Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.5% → 99.1%

Time: 17.7s

Alternatives: 26

Speedup: 1.5×

• 40.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

3. Simplified 95.8%

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

5. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

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

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

   3. distribute-lft-out N/A

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

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

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

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

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

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

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

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

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

   8. log-lowering-log.f64 99.2%

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

7. Simplified 99.2%

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

Alternative 2: 80.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.3e+82)
   (/ x (exp (* a (- b (log (- 1.0 z))))))
   (if (<= a 1.02e+93) (/ x (exp (* y (- t (log z))))) (/ x (exp (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.3e+82) {
		tmp = x / exp((a * (b - log((1.0 - z)))));
	} else if (a <= 1.02e+93) {
		tmp = x / exp((y * (t - log(z))));
	} else {
		tmp = x / exp((a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.3d+82)) then
        tmp = x / exp((a * (b - log((1.0d0 - z)))))
    else if (a <= 1.02d+93) then
        tmp = x / exp((y * (t - log(z))))
    else
        tmp = x / exp((a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.3e+82) {
		tmp = x / Math.exp((a * (b - Math.log((1.0 - z)))));
	} else if (a <= 1.02e+93) {
		tmp = x / Math.exp((y * (t - Math.log(z))));
	} else {
		tmp = x / Math.exp((a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.3e+82:
		tmp = x / math.exp((a * (b - math.log((1.0 - z)))))
	elif a <= 1.02e+93:
		tmp = x / math.exp((y * (t - math.log(z))))
	else:
		tmp = x / math.exp((a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.3e+82)
		tmp = Float64(x / exp(Float64(a * Float64(b - log(Float64(1.0 - z))))));
	elseif (a <= 1.02e+93)
		tmp = Float64(x / exp(Float64(y * Float64(t - log(z)))));
	else
		tmp = Float64(x / exp(Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.3e+82)
		tmp = x / exp((a * (b - log((1.0 - z)))));
	elseif (a <= 1.02e+93)
		tmp = x / exp((y * (t - log(z))));
	else
		tmp = x / exp((a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.3e+82], N[(x / N[Exp[N[(a * N[(b - N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+93], N[(x / N[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2999999999999999e82

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}} \]
   6. Step-by-step derivation

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

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

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

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \left(b - \log \left(1 - z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \log \left(1 - z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \mathsf{log.f64}\left(\left(1 - z\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 80.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \mathsf{log.f64}\left(\mathsf{\_.f64}\left(1, z\right)\right)\right)\right)\right)\right) \]

   7. Simplified 80.0%

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

   if -1.2999999999999999e82 < a < 1.0200000000000001e93

   1. Initial program 98.3%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 89.2%

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

   7. Simplified 89.2%

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

   if 1.0200000000000001e93 < a

   1. Initial program 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 77.4%

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

   7. Simplified 77.4%

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

Alternative 3: 80.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))))
   (if (<= a -8.2e+80)
     t_1
     (if (<= a 9.2e+93) (/ x (exp (* y (- t (log z))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((a * b));
	double tmp;
	if (a <= -8.2e+80) {
		tmp = t_1;
	} else if (a <= 9.2e+93) {
		tmp = x / exp((y * (t - log(z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / exp((a * b))
    if (a <= (-8.2d+80)) then
        tmp = t_1
    else if (a <= 9.2d+93) then
        tmp = x / exp((y * (t - log(z))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((a * b));
	double tmp;
	if (a <= -8.2e+80) {
		tmp = t_1;
	} else if (a <= 9.2e+93) {
		tmp = x / Math.exp((y * (t - Math.log(z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((a * b))
	tmp = 0
	if a <= -8.2e+80:
		tmp = t_1
	elif a <= 9.2e+93:
		tmp = x / math.exp((y * (t - math.log(z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(a * b)))
	tmp = 0.0
	if (a <= -8.2e+80)
		tmp = t_1;
	elseif (a <= 9.2e+93)
		tmp = Float64(x / exp(Float64(y * Float64(t - log(z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((a * b));
	tmp = 0.0;
	if (a <= -8.2e+80)
		tmp = t_1;
	elseif (a <= 9.2e+93)
		tmp = x / exp((y * (t - log(z))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+80], t$95$1, If[LessEqual[a, 9.2e+93], N[(x / N[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000003e80 or 9.2000000000000006e93 < a

   1. Initial program 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 77.6%

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

   7. Simplified 77.6%

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

   if -8.20000000000000003e80 < a < 9.2000000000000006e93

   1. Initial program 98.3%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 89.2%

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

   7. Simplified 89.2%

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

Alternative 4: 72.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{1}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y t)))))
   (if (<= t -2.3e+110)
     t_1
     (if (<= t -7.1e-156)
       (/ x (exp (* a b)))
       (if (<= t 4.8e-5) (/ x (/ 1.0 (pow z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * t));
	double tmp;
	if (t <= -2.3e+110) {
		tmp = t_1;
	} else if (t <= -7.1e-156) {
		tmp = x / exp((a * b));
	} else if (t <= 4.8e-5) {
		tmp = x / (1.0 / pow(z, 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 / exp((y * t))
    if (t <= (-2.3d+110)) then
        tmp = t_1
    else if (t <= (-7.1d-156)) then
        tmp = x / exp((a * b))
    else if (t <= 4.8d-5) then
        tmp = x / (1.0d0 / (z ** 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.exp((y * t));
	double tmp;
	if (t <= -2.3e+110) {
		tmp = t_1;
	} else if (t <= -7.1e-156) {
		tmp = x / Math.exp((a * b));
	} else if (t <= 4.8e-5) {
		tmp = x / (1.0 / Math.pow(z, y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * t))
	tmp = 0
	if t <= -2.3e+110:
		tmp = t_1
	elif t <= -7.1e-156:
		tmp = x / math.exp((a * b))
	elif t <= 4.8e-5:
		tmp = x / (1.0 / math.pow(z, y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (t <= -2.3e+110)
		tmp = t_1;
	elseif (t <= -7.1e-156)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (t <= 4.8e-5)
		tmp = Float64(x / Float64(1.0 / (z ^ y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((y * t));
	tmp = 0.0;
	if (t <= -2.3e+110)
		tmp = t_1;
	elseif (t <= -7.1e-156)
		tmp = x / exp((a * b));
	elseif (t <= 4.8e-5)
		tmp = x / (1.0 / (z ^ 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[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+110], t$95$1, If[LessEqual[t, -7.1e-156], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-5], N[(x / N[(1.0 / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e110 or 4.8000000000000001e-5 < t

   1. Initial program 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 85.5%

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

   7. Simplified 85.5%

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

   if -2.3e110 < t < -7.1000000000000005e-156

   1. Initial program 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

   if -7.1000000000000005e-156 < t < 4.8000000000000001e-5

   1. Initial program 96.3%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. exp-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 72.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 72.7%

       \[\leadsto \frac{x}{\color{blue}{\frac{1}{{z}^{y}}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 72.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y t)))))
   (if (<= t -3.6e+112)
     t_1
     (if (<= t -1.7e-155)
       (/ x (exp (* a b)))
       (if (<= t 4.9e-5) (* x (pow z y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * t));
	double tmp;
	if (t <= -3.6e+112) {
		tmp = t_1;
	} else if (t <= -1.7e-155) {
		tmp = x / exp((a * b));
	} else if (t <= 4.9e-5) {
		tmp = x * pow(z, 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 / exp((y * t))
    if (t <= (-3.6d+112)) then
        tmp = t_1
    else if (t <= (-1.7d-155)) then
        tmp = x / exp((a * b))
    else if (t <= 4.9d-5) then
        tmp = x * (z ** 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.exp((y * t));
	double tmp;
	if (t <= -3.6e+112) {
		tmp = t_1;
	} else if (t <= -1.7e-155) {
		tmp = x / Math.exp((a * b));
	} else if (t <= 4.9e-5) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * t))
	tmp = 0
	if t <= -3.6e+112:
		tmp = t_1
	elif t <= -1.7e-155:
		tmp = x / math.exp((a * b))
	elif t <= 4.9e-5:
		tmp = x * math.pow(z, y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (t <= -3.6e+112)
		tmp = t_1;
	elseif (t <= -1.7e-155)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (t <= 4.9e-5)
		tmp = Float64(x * (z ^ y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((y * t));
	tmp = 0.0;
	if (t <= -3.6e+112)
		tmp = t_1;
	elseif (t <= -1.7e-155)
		tmp = x / exp((a * b));
	elseif (t <= 4.9e-5)
		tmp = x * (z ^ 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[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+112], t$95$1, If[LessEqual[t, -1.7e-155], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-5], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e112 or 4.9e-5 < t

   1. Initial program 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 85.5%

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

   7. Simplified 85.5%

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

   if -3.6e112 < t < -1.7e-155

   1. Initial program 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 71.4%

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

   7. Simplified 71.4%

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

   if -1.7e-155 < t < 4.9e-5

   1. Initial program 96.3%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. exp-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 72.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 72.7%

       \[\leadsto \frac{x}{\color{blue}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. remove-double-div N/A

