = t_1;
	elseif (t <= 4.1e-154)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= 0.00055)
		tmp = Float64(x * Float64((z ^ y) / 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);
	tmp = 0.0;
	if (t <= -1.35e+56)
		tmp = t_1;
	elseif (t <= 4.1e-154)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= 0.00055)
		tmp = x * ((z ^ y) / 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]}, If[LessEqual[t, -1.35e+56], t$95$1, If[LessEqual[t, 4.1e-154], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00055], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000005e56 or 5.50000000000000033e-4 < 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 83.7%

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

   5. Simplified 83.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -1.35000000000000005e56 < t < 4.1e-154

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. 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. *-lowering-*.f64 N/A

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

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

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

      4. exp-lowering-exp.f64 75.0%

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

   8. Simplified 75.0%

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

   if 4.1e-154 < t < 5.50000000000000033e-4

   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 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 68.2%

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

   5. Simplified 68.2%

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

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

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

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

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

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

      7. pow-lowering-pow.f64 68.2%

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

   7. Applied egg-rr 68.2%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.3e+56)
     t_1
     (if (<= t 2.7e-155)
       (/ (/ x (exp b)) y)
       (if (<= t 0.00055) (* x (/ (pow z y) 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 tmp;
	if (t <= -1.3e+56) {
		tmp = t_1;
	} else if (t <= 2.7e-155) {
		tmp = (x / exp(b)) / y;
	} else if (t <= 0.00055) {
		tmp = x * (pow(z, y) / 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 * ((a ** t) / y)
    if (t <= (-1.3d+56)) then
        tmp = t_1
    else if (t <= 2.7d-155) then
        tmp = (x / exp(b)) / y
    else if (t <= 0.00055d0) then
        tmp = x * ((z ** y) / 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 tmp;
	if (t <= -1.3e+56) {
		tmp = t_1;
	} else if (t <= 2.7e-155) {
		tmp = (x / Math.exp(b)) / y;
	} else if (t <= 0.00055) {
		tmp = x * (Math.pow(z, y) / y);
	} 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 <= -1.3e+56:
		tmp = t_1
	elif t <= 2.7e-155:
		tmp = (x / math.exp(b)) / y
	elif t <= 0.00055:
		tmp = x * (math.pow(z, y) / y)
	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 <= -1.3e+56)
		tmp = t_1;
	elseif (t <= 2.7e-155)
		tmp = Float64(Float64(x / exp(b)) / y);
	elseif (t <= 0.00055)
		tmp = Float64(x * Float64((z ^ y) / 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);
	tmp = 0.0;
	if (t <= -1.3e+56)
		tmp = t_1;
	elseif (t <= 2.7e-155)
		tmp = (x / exp(b)) / y;
	elseif (t <= 0.00055)
		tmp = x * ((z ^ y) / 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]}, If[LessEqual[t, -1.3e+56], t$95$1, If[LessEqual[t, 2.7e-155], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.00055], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.30000000000000005e56 or 5.50000000000000033e-4 < 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 83.7%

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

   5. Simplified 83.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 83.7%

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

   7. Applied egg-rr 83.7%

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

   if -1.30000000000000005e56 < t < 2.69999999999999981e-155

   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. 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 57.8%

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

   5. Simplified 57.8%

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

      1. sub0-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. rec-exp N/A

         \[\leadsto \frac{x \cdot \frac{1}{e^{b}}}{y} \]

      3. div-inv N/A

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

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

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

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

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

      6. exp-lowering-exp.f64 57.8%

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

   7. Applied egg-rr 57.8%

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

   if 2.69999999999999981e-155 < t < 5.50000000000000033e-4

   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 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 68.2%

