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

Percentage Accurate: 96.5% → 99.2%

Time: 17.4s

Alternatives: 26

Speedup: 1.5×

• 41.2% 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: 99.2% 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 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in 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 100.0%

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

7. Simplified 100.0%

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

Alternative 2: 84.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{if}\;y \leq -2200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y (- t (log z)))))))
   (if (<= y -2200000000.0)
     t_1
     (if (<= y 1.9e-47) (/ x (exp (* a (- b (log (- 1.0 z)))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * (t - log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 1.9e-47) {
		tmp = x / exp((a * (b - log((1.0 - 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((y * (t - log(z))))
    if (y <= (-2200000000.0d0)) then
        tmp = t_1
    else if (y <= 1.9d-47) then
        tmp = x / exp((a * (b - log((1.0d0 - 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((y * (t - Math.log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 1.9e-47) {
		tmp = x / Math.exp((a * (b - Math.log((1.0 - z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * (t - math.log(z))))
	tmp = 0
	if y <= -2200000000.0:
		tmp = t_1
	elif y <= 1.9e-47:
		tmp = x / math.exp((a * (b - math.log((1.0 - z)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * Float64(t - log(z)))))
	tmp = 0.0
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 1.9e-47)
		tmp = Float64(x / exp(Float64(a * Float64(b - log(Float64(1.0 - z))))));
	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 - log(z))));
	tmp = 0.0;
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 1.9e-47)
		tmp = x / exp((a * (b - log((1.0 - 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[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2200000000.0], t$95$1, If[LessEqual[y, 1.9e-47], N[(x / N[Exp[N[(a * N[(b - N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e9 or 1.90000000000000007e-47 < y

   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 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 92.3%

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

   7. Simplified 92.3%

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

   if -2.2e9 < y < 1.90000000000000007e-47

   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 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 84.1%

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

   7. Simplified 84.1%

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

Alternative 3: 84.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{if}\;y \leq -2200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-49}:\\ \;\;\;\;x \cdot {\left(e^{-2}\right)}^{\left(\frac{a \cdot b}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y (- t (log z)))))))
   (if (<= y -2200000000.0)
     t_1
     (if (<= y 1.2e-49) (* x (pow (exp -2.0) (/ (* a b) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * (t - log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 1.2e-49) {
		tmp = x * pow(exp(-2.0), ((a * b) / 2.0));
	} 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 - log(z))))
    if (y <= (-2200000000.0d0)) then
        tmp = t_1
    else if (y <= 1.2d-49) then
        tmp = x * (exp((-2.0d0)) ** ((a * b) / 2.0d0))
    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 - Math.log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 1.2e-49) {
		tmp = x * Math.pow(Math.exp(-2.0), ((a * b) / 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * (t - math.log(z))))
	tmp = 0
	if y <= -2200000000.0:
		tmp = t_1
	elif y <= 1.2e-49:
		tmp = x * math.pow(math.exp(-2.0), ((a * b) / 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * Float64(t - log(z)))))
	tmp = 0.0
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 1.2e-49)
		tmp = Float64(x * (exp(-2.0) ^ Float64(Float64(a * b) / 2.0)));
	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 - log(z))));
	tmp = 0.0;
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 1.2e-49)
		tmp = x * (exp(-2.0) ^ ((a * b) / 2.0));
	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 * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2200000000.0], t$95$1, If[LessEqual[y, 1.2e-49], N[(x * N[Power[N[Exp[-2.0], $MachinePrecision], N[(N[(a * b), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e9 or 1.19999999999999996e-49 < y

   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 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 92.3%

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

   7. Simplified 92.3%

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

   if -2.2e9 < y < 1.19999999999999996e-49

   1. Initial program 92.3%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 82.5%

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

   5. Simplified 82.5%

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

      1. sub0-neg N/A

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

      2. neg-mul-1 N/A

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

      3. exp-prod N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \left(\color{blue}{a} \cdot b\right)\right)\right) \]

      6. *-lowering-*.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   7. Applied egg-rr 82.5%

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

      1. sqr-pow N/A

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

      2. pow-prod-down N/A

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

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

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

      4. rem-log-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\left(e^{\log \left(e^{-1}\right)} \cdot e^{-1}\right), \left(\frac{a \cdot b}{2}\right)\right)\right) \]

      5. rem-log-exp N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\left(e^{\log \left(e^{-1}\right)} \cdot e^{\log \left(e^{-1}\right)}\right), \left(\frac{a \cdot b}{2}\right)\right)\right) \]