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

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

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

       5. pow-lowering-pow.f64 72.7%

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

   12. Applied egg-rr 72.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(y \cdot \left(y \cdot \left(t \cdot 0.5\right)\right) - y\right)\right)\\ \mathbf{elif}\;t \leq -1600000000:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(t \cdot \left(y \cdot \left(t \cdot t\right)\right)\right) + 0.5 \cdot \left(t \cdot t\right)\right)\right)}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+177}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.15e+169)
   (* x (+ 1.0 (* t (- (* y (* y (* t 0.5))) y))))
   (if (<= t -1600000000.0)
     (/
      x
      (+
       1.0
       (*
        y
        (+
         t
         (*
          y
          (+ (* 0.16666666666666666 (* t (* y (* t t)))) (* 0.5 (* t t))))))))
     (if (<= t 6.9e+177) (* x (pow z y)) (* x (* (* t 0.5) (* t (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.15e+169) {
		tmp = x * (1.0 + (t * ((y * (y * (t * 0.5))) - y)));
	} else if (t <= -1600000000.0) {
		tmp = x / (1.0 + (y * (t + (y * ((0.16666666666666666 * (t * (y * (t * t)))) + (0.5 * (t * t)))))));
	} else if (t <= 6.9e+177) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * ((t * 0.5) * (t * (y * 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 <= (-1.15d+169)) then
        tmp = x * (1.0d0 + (t * ((y * (y * (t * 0.5d0))) - y)))
    else if (t <= (-1600000000.0d0)) then
        tmp = x / (1.0d0 + (y * (t + (y * ((0.16666666666666666d0 * (t * (y * (t * t)))) + (0.5d0 * (t * t)))))))
    else if (t <= 6.9d+177) then
        tmp = x * (z ** y)
    else
        tmp = x * ((t * 0.5d0) * (t * (y * 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 <= -1.15e+169) {
		tmp = x * (1.0 + (t * ((y * (y * (t * 0.5))) - y)));
	} else if (t <= -1600000000.0) {
		tmp = x / (1.0 + (y * (t + (y * ((0.16666666666666666 * (t * (y * (t * t)))) + (0.5 * (t * t)))))));
	} else if (t <= 6.9e+177) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.15e+169:
		tmp = x * (1.0 + (t * ((y * (y * (t * 0.5))) - y)))
	elif t <= -1600000000.0:
		tmp = x / (1.0 + (y * (t + (y * ((0.16666666666666666 * (t * (y * (t * t)))) + (0.5 * (t * t)))))))
	elif t <= 6.9e+177:
		tmp = x * math.pow(z, y)
	else:
		tmp = x * ((t * 0.5) * (t * (y * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.15e+169)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(y * Float64(y * Float64(t * 0.5))) - y))));
	elseif (t <= -1600000000.0)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(t + Float64(y * Float64(Float64(0.16666666666666666 * Float64(t * Float64(y * Float64(t * t)))) + Float64(0.5 * Float64(t * t))))))));
	elseif (t <= 6.9e+177)
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(Float64(t * 0.5) * Float64(t * Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.15e+169)
		tmp = x * (1.0 + (t * ((y * (y * (t * 0.5))) - y)));
	elseif (t <= -1600000000.0)
		tmp = x / (1.0 + (y * (t + (y * ((0.16666666666666666 * (t * (y * (t * t)))) + (0.5 * (t * t)))))));
	elseif (t <= 6.9e+177)
		tmp = x * (z ^ y);
	else
		tmp = x * ((t * 0.5) * (t * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.15e+169], N[(x * N[(1.0 + N[(t * N[(N[(y * N[(y * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1600000000.0], N[(x / N[(1.0 + N[(y * N[(t + N[(y * N[(N[(0.16666666666666666 * N[(t * N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.9e+177], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e169

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 62.3%

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

   8. Simplified 62.3%

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

   if -1.15e169 < t < -1.6e9

   1. Initial program 93.9%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. unpow3 N/A

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

      9. unpow2 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. unpow2 N/A

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

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

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

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

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

      18. unpow2 N/A

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

      19. *-lowering-*.f64 58.4%

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

   10. Simplified 58.4%

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

   if -1.6e9 < t < 6.89999999999999971e177

   1. Initial program 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. exp-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 68.6%

       \[\leadsto \frac{x}{\color{blue}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. remove-double-div N/A

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

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

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

       5. pow-lowering-pow.f64 68.6%

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

   12. Applied egg-rr 68.6%

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

   if 6.89999999999999971e177 < t

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 33.1%

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

   8. Simplified 33.1%

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

   9. Taylor expanded in t around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

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

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

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

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

       10. unpow2 N/A

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

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

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

       12. *-lowering-*.f64 62.1%

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

   11. Simplified 62.1%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(y \cdot \left(y \cdot \left(t \cdot 0.5\right)\right) - y\right)\right)\\ \mathbf{elif}\;t \leq -1600000000:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(t \cdot \left(y \cdot \left(t \cdot t\right)\right)\right) + 0.5 \cdot \left(t \cdot t\right)\right)\right)}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+177}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8800000000000:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -2.8e+22)
     t_1
     (if (<= y 8800000000000.0) (/ x (exp (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -2.8e+22) {
		tmp = t_1;
	} else if (y <= 8800000000000.0) {
		tmp = x / exp((a * 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 * (z ** y)
    if (y <= (-2.8d+22)) then
        tmp = t_1
    else if (y <= 8800000000000.0d0) then
        tmp = x / exp((a * 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(z, y);
	double tmp;
	if (y <= -2.8e+22) {
		tmp = t_1;
	} else if (y <= 8800000000000.0) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.8e+22:
		tmp = t_1
	elif y <= 8800000000000.0:
		tmp = x / math.exp((a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.8e+22)
		tmp = t_1;
	elseif (y <= 8800000000000.0)
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -2.8e+22)
		tmp = t_1;
	elseif (y <= 8800000000000.0)
		tmp = x / exp((a * 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[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+22], t$95$1, If[LessEqual[y, 8800000000000.0], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e22 or 8.8e12 < y

   1. Initial program 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. exp-neg N/A

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

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

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

      4. *-commutative N/A

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 74.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 74.4%

       \[\leadsto \frac{x}{\color{blue}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. remove-double-div N/A

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

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

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

       5. pow-lowering-pow.f64 74.4%

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

   12. Applied egg-rr 74.4%

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

   if -2.8e22 < y < 8.8e12

   1. Initial program 94.4%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 73.0%

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

   7. Simplified 73.0%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+22}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 8800000000000:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.9% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot t\right)\\ t_2 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{t\_1}}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-21}:\\ \;\;\;\;\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot t\_1\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t t))) (t_2 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_2)
     (if (<= y -8e+22)
       (/ (/ (* x 2.0) t_1) y)
       (if (<= y -1e-21)
         (* (* 0.5 (* t t)) (* x (* y y)))
         (if (<= y 7e-41)
           (/ x (+ 1.0 (* y (* 0.5 t_1))))
           (if (<= y 5.6e+143)
             (* (* x (* t (* t t))) (* (* y (* y y)) -0.16666666666666666))
             (/ x t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_2;
	} else if (y <= -8e+22) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -1e-21) {
		tmp = (0.5 * (t * t)) * (x * (y * y));
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 5.6e+143) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / 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 = y * (t * t)
    t_2 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_2
    else if (y <= (-8d+22)) then
        tmp = ((x * 2.0d0) / t_1) / y
    else if (y <= (-1d-21)) then
        tmp = (0.5d0 * (t * t)) * (x * (y * y))
    else if (y <= 7d-41) then
        tmp = x / (1.0d0 + (y * (0.5d0 * t_1)))
    else if (y <= 5.6d+143) then
        tmp = (x * (t * (t * t))) * ((y * (y * y)) * (-0.16666666666666666d0))
    else
        tmp = x / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_2;
	} else if (y <= -8e+22) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -1e-21) {
		tmp = (0.5 * (t * t)) * (x * (y * y));
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 5.6e+143) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * t)
	t_2 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_2
	elif y <= -8e+22:
		tmp = ((x * 2.0) / t_1) / y
	elif y <= -1e-21:
		tmp = (0.5 * (t * t)) * (x * (y * y))
	elif y <= 7e-41:
		tmp = x / (1.0 + (y * (0.5 * t_1)))
	elif y <= 5.6e+143:
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666)
	else:
		tmp = x / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * t))
	t_2 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_2);
	elseif (y <= -8e+22)
		tmp = Float64(Float64(Float64(x * 2.0) / t_1) / y);
	elseif (y <= -1e-21)
		tmp = Float64(Float64(0.5 * Float64(t * t)) * Float64(x * Float64(y * y)));
	elseif (y <= 7e-41)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(0.5 * t_1))));
	elseif (y <= 5.6e+143)
		tmp = Float64(Float64(x * Float64(t * Float64(t * t))) * Float64(Float64(y * Float64(y * y)) * -0.16666666666666666));
	else
		tmp = Float64(x / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * t);
	t_2 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_2;
	elseif (y <= -8e+22)
		tmp = ((x * 2.0) / t_1) / y;
	elseif (y <= -1e-21)
		tmp = (0.5 * (t * t)) * (x * (y * y));
	elseif (y <= 7e-41)
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	elseif (y <= 5.6e+143)
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	else
		tmp = x / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$2), $MachinePrecision], If[LessEqual[y, -8e+22], N[(N[(N[(x * 2.0), $MachinePrecision] / t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1e-21], N[(N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision] * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-41], N[(x / N[(1.0 + N[(y * N[(0.5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+143], N[(N[(x * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(x / t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 63.5%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in t around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