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

   5. Simplified 68.2%

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

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

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

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

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

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

      7. pow-lowering-pow.f64 68.2%

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

   7. Applied egg-rr 68.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;t \leq 0.00055:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{1}{\frac{\frac{y \cdot -6}{x}}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.75e+56)
     t_1
     (if (<= t 8.2e-120)
       (/ (/ x (exp b)) y)
       (if (<= t 3.4e-14) (/ 1.0 (/ (/ (* y -6.0) x) (* b (* b 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 <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 8.2e-120) {
		tmp = (x / exp(b)) / y;
	} else if (t <= 3.4e-14) {
		tmp = 1.0 / (((y * -6.0) / x) / (b * (b * 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 <= (-1.75d+56)) then
        tmp = t_1
    else if (t <= 8.2d-120) then
        tmp = (x / exp(b)) / y
    else if (t <= 3.4d-14) then
        tmp = 1.0d0 / (((y * (-6.0d0)) / x) / (b * (b * 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 <= -1.75e+56) {
		tmp = t_1;
	} else if (t <= 8.2e-120) {
		tmp = (x / Math.exp(b)) / y;
	} else if (t <= 3.4e-14) {
		tmp = 1.0 / (((y * -6.0) / x) / (b * (b * 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 <= -1.75e+56:
		tmp = t_1
	elif t <= 8.2e-120:
		tmp = (x / math.exp(b)) / y
	elif t <= 3.4e-14:
		tmp = 1.0 / (((y * -6.0) / x) / (b * (b * 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 <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 8.2e-120)
		tmp = Float64(Float64(x / exp(b)) / y);
	elseif (t <= 3.4e-14)
		tmp = Float64(1.0 / Float64(Float64(Float64(y * -6.0) / x) / Float64(b * Float64(b * 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 <= -1.75e+56)
		tmp = t_1;
	elseif (t <= 8.2e-120)
		tmp = (x / exp(b)) / y;
	elseif (t <= 3.4e-14)
		tmp = 1.0 / (((y * -6.0) / x) / (b * (b * 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, -1.75e+56], t$95$1, If[LessEqual[t, 8.2e-120], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 3.4e-14], N[(1.0 / N[(N[(N[(y * -6.0), $MachinePrecision] / x), $MachinePrecision] / N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e56 or 3.40000000000000003e-14 < 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 83.1%

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

   5. Simplified 83.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t}}}{y} \]
   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 83.1%

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

   7. Applied egg-rr 83.1%

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

   if -1.75e56 < t < 8.20000000000000068e-120

   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 55.5%

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

   5. Simplified 55.5%

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

      1. sub0-neg N/A

         \[\leadsto \frac{x \cdot e^{\mathsf{neg}\left(b\right)}}{y} \]

      2. rec-exp N/A

         \[\leadsto \frac{x \cdot \frac{1}{e^{b}}}{y} \]

      3. div-inv N/A

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

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

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

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

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

      6. exp-lowering-exp.f64 55.5%

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

   7. Applied egg-rr 55.5%

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

   if 8.20000000000000068e-120 < t < 3.40000000000000003e-14

   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 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 26.8%