      6. prod-exp N/A

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

      7. rem-log-exp N/A

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

      8. rem-log-exp N/A

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

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\left(e^{-2}\right), \left(\frac{\color{blue}{a} \cdot b}{2}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\left(e^{\mathsf{neg}\left(2\right)}\right), \left(\frac{\color{blue}{a} \cdot b}{2}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\left(\mathsf{neg}\left(2\right)\right)\right), \left(\frac{\color{blue}{a \cdot b}}{2}\right)\right)\right) \]

      12. metadata-eval N/A

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

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

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

      14. *-lowering-*.f64 82.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 2\right)\right)\right) \]

   9. Applied egg-rr 82.5%

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

Alternative 4: 84.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{if}\;y \leq -2200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-49}:\\ \;\;\;\;x \cdot {\left(e^{-1}\right)}^{\left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y (- t (log z)))))))
   (if (<= y -2200000000.0)
     t_1
     (if (<= y 2.8e-49) (* x (pow (exp -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 / exp((y * (t - log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-49) {
		tmp = x * pow(exp(-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 / exp((y * (t - log(z))))
    if (y <= (-2200000000.0d0)) then
        tmp = t_1
    else if (y <= 2.8d-49) then
        tmp = x * (exp((-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 / Math.exp((y * (t - Math.log(z))));
	double tmp;
	if (y <= -2200000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-49) {
		tmp = x * Math.pow(Math.exp(-1.0), (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * (t - math.log(z))))
	tmp = 0
	if y <= -2200000000.0:
		tmp = t_1
	elif y <= 2.8e-49:
		tmp = x * math.pow(math.exp(-1.0), (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * Float64(t - log(z)))))
	tmp = 0.0
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-49)
		tmp = Float64(x * (exp(-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 / exp((y * (t - log(z))));
	tmp = 0.0;
	if (y <= -2200000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-49)
		tmp = x * (exp(-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[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2200000000.0], t$95$1, If[LessEqual[y, 2.8e-49], N[(x * N[Power[N[Exp[-1.0], $MachinePrecision], N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e9 or 2.79999999999999997e-49 < y

   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 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 92.3%

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

   7. Simplified 92.3%

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

   if -2.2e9 < y < 2.79999999999999997e-49

   1. Initial program 92.3%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 82.5%

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

   5. Simplified 82.5%

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

      1. sub0-neg N/A

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

      2. neg-mul-1 N/A

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

      3. exp-prod N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \left(\color{blue}{a} \cdot b\right)\right)\right) \]

      6. *-lowering-*.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   7. Applied egg-rr 82.5%

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

Alternative 5: 68.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(e^{-1}\right)}^{\left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.16e-92)
   (/ x (exp (* a b)))
   (if (<= b 2.3e+44) (/ x (exp (* y t))) (* x (pow (exp -1.0) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e-92) {
		tmp = x / exp((a * b));
	} else if (b <= 2.3e+44) {
		tmp = x / exp((y * t));
	} else {
		tmp = x * pow(exp(-1.0), (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 (b <= (-1.16d-92)) then
        tmp = x / exp((a * b))
    else if (b <= 2.3d+44) then
        tmp = x / exp((y * t))
    else
        tmp = x * (exp((-1.0d0)) ** (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 (b <= -1.16e-92) {
		tmp = x / Math.exp((a * b));
	} else if (b <= 2.3e+44) {
		tmp = x / Math.exp((y * t));
	} else {
		tmp = x * Math.pow(Math.exp(-1.0), (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.16e-92:
		tmp = x / math.exp((a * b))
	elif b <= 2.3e+44:
		tmp = x / math.exp((y * t))
	else:
		tmp = x * math.pow(math.exp(-1.0), (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.16e-92)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (b <= 2.3e+44)
		tmp = Float64(x / exp(Float64(y * t)));
	else
		tmp = Float64(x * (exp(-1.0) ^ Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.16e-92)
		tmp = x / exp((a * b));
	elseif (b <= 2.3e+44)
		tmp = x / exp((y * t));
	else
		tmp = x * (exp(-1.0) ^ (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.16e-92], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+44], N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[N[Exp[-1.0], $MachinePrecision], N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1599999999999999e-92

   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 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 74.6%

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

   7. Simplified 74.6%

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

   if -1.1599999999999999e-92 < b < 2.30000000000000004e44

   1. Initial program 92.7%

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

   3. Simplified 92.7%

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

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

   7. Simplified 72.2%

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

   if 2.30000000000000004e44 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 87.1%

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

   5. Simplified 87.1%

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

      1. sub0-neg N/A

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

      2. neg-mul-1 N/A

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

      3. exp-prod N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \left(\color{blue}{a} \cdot b\right)\right)\right) \]

      6. *-lowering-*.f64 87.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(-1\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   7. Applied egg-rr 87.1%