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

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

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

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

       10. unpow2 N/A

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

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

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

       12. *-lowering-*.f64 75.4%

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

   11. Simplified 75.4%

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

   if -9.2000000000000004e219 < y < -8e22

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. unpow2 N/A

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

      8. *-lowering-*.f64 32.2%

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

   10. Simplified 32.2%

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

   11. Taylor expanded in y around inf

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

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

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

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

       4. associate-*r/ N/A

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

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

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

       6. *-commutative N/A

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

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

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

       8. unpow2 N/A

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

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

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

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

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

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

       3. associate-/l/ N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

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

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

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

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

       7. *-lowering-*.f64 68.5%

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

   15. Applied egg-rr 68.5%

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

   if -8e22 < y < -9.99999999999999908e-22

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 36.0%

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

   5. Simplified 36.0%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 27.8%

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

   8. Simplified 27.8%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

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

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

       5. unpow2 N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 59.2%

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

   11. Simplified 59.2%

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

   if -9.99999999999999908e-22 < y < 6.9999999999999999e-41

   1. Initial program 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. unpow2 N/A

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

      8. *-lowering-*.f64 53.1%

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

   10. Simplified 53.1%

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

   11. Taylor expanded in t around inf

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

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

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

       2. *-commutative N/A

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

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

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

       4. unpow2 N/A

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

       5. *-lowering-*.f64 53.1%

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

   13. Simplified 53.1%

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

   if 6.9999999999999999e-41 < y < 5.59999999999999996e143

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

   8. Simplified 25.1%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*l* N/A

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

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

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

       6. *-commutative N/A

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

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

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

       8. cube-mult N/A

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

       9. unpow2 N/A

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

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

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

       11. unpow2 N/A

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

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

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

       13. *-commutative N/A

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

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

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

       15. cube-mult N/A

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

       16. unpow2 N/A

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

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

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

       18. unpow2 N/A

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

       19. *-lowering-*.f64 52.3%

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

   11. Simplified 52.3%

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

   if 5.59999999999999996e143 < y

   1. Initial program 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. unpow2 N/A

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

      8. *-lowering-*.f64 50.0%

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

   10. Simplified 50.0%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

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

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

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

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

       10. unpow2 N/A

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

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

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

       12. *-lowering-*.f64 85.4%

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

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-21}:\\ \;\;\;\;\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.2% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot t\right)\\ t_2 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{t\_1}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-21}:\\ \;\;\;\;\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot t\_1\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot -0.16666666666666666\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t t))) (t_2 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_2)
     (if (<= y -3.9e+22)
       (/ (/ (* x 2.0) t_1) y)
       (if (<= y -2.35e-21)
         (* (* 0.5 (* t t)) (* x (* y y)))
         (if (<= y 2.3e-119)
           (/ x (+ 1.0 (* y (* 0.5 t_1))))
           (if (<= y 4e+146)
             (* x (* y (* y (* y (* t (* (* t t) -0.16666666666666666))))))
             (/ x t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_2;
	} else if (y <= -3.9e+22) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -2.35e-21) {
		tmp = (0.5 * (t * t)) * (x * (y * y));
	} else if (y <= 2.3e-119) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 4e+146) {
		tmp = x * (y * (y * (y * (t * ((t * t) * -0.16666666666666666)))));
	} else {
		tmp = x / 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 = y * (t * t)
    t_2 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_2
    else if (y <= (-3.9d+22)) then
        tmp = ((x * 2.0d0) / t_1) / y
    else if (y <= (-2.35d-21)) then
        tmp = (0.5d0 * (t * t)) * (x * (y * y))
    else if (y <= 2.3d-119) then
        tmp = x / (1.0d0 + (y * (0.5d0 * t_1)))
    else if (y <= 4d+146) then
        tmp = x * (y * (y * (y * (t * ((t * t) * (-0.16666666666666666d0))))))
    else
        tmp = x / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_2;
	} else if (y <= -3.9e+22) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -2.35e-21) {
		tmp = (0.5 * (t * t)) * (x * (y * y));
	} else if (y <= 2.3e-119) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 4e+146) {
		tmp = x * (y * (y * (y * (t * ((t * t) * -0.16666666666666666)))));
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * t)
	t_2 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_2
	elif y <= -3.9e+22:
		tmp = ((x * 2.0) / t_1) / y
	elif y <= -2.35e-21:
		tmp = (0.5 * (t * t)) * (x * (y * y))
	elif y <= 2.3e-119:
		tmp = x / (1.0 + (y * (0.5 * t_1)))
	elif y <= 4e+146:
		tmp = x * (y * (y * (y * (t * ((t * t) * -0.16666666666666666)))))
	else:
		tmp = x / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * t))
	t_2 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_2);
	elseif (y <= -3.9e+22)
		tmp = Float64(Float64(Float64(x * 2.0) / t_1) / y);
	elseif (y <= -2.35e-21)
		tmp = Float64(Float64(0.5 * Float64(t * t)) * Float64(x * Float64(y * y)));
	elseif (y <= 2.3e-119)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(0.5 * t_1))));
	elseif (y <= 4e+146)
		tmp = Float64(x * Float64(y * Float64(y * Float64(y * Float64(t * Float64(Float64(t * t) * -0.16666666666666666))))));
	else
		tmp = Float64(x / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * t);
	t_2 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_2;
	elseif (y <= -3.9e+22)
		tmp = ((x * 2.0) / t_1) / y;
	elseif (y <= -2.35e-21)
		tmp = (0.5 * (t * t)) * (x * (y * y));
	elseif (y <= 2.3e-119)
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	elseif (y <= 4e+146)
		tmp = x * (y * (y * (y * (t * ((t * t) * -0.16666666666666666)))));
	else
		tmp = x / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$2), $MachinePrecision], If[LessEqual[y, -3.9e+22], N[(N[(N[(x * 2.0), $MachinePrecision] / t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.35e-21], N[(N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision] * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-119], N[(x / N[(1.0 + N[(y * N[(0.5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+146], N[(x * N[(y * N[(y * N[(y * N[(t * N[(N[(t * t), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 63.5%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in t around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

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

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

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

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

       10. unpow2 N/A

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

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

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

       12. *-lowering-*.f64 75.4%

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

   11. Simplified 75.4%

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

   if -9.2000000000000004e219 < y < -3.90000000000000021e22

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. unpow2 N/A

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

      8. *-lowering-*.f64 32.2%

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

   10. Simplified 32.2%

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

   11. Taylor expanded in y around inf

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

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

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

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

       4. associate-*r/ N/A

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

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

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

       6. *-commutative N/A

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

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

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

       8. unpow2 N/A

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

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

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

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

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

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

       3. associate-/l/ N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

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

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

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

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

       7. *-lowering-*.f64 68.5%

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

   15. Applied egg-rr 68.5%

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

   if -3.90000000000000021e22 < y < -2.35000000000000015e-21

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 36.0%

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

   5. Simplified 36.0%

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

   6. Taylor expanded in t around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. unpow2 N/A

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

      15. associate-*r* N/A

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

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

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

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

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

      18. *-lowering-*.f64 27.8%

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

   8. Simplified 27.8%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

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

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

       5. unpow2 N/A

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

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

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

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

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

       8. unpow2 N/A

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

       9. *-lowering-*.f64 59.2%

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

   11. Simplified 59.2%

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

   if -2.35000000000000015e-21 < y < 2.29999999999999993e-119

   1. Initial program 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. unpow2 N/A

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

      8. *-lowering-*.f64 54.8%

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

   10. Simplified 54.8%

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

   11. Taylor expanded in t around inf

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

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

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

       2. *-commutative N/A

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

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

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

       4. unpow2 N/A

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

       5. *-lowering-*.f64 54.8%

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

   13. Simplified 54.8%

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

   if 2.29999999999999993e-119 < y < 3.99999999999999973e146

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

   8. Simplified 32.3%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

       3. cube-mult N/A

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

       4. unpow2 N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

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

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

       10. associate-*r* N/A

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

       11. *-commutative N/A

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

       12. unpow2 N/A

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

       13. associate-*r* N/A

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

       14. associate-*r* N/A

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

       15. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right)\right)}\right)\right)\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right)\right)}\right)\right)\right) \]

       17. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{-1}{6} \cdot {t}^{3}\right) \cdot \color{blue}{y}\right)\right)\right)\right) \]

       18. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{-1}{6} \cdot {t}^{3}\right)}\right)\right)\right)\right) \]

       19. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-1}{6} \cdot {t}^{3}\right)}\right)\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left({t}^{3} \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right) \]

       21. cube-mult N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(t \cdot \left(t \cdot t\right)\right) \cdot \frac{-1}{6}\right)\right)\right)\right)\right) \]

       22. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(t \cdot {t}^{2}\right) \cdot \frac{-1}{6}\right)\right)\right)\right)\right) \]

       23. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left({t}^{2} \cdot \frac{-1}{6}\right)}\right)\right)\right)\right)\right) \]

       24. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left({t}^{2} \cdot \frac{-1}{6}\right)}\right)\right)\right)\right)\right) \]

       25. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left({t}^{2}\right), \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

       26. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{-1}{6}\right)\right)\right)\right)\right)\right) \]

       27. *-lowering-*.f64 48.3%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{-1}{6}\right)\right)\right)\right)\right)\right) \]