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

   8. Simplified 26.8%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. *-lowering-*.f64 28.6%

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

   10. Applied egg-rr 28.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}} \]

   11. Taylor expanded in b around inf

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/r* N/A

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

       4. associate-*r/ N/A

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

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

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

       6. associate-*r/ N/A

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

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

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

       8. *-commutative N/A

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

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

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

       10. cube-mult N/A

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

       11. unpow2 N/A

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

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

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

       13. unpow2 N/A

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

       14. *-lowering-*.f64 53.0%

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

   13. Simplified 53.0%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{y \cdot -6}{x}}{b \cdot \left(b \cdot b\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{1}{\frac{\frac{y \cdot -6}{x}}{b \cdot \left(b \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.3% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+135}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) 0.5)) y)))
   (if (<= b -4.6e+92)
     t_1
     (if (<= b -3.8e-231)
       (/ x (* y a))
       (if (<= b 1.4e-247)
         t_1
         (if (<= b 8e+135) (/ (* x (/ 1.0 a)) y) (* b (/ x (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * 0.5)) / y;
	double tmp;
	if (b <= -4.6e+92) {
		tmp = t_1;
	} else if (b <= -3.8e-231) {
		tmp = x / (y * a);
	} else if (b <= 1.4e-247) {
		tmp = t_1;
	} else if (b <= 8e+135) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = b * (x / (y * 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 = (x * ((b * b) * 0.5d0)) / y
    if (b <= (-4.6d+92)) then
        tmp = t_1
    else if (b <= (-3.8d-231)) then
        tmp = x / (y * a)
    else if (b <= 1.4d-247) then
        tmp = t_1
    else if (b <= 8d+135) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = b * (x / (y * 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 = (x * ((b * b) * 0.5)) / y;
	double tmp;
	if (b <= -4.6e+92) {
		tmp = t_1;
	} else if (b <= -3.8e-231) {
		tmp = x / (y * a);
	} else if (b <= 1.4e-247) {
		tmp = t_1;
	} else if (b <= 8e+135) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = b * (x / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * 0.5)) / y
	tmp = 0
	if b <= -4.6e+92:
		tmp = t_1
	elif b <= -3.8e-231:
		tmp = x / (y * a)
	elif b <= 1.4e-247:
		tmp = t_1
	elif b <= 8e+135:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = b * (x / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * 0.5)) / y)
	tmp = 0.0
	if (b <= -4.6e+92)
		tmp = t_1;
	elseif (b <= -3.8e-231)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.4e-247)
		tmp = t_1;
	elseif (b <= 8e+135)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(b * Float64(x / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * 0.5)) / y;
	tmp = 0.0;
	if (b <= -4.6e+92)
		tmp = t_1;
	elseif (b <= -3.8e-231)
		tmp = x / (y * a);
	elseif (b <= 1.4e-247)
		tmp = t_1;
	elseif (b <= 8e+135)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = b * (x / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -4.6e+92], t$95$1, If[LessEqual[b, -3.8e-231], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-247], t$95$1, If[LessEqual[b, 8e+135], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(b * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.59999999999999997e92 or -3.80000000000000013e-231 < b < 1.39999999999999993e-247

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in b around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 63.2%

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

   11. Simplified 63.2%

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

   if -4.59999999999999997e92 < b < -3.80000000000000013e-231

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 68.7%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 38.8%

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

   11. Simplified 38.8%

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

   if 1.39999999999999993e-247 < b < 7.99999999999999969e135

   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 y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 60.3%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 35.5%

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

   11. Simplified 35.5%

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

   if 7.99999999999999969e135 < 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 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 1.3%

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

   8. Simplified 1.3%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{{b}^{3} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \left(b \cdot {b}^{2}\right) \cdot \left(-1 \cdot \color{blue}{\frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto b \cdot \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{\left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(b \cdot b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

       8. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right) + \color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}}\right)\right)\right) \]

       9. associate-+r+ N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \frac{1}{2} \cdot \frac{x}{b \cdot y}\right) + \frac{x}{{b}^{3} \cdot y}\right) + \color{blue}{-1} \cdot \frac{x}{{b}^{2} \cdot y}\right)\right)\right) \]

   11. Simplified 1.3%

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

   12. Taylor expanded in b around 0

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

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 42.0%

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

   14. Simplified 42.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+135}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.5% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-31}:\\ \;\;\;\;\left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.95e-31)
   (* (* b (* (* b b) -0.16666666666666666)) (/ x y))
   (if (<= b -4.2e-226)
     (/ x (* y a))
     (if (<= b 1.8e-247)
       (/ (* x (* (* b b) 0.5)) y)
       (/ (/ x (* a (+ 1.0 b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e-31) {
		tmp = (b * ((b * b) * -0.16666666666666666)) * (x / y);
	} else if (b <= -4.2e-226) {
		tmp = x / (y * a);
	} else if (b <= 1.8e-247) {
		tmp = (x * ((b * b) * 0.5)) / y;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.95d-31)) then
        tmp = (b * ((b * b) * (-0.16666666666666666d0))) * (x / y)
    else if (b <= (-4.2d-226)) then
        tmp = x / (y * a)
    else if (b <= 1.8d-247) then
        tmp = (x * ((b * b) * 0.5d0)) / y
    else
        tmp = (x / (a * (1.0d0 + b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e-31) {
		tmp = (b * ((b * b) * -0.16666666666666666)) * (x / y);
	} else if (b <= -4.2e-226) {
		tmp = x / (y * a);
	} else if (b <= 1.8e-247) {
		tmp = (x * ((b * b) * 0.5)) / y;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.95e-31:
		tmp = (b * ((b * b) * -0.16666666666666666)) * (x / y)
	elif b <= -4.2e-226:
		tmp = x / (y * a)
	elif b <= 1.8e-247:
		tmp = (x * ((b * b) * 0.5)) / y
	else:
		tmp = (x / (a * (1.0 + b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.95e-31)
		tmp = Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) * Float64(x / y));
	elseif (b <= -4.2e-226)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.8e-247)
		tmp = Float64(Float64(x * Float64(Float64(b * b) * 0.5)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.95e-31)
		tmp = (b * ((b * b) * -0.16666666666666666)) * (x / y);
	elseif (b <= -4.2e-226)
		tmp = x / (y * a);
	elseif (b <= 1.8e-247)
		tmp = (x * ((b * b) * 0.5)) / y;
	else
		tmp = (x / (a * (1.0 + b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.95e-31], N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.2e-226], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-247], N[(N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9500000000000001e-31

   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 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in b around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

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

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

       5. cube-mult N/A

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

       6. unpow2 N/A

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 56.3%

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

   11. Simplified 56.3%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

       6. associate-*l* N/A

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

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

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

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

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

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

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

       10. /-lowering-/.f64 53.8%

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

   13. Applied egg-rr 53.8%

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

   if -1.9500000000000001e-31 < b < -4.2000000000000003e-226

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 74.5%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 49.2%

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

   11. Simplified 49.2%

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

   if -4.2000000000000003e-226 < b < 1.7999999999999998e-247

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 11.5%

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

   5. Simplified 11.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 11.5%

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

   8. Simplified 11.5%

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

   9. Taylor expanded in b around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 50.9%

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

   11. Simplified 50.9%

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

   if 1.7999999999999998e-247 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. exp-lowering-exp.f64 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in b around 0

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

       1. *-commutative N/A

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

       2. distribute-rgt1-in N/A

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

       3. +-commutative N/A

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

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

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

       5. +-commutative N/A

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

       6. +-lowering-+.f64 41.8%

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

   11. Simplified 41.8%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-31}:\\ \;\;\;\;\left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.0% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(b \cdot \frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y}\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+58)
   (* b (* b (/ (* x (* b -0.16666666666666666)) y)))
   (if (<= b -5.5e-229)
     (/ x (* y a))
     (if (<= b 1.35e-247)
       (/ (* x (* (* b b) 0.5)) y)
       (/ (/ x (* a (+ 1.0 b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+58) {
		tmp = b * (b * ((x * (b * -0.16666666666666666)) / y));
	} else if (b <= -5.5e-229) {
		tmp = x / (y * a);
	} else if (b <= 1.35e-247) {
		tmp = (x * ((b * b) * 0.5)) / y;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d+58)) then
        tmp = b * (b * ((x * (b * (-0.16666666666666666d0))) / y))
    else if (b <= (-5.5d-229)) then
        tmp = x / (y * a)
    else if (b <= 1.35d-247) then
        tmp = (x * ((b * b) * 0.5d0)) / y
    else
        tmp = (x / (a * (1.0d0 + b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+58) {
		tmp = b * (b * ((x * (b * -0.16666666666666666)) / y));
	} else if (b <= -5.5e-229) {
		tmp = x / (y * a);
	} else if (b <= 1.35e-247) {
		tmp = (x * ((b * b) * 0.5)) / y;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+58:
		tmp = b * (b * ((x * (b * -0.16666666666666666)) / y))
	elif b <= -5.5e-229:
		tmp = x / (y * a)
	elif b <= 1.35e-247:
		tmp = (x * ((b * b) * 0.5)) / y
	else:
		tmp = (x / (a * (1.0 + b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+58)
		tmp = Float64(b * Float64(b * Float64(Float64(x * Float64(b * -0.16666666666666666)) / y)));
	elseif (b <= -5.5e-229)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.35e-247)
		tmp = Float64(Float64(x * Float64(Float64(b * b) * 0.5)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+58)
		tmp = b * (b * ((x * (b * -0.16666666666666666)) / y));
	elseif (b <= -5.5e-229)
		tmp = x / (y * a);
	elseif (b <= 1.35e-247)
		tmp = (x * ((b * b) * 0.5)) / y;
	else
		tmp = (x / (a * (1.0 + b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+58], N[(b * N[(b * N[(N[(x * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-229], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e-247], N[(N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.49999999999999993e58