   11. Simplified 48.3%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(y \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot -0.16666666666666666\right)\right)\right)\right)\right)} \]

   if 3.99999999999999973e146 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-21}:\\ \;\;\;\;\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(t \cdot \left(\left(t \cdot t\right) \cdot -0.16666666666666666\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.3% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot t\right)\\ t_2 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ t_3 := 0.5 \cdot \left(t \cdot t\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{t\_1}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-21}:\\ \;\;\;\;t\_3 \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot t\_1\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot t\_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t t)))
        (t_2 (* (* t 0.5) (* t (* y y))))
        (t_3 (* 0.5 (* t t))))
   (if (<= y -4.5e+220)
     (* x t_2)
     (if (<= y -5e+24)
       (/ (/ (* x 2.0) t_1) y)
       (if (<= y -2.35e-21)
         (* t_3 (* x (* y y)))
         (if (<= y 1.96e-119)
           (/ x (+ 1.0 (* y (* 0.5 t_1))))
           (if (<= y 1.7e+146) (* y (* y (* x t_3))) (/ x t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double t_3 = 0.5 * (t * t);
	double tmp;
	if (y <= -4.5e+220) {
		tmp = x * t_2;
	} else if (y <= -5e+24) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -2.35e-21) {
		tmp = t_3 * (x * (y * y));
	} else if (y <= 1.96e-119) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 1.7e+146) {
		tmp = y * (y * (x * t_3));
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t * t)
    t_2 = (t * 0.5d0) * (t * (y * y))
    t_3 = 0.5d0 * (t * t)
    if (y <= (-4.5d+220)) then
        tmp = x * t_2
    else if (y <= (-5d+24)) then
        tmp = ((x * 2.0d0) / t_1) / y
    else if (y <= (-2.35d-21)) then
        tmp = t_3 * (x * (y * y))
    else if (y <= 1.96d-119) then
        tmp = x / (1.0d0 + (y * (0.5d0 * t_1)))
    else if (y <= 1.7d+146) then
        tmp = y * (y * (x * t_3))
    else
        tmp = x / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * t);
	double t_2 = (t * 0.5) * (t * (y * y));
	double t_3 = 0.5 * (t * t);
	double tmp;
	if (y <= -4.5e+220) {
		tmp = x * t_2;
	} else if (y <= -5e+24) {
		tmp = ((x * 2.0) / t_1) / y;
	} else if (y <= -2.35e-21) {
		tmp = t_3 * (x * (y * y));
	} else if (y <= 1.96e-119) {
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	} else if (y <= 1.7e+146) {
		tmp = y * (y * (x * t_3));
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * t)
	t_2 = (t * 0.5) * (t * (y * y))
	t_3 = 0.5 * (t * t)
	tmp = 0
	if y <= -4.5e+220:
		tmp = x * t_2
	elif y <= -5e+24:
		tmp = ((x * 2.0) / t_1) / y
	elif y <= -2.35e-21:
		tmp = t_3 * (x * (y * y))
	elif y <= 1.96e-119:
		tmp = x / (1.0 + (y * (0.5 * t_1)))
	elif y <= 1.7e+146:
		tmp = y * (y * (x * t_3))
	else:
		tmp = x / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * t))
	t_2 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	t_3 = Float64(0.5 * Float64(t * t))
	tmp = 0.0
	if (y <= -4.5e+220)
		tmp = Float64(x * t_2);
	elseif (y <= -5e+24)
		tmp = Float64(Float64(Float64(x * 2.0) / t_1) / y);
	elseif (y <= -2.35e-21)
		tmp = Float64(t_3 * Float64(x * Float64(y * y)));
	elseif (y <= 1.96e-119)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(0.5 * t_1))));
	elseif (y <= 1.7e+146)
		tmp = Float64(y * Float64(y * Float64(x * t_3)));
	else
		tmp = Float64(x / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * t);
	t_2 = (t * 0.5) * (t * (y * y));
	t_3 = 0.5 * (t * t);
	tmp = 0.0;
	if (y <= -4.5e+220)
		tmp = x * t_2;
	elseif (y <= -5e+24)
		tmp = ((x * 2.0) / t_1) / y;
	elseif (y <= -2.35e-21)
		tmp = t_3 * (x * (y * y));
	elseif (y <= 1.96e-119)
		tmp = x / (1.0 + (y * (0.5 * t_1)));
	elseif (y <= 1.7e+146)
		tmp = y * (y * (x * t_3));
	else
		tmp = x / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+220], N[(x * t$95$2), $MachinePrecision], If[LessEqual[y, -5e+24], N[(N[(N[(x * 2.0), $MachinePrecision] / t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.35e-21], N[(t$95$3 * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.96e-119], N[(x / N[(1.0 + N[(y * N[(0.5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+146], N[(y * N[(y * N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.50000000000000011e220

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -4.50000000000000011e220 < y < -5.00000000000000045e24

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.5%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{t \cdot t}}{y}\right), \color{blue}{y}\right) \]

       3. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}\right), y\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \left(t \cdot t\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 68.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, t\right)\right)\right), y\right) \]

   15. Applied egg-rr 68.5%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}} \]

   if -5.00000000000000045e24 < y < -2.35000000000000015e-21

   1. Initial program 91.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 36.0%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 27.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 27.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {t}^{2}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right) \]

       9. *-lowering-*.f64 59.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 59.2%

       \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)} \]

   if -2.35000000000000015e-21 < y < 1.9600000000000001e-119

   1. Initial program 93.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 54.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 54.8%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in t around inf

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 54.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 54.8%

       \[\leadsto \frac{x}{1 + y \cdot \color{blue}{\left(0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   if 1.9600000000000001e-119 < y < 1.69999999999999995e146

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 26.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 44.9%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if 1.69999999999999995e146 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-21}:\\ \;\;\;\;\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + y \cdot \left(0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -1.56 \cdot 10^{+220}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + b \cdot \left(a + 0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+144}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -1.56e+220)
     (* x t_1)
     (if (<= y -3.65e+22)
       (/ (/ (* x 2.0) (* y (* t t))) y)
       (if (<= y 7e-41)
         (/ x (+ 1.0 (* b (+ a (* 0.5 (* b (* a a)))))))
         (if (<= y 4.6e+144)
           (* (* x (* t (* t t))) (* (* y (* y y)) -0.16666666666666666))
           (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -1.56e+220) {
		tmp = x * t_1;
	} else if (y <= -3.65e+22) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (b * (a + (0.5 * (b * (a * a))))));
	} else if (y <= 4.6e+144) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-1.56d+220)) then
        tmp = x * t_1
    else if (y <= (-3.65d+22)) then
        tmp = ((x * 2.0d0) / (y * (t * t))) / y
    else if (y <= 7d-41) then
        tmp = x / (1.0d0 + (b * (a + (0.5d0 * (b * (a * a))))))
    else if (y <= 4.6d+144) then
        tmp = (x * (t * (t * t))) * ((y * (y * y)) * (-0.16666666666666666d0))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -1.56e+220) {
		tmp = x * t_1;
	} else if (y <= -3.65e+22) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (b * (a + (0.5 * (b * (a * a))))));
	} else if (y <= 4.6e+144) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -1.56e+220:
		tmp = x * t_1
	elif y <= -3.65e+22:
		tmp = ((x * 2.0) / (y * (t * t))) / y
	elif y <= 7e-41:
		tmp = x / (1.0 + (b * (a + (0.5 * (b * (a * a))))))
	elif y <= 4.6e+144:
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666)
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -1.56e+220)
		tmp = Float64(x * t_1);
	elseif (y <= -3.65e+22)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(y * Float64(t * t))) / y);
	elseif (y <= 7e-41)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(a + Float64(0.5 * Float64(b * Float64(a * a)))))));
	elseif (y <= 4.6e+144)
		tmp = Float64(Float64(x * Float64(t * Float64(t * t))) * Float64(Float64(y * Float64(y * y)) * -0.16666666666666666));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -1.56e+220)
		tmp = x * t_1;
	elseif (y <= -3.65e+22)
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	elseif (y <= 7e-41)
		tmp = x / (1.0 + (b * (a + (0.5 * (b * (a * a))))));
	elseif (y <= 4.6e+144)
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.56e+220], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -3.65e+22], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7e-41], N[(x / N[(1.0 + N[(b * N[(a + N[(0.5 * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+144], N[(N[(x * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.56e220

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -1.56e220 < y < -3.6499999999999999e22

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.5%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{t \cdot t}}{y}\right), \color{blue}{y}\right) \]

       3. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}\right), y\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \left(t \cdot t\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 68.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, t\right)\right)\right), y\right) \]

   15. Applied egg-rr 68.5%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}} \]

   if -3.6499999999999999e22 < y < 6.9999999999999999e-41

   1. Initial program 93.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(a + \left({a}^{2} \cdot b\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(a + \left(b \cdot {a}^{2}\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(a + b \cdot \color{blue}{\left({a}^{2} \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(a + b \cdot \left(\frac{1}{2} \cdot \color{blue}{{a}^{2}}\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot {a}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left({a}^{2} \cdot b\right) \cdot \frac{1}{2}\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{1}{2} \cdot \color{blue}{\left({a}^{2} \cdot b\right)}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot b\right)}\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{{a}^{2}}\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{\left({a}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 56.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 56.9%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + 0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right)\right)}} \]

   if 6.9999999999999999e-41 < y < 4.6000000000000003e144

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 51.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) - \color{blue}{t}\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right), \color{blue}{t}\right)\right)\right)\right) \]