   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 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot x}{y} \cdot \color{blue}{\frac{-1}{6}} \]

       2. associate-/l* N/A

          \[\leadsto \left({b}^{3} \cdot \frac{x}{y}\right) \cdot \frac{-1}{6} \]

       3. associate-*r* N/A

          \[\leadsto {b}^{3} \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{-1}{6}\right)} \]

       4. *-commutative N/A

          \[\leadsto {b}^{3} \cdot \left(\frac{-1}{6} \cdot \color{blue}{\frac{x}{y}}\right) \]

       5. cube-mult N/A

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

       6. unpow2 N/A

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

       7. associate-*l* N/A

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

       8. associate-*r/ N/A

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

       9. associate-*r/ N/A

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

       10. unpow2 N/A

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

       11. associate-*l* N/A

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

       12. *-commutative N/A

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

       13. associate-*r* N/A

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

       14. *-commutative N/A

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

       15. associate-*r/ N/A

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

       16. associate-*r/ N/A

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

       17. *-commutative N/A

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

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

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

       19. *-commutative N/A

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

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

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

       21. associate-*r/ N/A

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

       22. /-lowering-/.f64 N/A

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

   11. Simplified 63.8%

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

   if -2.49999999999999993e58 < b < -5.5000000000000001e-229

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 70.3%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 40.5%

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

   11. Simplified 40.5%

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

   if -5.5000000000000001e-229 < b < 1.35000000000000004e-247

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 11.5%

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

   5. Simplified 11.5%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 11.5%

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

   8. Simplified 11.5%

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

   9. Taylor expanded in b around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 50.9%

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

   11. Simplified 50.9%

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

   if 1.35000000000000004e-247 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. exp-lowering-exp.f64 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in b around 0