   8. Simplified 25.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right) + \left(\left(y \cdot \left(t \cdot t\right)\right) \cdot t\right) \cdot -0.16666666666666666\right) - t\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \left({t}^{3} \cdot \left(x \cdot {y}^{3}\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{-1}{6} \cdot \left(\left({t}^{3} \cdot x\right) \cdot \color{blue}{{y}^{3}}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot x\right)\right) \cdot \color{blue}{{y}^{3}} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({t}^{3} \cdot x\right) \cdot \frac{-1}{6}\right) \cdot {\color{blue}{y}}^{3} \]

       4. associate-*l* N/A

          \[\leadsto \left({t}^{3} \cdot x\right) \cdot \color{blue}{\left(\frac{-1}{6} \cdot {y}^{3}\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({t}^{3} \cdot x\right), \color{blue}{\left(\frac{-1}{6} \cdot {y}^{3}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x \cdot {t}^{3}\right), \left(\color{blue}{\frac{-1}{6}} \cdot {y}^{3}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{3}\right)\right), \left(\color{blue}{\frac{-1}{6}} \cdot {y}^{3}\right)\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot \left(t \cdot t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot {t}^{2}\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left({t}^{2}\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       11. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(t \cdot t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \left({y}^{3} \cdot \color{blue}{\frac{-1}{6}}\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left({y}^{3}\right), \color{blue}{\frac{-1}{6}}\right)\right) \]

       15. cube-mult N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot y\right)\right), \frac{-1}{6}\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left(y \cdot {y}^{2}\right), \frac{-1}{6}\right)\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left({y}^{2}\right)\right), \frac{-1}{6}\right)\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(y \cdot y\right)\right), \frac{-1}{6}\right)\right) \]

       19. *-lowering-*.f64 52.3%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), \frac{-1}{6}\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)} \]

   if 4.6000000000000003e144 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + b \cdot \left(a + 0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+144}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+220}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + a \cdot \left(b + a \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -1.1e+220)
     (* x t_1)
     (if (<= y -3.65e+22)
       (/ (/ (* x 2.0) (* y (* t t))) y)
       (if (<= y 7e-41)
         (/ x (+ 1.0 (* a (+ b (* a (* b (* b 0.5)))))))
         (if (<= y 3.5e+144)
           (* (* x (* t (* t t))) (* (* y (* y y)) -0.16666666666666666))
           (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -1.1e+220) {
		tmp = x * t_1;
	} else if (y <= -3.65e+22) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (a * (b + (a * (b * (b * 0.5))))));
	} else if (y <= 3.5e+144) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-1.1d+220)) then
        tmp = x * t_1
    else if (y <= (-3.65d+22)) then
        tmp = ((x * 2.0d0) / (y * (t * t))) / y
    else if (y <= 7d-41) then
        tmp = x / (1.0d0 + (a * (b + (a * (b * (b * 0.5d0))))))
    else if (y <= 3.5d+144) then
        tmp = (x * (t * (t * t))) * ((y * (y * y)) * (-0.16666666666666666d0))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -1.1e+220) {
		tmp = x * t_1;
	} else if (y <= -3.65e+22) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 7e-41) {
		tmp = x / (1.0 + (a * (b + (a * (b * (b * 0.5))))));
	} else if (y <= 3.5e+144) {
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -1.1e+220:
		tmp = x * t_1
	elif y <= -3.65e+22:
		tmp = ((x * 2.0) / (y * (t * t))) / y
	elif y <= 7e-41:
		tmp = x / (1.0 + (a * (b + (a * (b * (b * 0.5))))))
	elif y <= 3.5e+144:
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666)
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -1.1e+220)
		tmp = Float64(x * t_1);
	elseif (y <= -3.65e+22)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(y * Float64(t * t))) / y);
	elseif (y <= 7e-41)
		tmp = Float64(x / Float64(1.0 + Float64(a * Float64(b + Float64(a * Float64(b * Float64(b * 0.5)))))));
	elseif (y <= 3.5e+144)
		tmp = Float64(Float64(x * Float64(t * Float64(t * t))) * Float64(Float64(y * Float64(y * y)) * -0.16666666666666666));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -1.1e+220)
		tmp = x * t_1;
	elseif (y <= -3.65e+22)
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	elseif (y <= 7e-41)
		tmp = x / (1.0 + (a * (b + (a * (b * (b * 0.5))))));
	elseif (y <= 3.5e+144)
		tmp = (x * (t * (t * t))) * ((y * (y * y)) * -0.16666666666666666);
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+220], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -3.65e+22], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7e-41], N[(x / N[(1.0 + N[(a * N[(b + N[(a * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+144], N[(N[(x * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.09999999999999995e220

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -1.09999999999999995e220 < y < -3.6499999999999999e22

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.5%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 65.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{t \cdot t}}{y}\right), \color{blue}{y}\right) \]

       3. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}\right), y\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \left(t \cdot t\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 68.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, t\right)\right)\right), y\right) \]

   15. Applied egg-rr 68.5%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}} \]

   if -3.6499999999999999e22 < y < 6.9999999999999999e-41

   1. Initial program 93.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + \frac{1}{2} \cdot \left({b}^{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + \left(\frac{1}{2} \cdot {b}^{2}\right) \cdot \color{blue}{a}\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \color{blue}{\left(\left(\frac{1}{2} \cdot {b}^{2}\right) \cdot a\right)}\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \left(\frac{1}{2} \cdot \color{blue}{\left({b}^{2} \cdot a\right)}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \left(\frac{1}{2} \cdot \left(a \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \left(\left(a \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \left(a \cdot \color{blue}{\left({b}^{2} \cdot \frac{1}{2}\right)}\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \left(\left(\frac{1}{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot b\right), \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 53.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, b\right), b\right)\right)\right)\right)\right)\right) \]

   10. Simplified 53.3%

       \[\leadsto \frac{x}{\color{blue}{1 + a \cdot \left(b + a \cdot \left(\left(0.5 \cdot b\right) \cdot b\right)\right)}} \]

   if 6.9999999999999999e-41 < y < 3.4999999999999998e144

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 51.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot t + y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right) - \color{blue}{t}\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(y \cdot \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right), \color{blue}{t}\right)\right)\right)\right) \]

   8. Simplified 25.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right) + \left(\left(y \cdot \left(t \cdot t\right)\right) \cdot t\right) \cdot -0.16666666666666666\right) - t\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \left({t}^{3} \cdot \left(x \cdot {y}^{3}\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{-1}{6} \cdot \left(\left({t}^{3} \cdot x\right) \cdot \color{blue}{{y}^{3}}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot \left({t}^{3} \cdot x\right)\right) \cdot \color{blue}{{y}^{3}} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({t}^{3} \cdot x\right) \cdot \frac{-1}{6}\right) \cdot {\color{blue}{y}}^{3} \]

       4. associate-*l* N/A

          \[\leadsto \left({t}^{3} \cdot x\right) \cdot \color{blue}{\left(\frac{-1}{6} \cdot {y}^{3}\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({t}^{3} \cdot x\right), \color{blue}{\left(\frac{-1}{6} \cdot {y}^{3}\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(x \cdot {t}^{3}\right), \left(\color{blue}{\frac{-1}{6}} \cdot {y}^{3}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{3}\right)\right), \left(\color{blue}{\frac{-1}{6}} \cdot {y}^{3}\right)\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot \left(t \cdot t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot {t}^{2}\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left({t}^{2}\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       11. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \left(t \cdot t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \left(\frac{-1}{6} \cdot {y}^{3}\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \left({y}^{3} \cdot \color{blue}{\frac{-1}{6}}\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left({y}^{3}\right), \color{blue}{\frac{-1}{6}}\right)\right) \]

       15. cube-mult N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot y\right)\right), \frac{-1}{6}\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\left(y \cdot {y}^{2}\right), \frac{-1}{6}\right)\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left({y}^{2}\right)\right), \frac{-1}{6}\right)\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(y \cdot y\right)\right), \frac{-1}{6}\right)\right) \]

       19. *-lowering-*.f64 52.3%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), \frac{-1}{6}\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto \color{blue}{\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)} \]

   if 3.4999999999999998e144 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + a \cdot \left(b + a \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) \cdot \left(\left(y \cdot \left(y \cdot y\right)\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.1% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_1)
     (if (<= y -5.2e-31)
       (/ (/ (* x 2.0) (* y (* t t))) y)
       (if (<= y 1.05e-119)
         (/ x (+ 1.0 (* a b)))
         (if (<= y 5.4e+144) (* y (* y (* x (* 0.5 (* t t))))) (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -5.2e-31) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 1.05e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 5.4e+144) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_1
    else if (y <= (-5.2d-31)) then
        tmp = ((x * 2.0d0) / (y * (t * t))) / y
    else if (y <= 1.05d-119) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 5.4d+144) then
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -5.2e-31) {
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	} else if (y <= 1.05e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 5.4e+144) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_1
	elif y <= -5.2e-31:
		tmp = ((x * 2.0) / (y * (t * t))) / y
	elif y <= 1.05e-119:
		tmp = x / (1.0 + (a * b))
	elif y <= 5.4e+144:
		tmp = y * (y * (x * (0.5 * (t * t))))
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_1);
	elseif (y <= -5.2e-31)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(y * Float64(t * t))) / y);
	elseif (y <= 1.05e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 5.4e+144)
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_1;
	elseif (y <= -5.2e-31)
		tmp = ((x * 2.0) / (y * (t * t))) / y;
	elseif (y <= 1.05e-119)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 5.4e+144)
		tmp = y * (y * (x * (0.5 * (t * t))));
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -5.2e-31], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.05e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+144], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -9.2000000000000004e219 < y < -5.19999999999999991e-31

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 54.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \frac{\frac{\frac{x \cdot 2}{t \cdot t}}{y}}{\color{blue}{y}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{t \cdot t}}{y}\right), \color{blue}{y}\right) \]

       3. associate-/l/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}\right), y\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(y \cdot \left(t \cdot t\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \left(t \cdot t\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 56.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, t\right)\right)\right), y\right) \]

   15. Applied egg-rr 56.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}} \]

   if -5.19999999999999991e-31 < y < 1.05e-119

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 1.05e-119 < y < 5.4000000000000003e144

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 26.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 44.9%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if 5.4000000000000003e144 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y \cdot \left(t \cdot t\right)}}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.2% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_1)
     (if (<= y -6.2e-31)
       (/ (/ (* x 2.0) (* t t)) (* y y))
       (if (<= y 2.4e-119)
         (/ x (+ 1.0 (* a b)))
         (if (<= y 2.9e+146) (* y (* y (* x (* 0.5 (* t t))))) (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -6.2e-31) {
		tmp = ((x * 2.0) / (t * t)) / (y * y);
	} else if (y <= 2.4e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 2.9e+146) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_1
    else if (y <= (-6.2d-31)) then
        tmp = ((x * 2.0d0) / (t * t)) / (y * y)
    else if (y <= 2.4d-119) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 2.9d+146) then
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -6.2e-31) {
		tmp = ((x * 2.0) / (t * t)) / (y * y);
	} else if (y <= 2.4e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 2.9e+146) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_1
	elif y <= -6.2e-31:
		tmp = ((x * 2.0) / (t * t)) / (y * y)
	elif y <= 2.4e-119:
		tmp = x / (1.0 + (a * b))
	elif y <= 2.9e+146:
		tmp = y * (y * (x * (0.5 * (t * t))))
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_1);
	elseif (y <= -6.2e-31)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(t * t)) / Float64(y * y));
	elseif (y <= 2.4e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 2.9e+146)
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_1;
	elseif (y <= -6.2e-31)
		tmp = ((x * 2.0) / (t * t)) / (y * y);
	elseif (y <= 2.4e-119)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 2.9e+146)
		tmp = y * (y * (x * (0.5 * (t * t))));
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -6.2e-31], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+146], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -9.2000000000000004e219 < y < -6.19999999999999999e-31

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 54.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]

   if -6.19999999999999999e-31 < y < 2.40000000000000009e-119

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.40000000000000009e-119 < y < 2.8999999999999998e146

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 26.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 44.9%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if 2.8999999999999998e146 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.2% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;\frac{x \cdot \frac{2}{t \cdot t}}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_1)
     (if (<= y -1.02e-30)
       (/ (* x (/ 2.0 (* t t))) (* y y))
       (if (<= y 2.35e-119)
         (/ x (+ 1.0 (* a b)))
         (if (<= y 3.5e+146) (* y (* y (* x (* 0.5 (* t t))))) (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -1.02e-30) {
		tmp = (x * (2.0 / (t * t))) / (y * y);
	} else if (y <= 2.35e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 3.5e+146) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_1
    else if (y <= (-1.02d-30)) then
        tmp = (x * (2.0d0 / (t * t))) / (y * y)
    else if (y <= 2.35d-119) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 3.5d+146) then
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -1.02e-30) {
		tmp = (x * (2.0 / (t * t))) / (y * y);
	} else if (y <= 2.35e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 3.5e+146) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_1
	elif y <= -1.02e-30:
		tmp = (x * (2.0 / (t * t))) / (y * y)
	elif y <= 2.35e-119:
		tmp = x / (1.0 + (a * b))
	elif y <= 3.5e+146:
		tmp = y * (y * (x * (0.5 * (t * t))))
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_1);
	elseif (y <= -1.02e-30)
		tmp = Float64(Float64(x * Float64(2.0 / Float64(t * t))) / Float64(y * y));
	elseif (y <= 2.35e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 3.5e+146)
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_1;
	elseif (y <= -1.02e-30)
		tmp = (x * (2.0 / (t * t))) / (y * y);
	elseif (y <= 2.35e-119)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 3.5e+146)
		tmp = y * (y * (x * (0.5 * (t * t))));
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -1.02e-30], N[(N[(x * N[(2.0 / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+146], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -9.2000000000000004e219 < y < -1.0199999999999999e-30

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 54.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{2}{t \cdot t}\right), \mathsf{*.f64}\left(\color{blue}{y}, y\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t \cdot t} \cdot x\right), \mathsf{*.f64}\left(\color{blue}{y}, y\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{t \cdot t}\right), x\right), \mathsf{*.f64}\left(\color{blue}{y}, y\right)\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, \left(t \cdot t\right)\right), x\right), \mathsf{*.f64}\left(y, y\right)\right) \]

       5. *-lowering-*.f64 54.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, t\right)\right), x\right), \mathsf{*.f64}\left(y, y\right)\right) \]

   15. Applied egg-rr 54.7%

       \[\leadsto \frac{\color{blue}{\frac{2}{t \cdot t} \cdot x}}{y \cdot y} \]

   if -1.0199999999999999e-30 < y < 2.35000000000000001e-119

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.35000000000000001e-119 < y < 3.5000000000000001e146

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 26.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 44.9%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if 3.5000000000000001e146 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;\frac{x \cdot \frac{2}{t \cdot t}}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.4% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{2}{t \cdot t} \cdot \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t 0.5) (* t (* y y)))))
   (if (<= y -9.2e+219)
     (* x t_1)
     (if (<= y -2.05e-30)
       (* (/ 2.0 (* t t)) (/ x (* y y)))
       (if (<= y 2.05e-119)
         (/ x (+ 1.0 (* a b)))
         (if (<= y 6e+145) (* y (* y (* x (* 0.5 (* t t))))) (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -2.05e-30) {
		tmp = (2.0 / (t * t)) * (x / (y * y));
	} else if (y <= 2.05e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 6e+145) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * 0.5d0) * (t * (y * y))
    if (y <= (-9.2d+219)) then
        tmp = x * t_1
    else if (y <= (-2.05d-30)) then
        tmp = (2.0d0 / (t * t)) * (x / (y * y))
    else if (y <= 2.05d-119) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 6d+145) then
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    else
        tmp = x / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * 0.5) * (t * (y * y));
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * t_1;
	} else if (y <= -2.05e-30) {
		tmp = (2.0 / (t * t)) * (x / (y * y));
	} else if (y <= 2.05e-119) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 6e+145) {
		tmp = y * (y * (x * (0.5 * (t * t))));
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * 0.5) * (t * (y * y))
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * t_1
	elif y <= -2.05e-30:
		tmp = (2.0 / (t * t)) * (x / (y * y))
	elif y <= 2.05e-119:
		tmp = x / (1.0 + (a * b))
	elif y <= 6e+145:
		tmp = y * (y * (x * (0.5 * (t * t))))
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * 0.5) * Float64(t * Float64(y * y)))
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * t_1);
	elseif (y <= -2.05e-30)
		tmp = Float64(Float64(2.0 / Float64(t * t)) * Float64(x / Float64(y * y)));
	elseif (y <= 2.05e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 6e+145)
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * 0.5) * (t * (y * y));
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * t_1;
	elseif (y <= -2.05e-30)
		tmp = (2.0 / (t * t)) * (x / (y * y));
	elseif (y <= 2.05e-119)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 6e+145)
		tmp = y * (y * (x * (0.5 * (t * t))));
	else
		tmp = x / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+219], N[(x * t$95$1), $MachinePrecision], If[LessEqual[y, -2.05e-30], N[(N[(2.0 / N[(t * t), $MachinePrecision]), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+145], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -9.2000000000000004e219 < y < -2.0500000000000002e-30

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 54.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y \cdot y\right) \cdot \left(t \cdot t\right)}} \]

       2. times-frac N/A

          \[\leadsto \frac{x}{y \cdot y} \cdot \color{blue}{\frac{2}{t \cdot t}} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\frac{2}{t \cdot t}\right)}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(y \cdot y\right)\right), \left(\frac{\color{blue}{2}}{t \cdot t}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{2}{t \cdot t}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot t\right)}\right)\right) \]

       7. *-lowering-*.f64 49.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right) \]

   15. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot \frac{2}{t \cdot t}} \]

   if -2.0500000000000002e-30 < y < 2.0500000000000001e-119

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.0500000000000001e-119 < y < 6.0000000000000005e145

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 26.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 44.9%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if 6.0000000000000005e145 < y