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

       1. *-commutative N/A

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

       2. distribute-rgt1-in N/A

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

       3. +-commutative N/A

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

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

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

       5. +-commutative N/A

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

       6. +-lowering-+.f64 41.8%

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

   11. Simplified 41.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(b \cdot \frac{x \cdot \left(b \cdot -0.16666666666666666\right)}{y}\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) 0.5)) y)))
   (if (<= b -3.4e+92)
     t_1
     (if (<= b -1.35e-224)
       (/ x (* y a))
       (if (<= b 1.8e-247) t_1 (/ (/ x (* a (+ 1.0 b))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * 0.5)) / y;
	double tmp;
	if (b <= -3.4e+92) {
		tmp = t_1;
	} else if (b <= -1.35e-224) {
		tmp = x / (y * a);
	} else if (b <= 1.8e-247) {
		tmp = t_1;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((b * b) * 0.5d0)) / y
    if (b <= (-3.4d+92)) then
        tmp = t_1
    else if (b <= (-1.35d-224)) then
        tmp = x / (y * a)
    else if (b <= 1.8d-247) then
        tmp = t_1
    else
        tmp = (x / (a * (1.0d0 + b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * 0.5)) / y;
	double tmp;
	if (b <= -3.4e+92) {
		tmp = t_1;
	} else if (b <= -1.35e-224) {
		tmp = x / (y * a);
	} else if (b <= 1.8e-247) {
		tmp = t_1;
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * 0.5)) / y
	tmp = 0
	if b <= -3.4e+92:
		tmp = t_1
	elif b <= -1.35e-224:
		tmp = x / (y * a)
	elif b <= 1.8e-247:
		tmp = t_1
	else:
		tmp = (x / (a * (1.0 + b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * 0.5)) / y)
	tmp = 0.0
	if (b <= -3.4e+92)
		tmp = t_1;
	elseif (b <= -1.35e-224)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.8e-247)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * 0.5)) / y;
	tmp = 0.0;
	if (b <= -3.4e+92)
		tmp = t_1;
	elseif (b <= -1.35e-224)
		tmp = x / (y * a);
	elseif (b <= 1.8e-247)
		tmp = t_1;
	else
		tmp = (x / (a * (1.0 + b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.4e+92], t$95$1, If[LessEqual[b, -1.35e-224], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-247], t$95$1, N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3999999999999998e92 or -1.34999999999999999e-224 < b < 1.7999999999999998e-247

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in b around inf

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

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

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

       2. unpow2 N/A

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

       3. *-lowering-*.f64 63.2%

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

   11. Simplified 63.2%

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

   if -3.3999999999999998e92 < b < -1.34999999999999999e-224

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. exp-to-pow N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. exp-lowering-exp.f64 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 68.7%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 38.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   11. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 1.7999999999999998e-247 < b

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 66.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 66.1%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a \cdot e^{b}}\right)}, y\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-lowering-exp.f64 63.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 63.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a + b \cdot a\right)\right), y\right) \]

       2. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(b + 1\right) \cdot a\right)\right), y\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(1 + b\right) \cdot a\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(1 + b\right), a\right)\right), y\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(b + 1\right), a\right)\right), y\right) \]

       6. +-lowering-+.f64 41.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), a\right)\right), y\right) \]

   11. Simplified 41.8%

       \[\leadsto \frac{\frac{x}{\color{blue}{\left(b + 1\right) \cdot a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.4% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5e-122)
   (* x (/ (* b (* (* b b) -0.16666666666666666)) y))
   (/
    (/ x (* a (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
    y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e-122) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5d-122) then
        tmp = x * ((b * ((b * b) * (-0.16666666666666666d0))) / y)
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e-122) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5e-122:
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y)
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5e-122)
		tmp = Float64(x * Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) / y));
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5e-122)
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5e-122], N[(x * N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / 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] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.9999999999999999e-122

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 41.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 41.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(x\right)\right) + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 35.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 35.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 46.1%

       \[\leadsto \frac{\color{blue}{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}}{y} \]
   12. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y} \cdot \color{blue}{x} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\right), \color{blue}{x}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot b\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(b \cdot \frac{-1}{6}\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       10. *-lowering-*.f64 49.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right), x\right) \]

   13. Applied egg-rr 49.0%

       \[\leadsto \color{blue}{\frac{b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot b\right)\right)}{y} \cdot x} \]

   if 4.9999999999999999e-122 < b

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 66.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 66.8%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a \cdot e^{b}}\right)}, y\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-lowering-exp.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 73.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right)\right), y\right) \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right)\right), y\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{1}{6}\right)\right)\right)\right)\right)\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 66.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right)\right)\right)\right)\right)\right)\right), y\right) \]