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 64.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 50.0%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 85.4%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 85.4%

       \[\leadsto \frac{x}{\color{blue}{\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{2}{t \cdot t} \cdot \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.0% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{2}{t \cdot t} \cdot \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+219)
   (* x (* (* t 0.5) (* t (* y y))))
   (if (<= y -3.8e-31)
     (* (/ 2.0 (* t t)) (/ x (* y y)))
     (if (<= y 2.3e-119)
       (/ x (+ 1.0 (* a b)))
       (* y (* y (* x (* 0.5 (* t t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= -3.8e-31) {
		tmp = (2.0 / (t * t)) * (x / (y * y));
	} else if (y <= 2.3e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = y * (y * (x * (0.5 * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.2d+219)) then
        tmp = x * ((t * 0.5d0) * (t * (y * y)))
    else if (y <= (-3.8d-31)) then
        tmp = (2.0d0 / (t * t)) * (x / (y * y))
    else if (y <= 2.3d-119) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+219) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= -3.8e-31) {
		tmp = (2.0 / (t * t)) * (x / (y * y));
	} else if (y <= 2.3e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = y * (y * (x * (0.5 * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+219:
		tmp = x * ((t * 0.5) * (t * (y * y)))
	elif y <= -3.8e-31:
		tmp = (2.0 / (t * t)) * (x / (y * y))
	elif y <= 2.3e-119:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = y * (y * (x * (0.5 * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+219)
		tmp = Float64(x * Float64(Float64(t * 0.5) * Float64(t * Float64(y * y))));
	elseif (y <= -3.8e-31)
		tmp = Float64(Float64(2.0 / Float64(t * t)) * Float64(x / Float64(y * y)));
	elseif (y <= 2.3e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e+219)
		tmp = x * ((t * 0.5) * (t * (y * y)));
	elseif (y <= -3.8e-31)
		tmp = (2.0 / (t * t)) * (x / (y * y));
	elseif (y <= 2.3e-119)
		tmp = x / (1.0 + (a * b));
	else
		tmp = y * (y * (x * (0.5 * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+219], N[(x * N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-31], N[(N[(2.0 / N[(t * t), $MachinePrecision]), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.2000000000000004e219

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 63.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 75.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -9.2000000000000004e219 < y < -3.8e-31

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 50.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + \frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot y\right)}\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{{t}^{2}}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 32.2%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + 0.5 \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)}} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{t}^{2} \cdot {y}^{2}}} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{t}^{2}}}{\color{blue}{{y}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{t}^{2}}\right), \color{blue}{\left({y}^{2}\right)}\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot x}{{t}^{2}}\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(2 \cdot x\right), \left({t}^{2}\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left({t}^{2}\right)\right), \left({y}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot t\right)\right), \left({y}^{2}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left({y}^{2}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       11. *-lowering-*.f64 54.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(t, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{t \cdot t}}{y \cdot y}} \]
   14. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y \cdot y\right) \cdot \left(t \cdot t\right)}} \]

       2. times-frac N/A

          \[\leadsto \frac{x}{y \cdot y} \cdot \color{blue}{\frac{2}{t \cdot t}} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\frac{2}{t \cdot t}\right)}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(y \cdot y\right)\right), \left(\frac{\color{blue}{2}}{t \cdot t}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{2}{t \cdot t}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot t\right)}\right)\right) \]

       7. *-lowering-*.f64 49.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right) \]

   15. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot \frac{2}{t \cdot t}} \]

   if -3.8e-31 < y < 2.29999999999999993e-119

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 80.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.29999999999999993e-119 < y

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 59.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 27.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 27.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 17.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 48.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 48.8%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{2}{t \cdot t} \cdot \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.5% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(t \cdot \left(0 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.5e+131)
   (/ x (+ 1.0 (* y t)))
   (if (<= y 7.5e+14)
     (- x (* a (* x b)))
     (if (<= y 4.1e+191) (* x (* t (- 0.0 y))) (* y (- (/ x y) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e+131) {
		tmp = x / (1.0 + (y * t));
	} else if (y <= 7.5e+14) {
		tmp = x - (a * (x * b));
	} else if (y <= 4.1e+191) {
		tmp = x * (t * (0.0 - y));
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.5d+131)) then
        tmp = x / (1.0d0 + (y * t))
    else if (y <= 7.5d+14) then
        tmp = x - (a * (x * b))
    else if (y <= 4.1d+191) then
        tmp = x * (t * (0.0d0 - y))
    else
        tmp = y * ((x / y) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e+131) {
		tmp = x / (1.0 + (y * t));
	} else if (y <= 7.5e+14) {
		tmp = x - (a * (x * b));
	} else if (y <= 4.1e+191) {
		tmp = x * (t * (0.0 - y));
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.5e+131:
		tmp = x / (1.0 + (y * t))
	elif y <= 7.5e+14:
		tmp = x - (a * (x * b))
	elif y <= 4.1e+191:
		tmp = x * (t * (0.0 - y))
	else:
		tmp = y * ((x / y) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.5e+131)
		tmp = Float64(x / Float64(1.0 + Float64(y * t)));
	elseif (y <= 7.5e+14)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	elseif (y <= 4.1e+191)
		tmp = Float64(x * Float64(t * Float64(0.0 - y)));
	else
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.5e+131)
		tmp = x / (1.0 + (y * t));
	elseif (y <= 7.5e+14)
		tmp = x - (a * (x * b));
	elseif (y <= 4.1e+191)
		tmp = x * (t * (0.0 - y));
	else
		tmp = y * ((x / y) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.5e+131], N[(x / N[(1.0 + N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+14], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+191], N[(x * N[(t * N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.50000000000000015e131

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.5%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 32.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -9.50000000000000015e131 < y < 7.5e14

   1. Initial program 95.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 69.2%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 43.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 43.4%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   if 7.5e14 < y < 4.0999999999999999e191

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 57.1%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(t \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{t \cdot y}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

      5. *-lowering-*.f64 21.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 21.2%

      \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{t \cdot \left(x \cdot y\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(x \cdot y\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{t}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(y \cdot t\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \left(t \cdot \color{blue}{y}\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

       9. *-lowering-*.f64 30.9%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 30.9%

       \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot t\right)} \]

   if 4.0999999999999999e191 < y

   1. Initial program 94.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 54.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(t \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{t \cdot y}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

      5. *-lowering-*.f64 13.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 13.5%

      \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(t \cdot x\right) + \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \frac{x}{y}\right)}\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(t \cdot x\right)\right) + \frac{\color{blue}{x}}{y}\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)}\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{x}{y} - \color{blue}{t \cdot x}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(x \cdot \color{blue}{t}\right)\right)\right) \]

       8. *-lowering-*.f64 43.4%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 43.4%

       \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - x \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(t \cdot \left(0 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.95e-22)
   (* x (* (* t 0.5) (* t (* y y))))
   (if (<= y 2.1e-119)
     (/ x (+ 1.0 (* a b)))
     (* y (* y (* x (* 0.5 (* t t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-22) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= 2.1e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = y * (y * (x * (0.5 * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.95d-22)) then
        tmp = x * ((t * 0.5d0) * (t * (y * y)))
    else if (y <= 2.1d-119) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = y * (y * (x * (0.5d0 * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-22) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= 2.1e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = y * (y * (x * (0.5 * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.95e-22:
		tmp = x * ((t * 0.5) * (t * (y * y)))
	elif y <= 2.1e-119:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = y * (y * (x * (0.5 * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.95e-22)
		tmp = Float64(x * Float64(Float64(t * 0.5) * Float64(t * Float64(y * y))));
	elseif (y <= 2.1e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(y * Float64(y * Float64(x * Float64(0.5 * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.95e-22)
		tmp = x * ((t * 0.5) * (t * (y * y)));
	elseif (y <= 2.1e-119)
		tmp = x / (1.0 + (a * b));
	else
		tmp = y * (y * (x * (0.5 * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.95e-22], N[(x * N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * N[(x * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.94999999999999999e-22

   1. Initial program 97.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 49.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 31.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 42.8%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 42.8%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -1.94999999999999999e-22 < y < 2.1e-119

   1. Initial program 93.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 79.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 79.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.1e-119 < y

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 59.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 27.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 27.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 17.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{\left(x \cdot {y}^{2}\right)} \]

       2. unpow2 N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot \left(y \cdot \color{blue}{y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{y}\right) \]

       4. associate-*l* N/A

          \[\leadsto \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{y} \]

       5. associate-*r* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right) \cdot y \]

       6. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{y}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{y}\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       16. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 48.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 48.8%

       \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.3% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.9e-22)
   (* x (* (* t 0.5) (* t (* y y))))
   (if (<= y 1.55e-119)
     (/ x (+ 1.0 (* a b)))
     (* x (* y (* y (* 0.5 (* t t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e-22) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= 1.55e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x * (y * (y * (0.5 * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.9d-22)) then
        tmp = x * ((t * 0.5d0) * (t * (y * y)))
    else if (y <= 1.55d-119) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = x * (y * (y * (0.5d0 * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e-22) {
		tmp = x * ((t * 0.5) * (t * (y * y)));
	} else if (y <= 1.55e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x * (y * (y * (0.5 * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.9e-22:
		tmp = x * ((t * 0.5) * (t * (y * y)))
	elif y <= 1.55e-119:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = x * (y * (y * (0.5 * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.9e-22)
		tmp = Float64(x * Float64(Float64(t * 0.5) * Float64(t * Float64(y * y))));
	elseif (y <= 1.55e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(x * Float64(y * Float64(y * Float64(0.5 * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.9e-22)
		tmp = x * ((t * 0.5) * (t * (y * y)));
	elseif (y <= 1.55e-119)
		tmp = x / (1.0 + (a * b));
	else
		tmp = x * (y * (y * (0.5 * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.9e-22], N[(x * N[(N[(t * 0.5), $MachinePrecision] * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(y * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000012e-22