   11. Simplified 66.5%

       \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.6 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.6e-121)
   (* x (/ (* b (* (* b b) -0.16666666666666666)) y))
   (/ (/ x (* a (+ 1.0 (* b (+ 1.0 (* b 0.5)))))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.6e-121) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.6d-121) then
        tmp = x * ((b * ((b * b) * (-0.16666666666666666d0))) / y)
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * 0.5d0)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.6e-121) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.6e-121:
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y)
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.6e-121)
		tmp = Float64(x * Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) / y));
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.6e-121)
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.6e-121], N[(x * N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.6000000000000002e-121

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 41.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 41.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(x\right)\right) + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 35.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 35.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 46.1%

       \[\leadsto \frac{\color{blue}{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}}{y} \]
   12. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y} \cdot \color{blue}{x} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\right), \color{blue}{x}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot b\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(b \cdot \frac{-1}{6}\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       10. *-lowering-*.f64 49.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right), x\right) \]

   13. Applied egg-rr 49.0%

       \[\leadsto \color{blue}{\frac{b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot b\right)\right)}{y} \cdot x} \]

   if 5.6000000000000002e-121 < b

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 66.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 66.8%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a \cdot e^{b}}\right)}, y\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-lowering-exp.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 73.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right)\right), y\right) \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right)\right), y\right) \]

       5. *-lowering-*.f64 62.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right)\right), y\right) \]

   11. Simplified 62.8%

       \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.6 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.3% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.5e-121)
   (* x (/ (* b (* (* b b) -0.16666666666666666)) y))
   (/ (/ x (* a (+ 1.0 b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.5e-121) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.5d-121) then
        tmp = x * ((b * ((b * b) * (-0.16666666666666666d0))) / y)
    else
        tmp = (x / (a * (1.0d0 + b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.5e-121) {
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	} else {
		tmp = (x / (a * (1.0 + b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.5e-121:
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y)
	else:
		tmp = (x / (a * (1.0 + b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.5e-121)
		tmp = Float64(x * Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) / y));
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.5e-121)
		tmp = x * ((b * ((b * b) * -0.16666666666666666)) / y);
	else
		tmp = (x / (a * (1.0 + b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.5e-121], N[(x * N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.50000000000000031e-121

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 41.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 41.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(x\right)\right) + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 35.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 35.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 46.1%

       \[\leadsto \frac{\color{blue}{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}}{y} \]
   12. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto x \cdot \color{blue}{\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y} \cdot \color{blue}{x} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\right), \color{blue}{x}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{6} \cdot \left(b \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot b\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(b \cdot \frac{-1}{6}\right) \cdot \left(b \cdot b\right)\right), y\right), x\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot b\right)\right)\right), y\right), x\right) \]

       10. *-lowering-*.f64 49.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right), x\right) \]

   13. Applied egg-rr 49.0%

       \[\leadsto \color{blue}{\frac{b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot b\right)\right)}{y} \cdot x} \]

   if 5.50000000000000031e-121 < b

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 66.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 66.8%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a \cdot e^{b}}\right)}, y\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-lowering-exp.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 73.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a + b \cdot a\right)\right), y\right) \]

       2. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(b + 1\right) \cdot a\right)\right), y\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(1 + b\right) \cdot a\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(1 + b\right), a\right)\right), y\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(b + 1\right), a\right)\right), y\right) \]

       6. +-lowering-+.f64 43.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), a\right)\right), y\right) \]

   11. Simplified 43.1%

       \[\leadsto \frac{\frac{x}{\color{blue}{\left(b + 1\right) \cdot a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 4.8e-18) (/ x (* y a)) (* b (/ x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 4.8e-18) {
		tmp = x / (y * a);
	} else {
		tmp = b * (x / (y * 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 (t <= 4.8d-18) then
        tmp = x / (y * a)
    else
        tmp = b * (x / (y * 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 (t <= 4.8e-18) {
		tmp = x / (y * a);
	} else {
		tmp = b * (x / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 4.8e-18:
		tmp = x / (y * a)
	else:
		tmp = b * (x / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 4.8e-18)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(b * Float64(x / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 4.8e-18)
		tmp = x / (y * a);
	else
		tmp = b * (x / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 4.8e-18], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(b * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.79999999999999988e-18

   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 y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 65.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 65.6%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 52.3%

      \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot \color{blue}{x}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 34.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   11. Simplified 34.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 4.79999999999999988e-18 < 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 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 48.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 48.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(x\right)\right) + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 29.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 29.5%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{{b}^{3} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \left(b \cdot {b}^{2}\right) \cdot \left(-1 \cdot \color{blue}{\frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto b \cdot \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left({b}^{2} \cdot \left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{\left(-1 \cdot \frac{x}{{b}^{2} \cdot y} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(b \cdot b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}} + \left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right)\right)\right)\right) \]

       8. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \left(\frac{1}{2} \cdot \frac{x}{b \cdot y} + \frac{x}{{b}^{3} \cdot y}\right)\right) + \color{blue}{-1 \cdot \frac{x}{{b}^{2} \cdot y}}\right)\right)\right) \]

       9. associate-+r+ N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\left(\left(\frac{-1}{6} \cdot \frac{x}{y} + \frac{1}{2} \cdot \frac{x}{b \cdot y}\right) + \frac{x}{{b}^{3} \cdot y}\right) + \color{blue}{-1} \cdot \frac{x}{{b}^{2} \cdot y}\right)\right)\right) \]

   11. Simplified 24.5%

       \[\leadsto \color{blue}{b \cdot \left(\left(b \cdot b\right) \cdot \left(\frac{x}{y} \cdot \left(-0.16666666666666666 + \frac{0.5}{b}\right) + \left(\frac{x}{b \cdot \left(y \cdot \left(b \cdot b\right)\right)} - \frac{x}{y \cdot \left(b \cdot b\right)}\right)\right)\right)} \]

   12. Taylor expanded in b around 0

       \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{x}{b \cdot y}\right)}\right) \]
   13. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(x, \color{blue}{\left(b \cdot y\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{b}\right)\right)\right) \]

       3. *-lowering-*.f64 37.5%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right)\right) \]

   14. Simplified 37.5%

       \[\leadsto b \cdot \color{blue}{\frac{x}{y \cdot b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.28 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.28e-5) (/ x (* y a)) (/ 1.0 (/ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.28e-5) {
		tmp = x / (y * a);
	} else {
		tmp = 1.0 / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.28d-5) then
        tmp = x / (y * a)
    else
        tmp = 1.0d0 / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.28e-5) {
		tmp = x / (y * a);
	} else {
		tmp = 1.0 / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.28e-5:
		tmp = x / (y * a)
	else:
		tmp = 1.0 / (y / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.28e-5)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(1.0 / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.28e-5)
		tmp = x / (y * a);
	else
		tmp = 1.0 / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.28e-5], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2799999999999999e-5

   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 y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right) - b}\right)}, y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right), y\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}\right), y\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot \frac{x}{e^{b}}\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(\frac{x}{e^{b}}\right)\right), y\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \left(e^{b}\right)\right)\right), y\right) \]

      12. exp-lowering-exp.f64 66.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 66.0%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t + -1\right)} \cdot \frac{x}{e^{b}}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \color{blue}{x}\right), y\right) \]
   7. Step-by-step derivation

   8. Simplified 52.3%

      \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot \color{blue}{x}}{y} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 34.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   11. Simplified 34.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 1.2799999999999999e-5 < 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 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 48.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 48.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 22.3%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   8. Simplified 22.3%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      3. /-lowering-/.f64 22.5%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   10. Applied egg-rr 22.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.28 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 16.6% 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 99.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
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 48.5%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 48.5%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 16.1%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 16.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

   3. /-lowering-/.f64 16.5%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

10. Applied egg-rr 16.5%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
11. Add Preprocessing

Alternative 20: 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 99.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
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 48.5%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 48.5%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 16.1%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 16.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 71.4% 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 2024152 
(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))