   1. Initial program 97.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 49.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 31.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({y}^{2} \cdot \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({y}^{2} \cdot t\right) \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left(t \cdot {y}^{2}\right) \cdot t\right)\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right) \cdot \color{blue}{t}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right) \cdot t\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(t \cdot {y}^{2}\right) \cdot \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot {y}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot t\right)}\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left({y}^{2}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot t\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{2} \cdot t\right)\right)\right) \]

       12. *-lowering-*.f64 42.8%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, y\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 42.8%

       \[\leadsto x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot t\right)\right)} \]

   if -1.90000000000000012e-22 < y < 1.54999999999999989e-119

   1. Initial program 93.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 79.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 79.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 1.54999999999999989e-119 < y

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 59.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 27.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 27.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 17.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot y\right) \cdot \color{blue}{y}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right) \cdot \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{y}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 42.6%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 42.6%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(\left(t \cdot 0.5\right) \cdot \left(t \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 42.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -1.66 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* y (* y (* 0.5 (* t t)))))))
   (if (<= y -1.66e-21) t_1 (if (<= y 1.08e-119) (/ x (+ 1.0 (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * (y * (0.5 * (t * t))));
	double tmp;
	if (y <= -1.66e-21) {
		tmp = t_1;
	} else if (y <= 1.08e-119) {
		tmp = x / (1.0 + (a * 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 * (y * (y * (0.5d0 * (t * t))))
    if (y <= (-1.66d-21)) then
        tmp = t_1
    else if (y <= 1.08d-119) then
        tmp = x / (1.0d0 + (a * 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 * (y * (y * (0.5 * (t * t))));
	double tmp;
	if (y <= -1.66e-21) {
		tmp = t_1;
	} else if (y <= 1.08e-119) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y * (y * (0.5 * (t * t))))
	tmp = 0
	if y <= -1.66e-21:
		tmp = t_1
	elif y <= 1.08e-119:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y * Float64(y * Float64(0.5 * Float64(t * t)))))
	tmp = 0.0
	if (y <= -1.66e-21)
		tmp = t_1;
	elseif (y <= 1.08e-119)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y * (y * (0.5 * (t * t))));
	tmp = 0.0;
	if (y <= -1.66e-21)
		tmp = t_1;
	elseif (y <= 1.08e-119)
		tmp = x / (1.0 + (a * 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[(y * N[(y * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.66e-21], t$95$1, If[LessEqual[y, 1.08e-119], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65999999999999993e-21 or 1.0799999999999999e-119 < y

   1. Initial program 97.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 55.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 55.0%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \color{blue}{-1 \cdot y}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right) - \color{blue}{y}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2} - y\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right) - y\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right) - y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{2} \cdot {y}^{2}\right)\right), \color{blue}{y}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(t \cdot \left({y}^{2} \cdot \frac{1}{2}\right)\right), y\right)\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(t \cdot {y}^{2}\right) \cdot \frac{1}{2}\right), y\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right), y\right)\right)\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot {y}^{2}\right), y\right)\right)\right)\right) \]

      14. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot \left(y \cdot y\right)\right), y\right)\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right), y\right), y\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), y\right), y\right), y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 29.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), y\right), y\right), y\right)\right)\right)\right) \]

   8. Simplified 29.1%

      \[\leadsto x \cdot \color{blue}{\left(1 + t \cdot \left(\left(\left(0.5 \cdot t\right) \cdot y\right) \cdot y - y\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y - y\right) \cdot \color{blue}{t}\right)\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y} \cdot t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\frac{\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t}{\color{blue}{\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) \cdot \left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y\right) - y \cdot y\right) \cdot t\right), \color{blue}{\left(\left(\left(\frac{1}{2} \cdot t\right) \cdot y\right) \cdot y + y\right)}\right)\right)\right) \]

   10. Applied egg-rr 16.5%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(\left(\left(t \cdot \frac{y}{2} + 1\right) \cdot y\right) \cdot \left(y \cdot \left(t \cdot \frac{y}{2}\right) - y\right)\right) \cdot t}{\left(t \cdot \frac{y}{2} + 1\right) \cdot y}}\right) \]

   11. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot {y}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({t}^{2} \cdot y\right) \cdot \color{blue}{y}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right) \cdot \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{y}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 38.5%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right) \]

   13. Simplified 38.5%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)} \]

   if -1.65999999999999993e-21 < y < 1.0799999999999999e-119

   1. Initial program 93.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 79.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 79.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 54.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 54.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 8800000000000:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(0 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.2e+132)
   (* x (- 1.0 (* y t)))
   (if (<= y 8800000000000.0) (- x (* a (* x b))) (* x (* t (- 0.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e+132) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 8800000000000.0) {
		tmp = x - (a * (x * b));
	} else {
		tmp = x * (t * (0.0 - 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 (y <= (-4.2d+132)) then
        tmp = x * (1.0d0 - (y * t))
    else if (y <= 8800000000000.0d0) then
        tmp = x - (a * (x * b))
    else
        tmp = x * (t * (0.0d0 - 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 (y <= -4.2e+132) {
		tmp = x * (1.0 - (y * t));
	} else if (y <= 8800000000000.0) {
		tmp = x - (a * (x * b));
	} else {
		tmp = x * (t * (0.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.2e+132:
		tmp = x * (1.0 - (y * t))
	elif y <= 8800000000000.0:
		tmp = x - (a * (x * b))
	else:
		tmp = x * (t * (0.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.2e+132)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (y <= 8800000000000.0)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(x * Float64(t * Float64(0.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.2e+132)
		tmp = x * (1.0 - (y * t));
	elseif (y <= 8800000000000.0)
		tmp = x - (a * (x * b));
	else
		tmp = x * (t * (0.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.2e+132], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8800000000000.0], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999987e132

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 65.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 65.3%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(t \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{t \cdot y}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

      5. *-lowering-*.f64 30.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 30.1%

      \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]

   if -4.19999999999999987e132 < y < 8.8e12

   1. Initial program 95.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 68.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 68.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 43.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 43.1%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   if 8.8e12 < y

   1. Initial program 97.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

      5. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(t \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{t \cdot y}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

      5. *-lowering-*.f64 18.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 18.0%

      \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{t \cdot \left(x \cdot y\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(x \cdot y\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{t}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(y \cdot t\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \left(t \cdot \color{blue}{y}\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

       9. *-lowering-*.f64 23.7%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 23.7%

       \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;y \leq 8800000000000:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(0 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 5.2e+169) (/ x (+ 1.0 (* y t))) (- x (* a (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 5.2e+169) {
		tmp = x / (1.0 + (y * t));
	} else {
		tmp = x - (a * (x * 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 (x <= 5.2d+169) then
        tmp = x / (1.0d0 + (y * t))
    else
        tmp = x - (a * (x * 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 (x <= 5.2e+169) {
		tmp = x / (1.0 + (y * t));
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 5.2e+169:
		tmp = x / (1.0 + (y * t))
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 5.2e+169)
		tmp = Float64(x / Float64(1.0 + Float64(y * t)));
	else
		tmp = Float64(x - Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 5.2e+169)
		tmp = x / (1.0 + (y * t));
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 5.2e+169], N[(x / N[(1.0 + N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.19999999999999999e169

   1. Initial program 96.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 56.9%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 30.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 30.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if 5.19999999999999999e169 < x

   1. Initial program 93.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 73.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 73.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 52.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 52.6%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 2.7e-15) (/ x (+ 1.0 (* a b))) (- x (* a (* x b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.7e-15) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (a * (x * 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 (x <= 2.7d-15) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = x - (a * (x * 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 (x <= 2.7e-15) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.7e-15:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = x - (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.7e-15)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(x - Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.7e-15)
		tmp = x / (1.0 + (a * b));
	else
		tmp = x - (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.7e-15], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.70000000000000009e-15

   1. Initial program 97.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 55.9%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot b\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot b + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{1}\right)\right) \]

      3. *-lowering-*.f64 30.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 30.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.70000000000000009e-15 < x

   1. Initial program 92.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 63.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 63.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 34.5%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.0% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (- 1.0 (* y t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 - (y * t));
}

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 * (1.0d0 - (y * t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 - (y * t));
}

Python

def code(x, y, z, t, a, b):
	return x * (1.0 - (y * t))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(1.0 - Float64(y * t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (1.0 - (y * t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot y\right)\right)}\right)\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - t \cdot y\right)\right)\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y\right)\right)\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot t\right)\right)\right)\right) \]

   5. *-lowering-*.f64 58.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, t\right)\right)\right)\right) \]

5. Simplified 58.0%

   \[\leadsto x \cdot e^{\color{blue}{0 - y \cdot t}} \]

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(t \cdot y\right)\right)}\right) \]
7. Step-by-step derivation

   1. neg-mul-1 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(t \cdot y\right)\right)\right)\right) \]

   2. unsub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{t \cdot y}\right)\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(t \cdot y\right)}\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(y \cdot \color{blue}{t}\right)\right)\right) \]

   5. *-lowering-*.f64 30.7%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

8. Simplified 30.7%

   \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot t\right)} \]
9. Add Preprocessing

Alternative 26: 19.6% accurate, 315.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.8%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

3. Simplified 95.8%

   \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
6. Step-by-step derivation

   1. *-lowering-*.f64 57.8%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

7. Simplified 57.8%

   \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

8. Taylor expanded in a around 0

   \[\leadsto \color{blue}{x} \]
9. Step-by-step derivation

10. Simplified 23.9%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))