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

Alternative 6: 68.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -3400000000:\\ \;\;\;\;\frac{2 \cdot \frac{x}{b \cdot b}}{a \cdot a}\\ \mathbf{elif}\;y \leq 1700:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right) + \frac{0.5 \cdot \left(b \cdot b\right)}{a}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.45e+179)
   (* x (+ 1.0 (* t (- (* 0.5 (* t (* y y))) y))))
   (if (<= y -3400000000.0)
     (/ (* 2.0 (/ x (* b b))) (* a a))
     (if (<= y 1700.0)
       (/ x (exp (* a b)))
       (if (<= y 7.2e+134)
         (*
          x
          (*
           a
           (*
            (* a a)
            (+ (* b (* (* b b) -0.16666666666666666)) (/ (* 0.5 (* b b)) a)))))
         (/ x (+ 1.0 (* t (+ y (* t (* 0.5 (* y y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -3400000000.0) {
		tmp = (2.0 * (x / (b * b))) / (a * a);
	} else if (y <= 1700.0) {
		tmp = x / exp((a * b));
	} else if (y <= 7.2e+134) {
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + ((0.5 * (b * b)) / a))));
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (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 (y <= (-2.45d+179)) then
        tmp = x * (1.0d0 + (t * ((0.5d0 * (t * (y * y))) - y)))
    else if (y <= (-3400000000.0d0)) then
        tmp = (2.0d0 * (x / (b * b))) / (a * a)
    else if (y <= 1700.0d0) then
        tmp = x / exp((a * b))
    else if (y <= 7.2d+134) then
        tmp = x * (a * ((a * a) * ((b * ((b * b) * (-0.16666666666666666d0))) + ((0.5d0 * (b * b)) / a))))
    else
        tmp = x / (1.0d0 + (t * (y + (t * (0.5d0 * (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 (y <= -2.45e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -3400000000.0) {
		tmp = (2.0 * (x / (b * b))) / (a * a);
	} else if (y <= 1700.0) {
		tmp = x / Math.exp((a * b));
	} else if (y <= 7.2e+134) {
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + ((0.5 * (b * b)) / a))));
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.45e+179:
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)))
	elif y <= -3400000000.0:
		tmp = (2.0 * (x / (b * b))) / (a * a)
	elif y <= 1700.0:
		tmp = x / math.exp((a * b))
	elif y <= 7.2e+134:
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + ((0.5 * (b * b)) / a))))
	else:
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.45e+179)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(0.5 * Float64(t * Float64(y * y))) - y))));
	elseif (y <= -3400000000.0)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(b * b))) / Float64(a * a));
	elseif (y <= 1700.0)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (y <= 7.2e+134)
		tmp = Float64(x * Float64(a * Float64(Float64(a * a) * Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) + Float64(Float64(0.5 * Float64(b * b)) / a)))));
	else
		tmp = Float64(x / Float64(1.0 + Float64(t * Float64(y + Float64(t * Float64(0.5 * Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.45e+179)
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	elseif (y <= -3400000000.0)
		tmp = (2.0 * (x / (b * b))) / (a * a);
	elseif (y <= 1700.0)
		tmp = x / exp((a * b));
	elseif (y <= 7.2e+134)
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + ((0.5 * (b * b)) / a))));
	else
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.45e+179], N[(x * N[(1.0 + N[(t * N[(N[(0.5 * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3400000000.0], N[(N[(2.0 * N[(x / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1700.0], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+134], N[(x * N[(a * N[(N[(a * a), $MachinePrecision] * N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(t * N[(y + N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4499999999999999e179

   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 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

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

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

   10. Simplified 63.9%

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

   11. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

       7. unpow2 N/A

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

       8. *-lowering-*.f64 67.2%

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

   13. Simplified 67.2%

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

   if -2.4499999999999999e179 < y < -3.4e9

   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 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 30.8%

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

   7. Simplified 30.8%

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

   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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 23.9%

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

   10. Simplified 23.9%

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

   11. Taylor expanded in a around inf

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

       1. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot x}{\color{blue}{{a}^{2} \cdot {b}^{2}}} \]

       2. *-commutative N/A

          \[\leadsto \frac{2 \cdot x}{{b}^{2} \cdot \color{blue}{{a}^{2}}} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{2 \cdot x}{{b}^{2}}}{\color{blue}{{a}^{2}}} \]

       4. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{b}^{2}}}{{\color{blue}{a}}^{2}} \]

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

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

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

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

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

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

       8. unpow2 N/A

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

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

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

       10. unpow2 N/A

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

       11. *-lowering-*.f64 68.5%

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

   13. Simplified 68.5%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{b \cdot b}}{a \cdot a}} \]

   if -3.4e9 < y < 1700

   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 82.0%

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

   7. Simplified 82.0%

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

   if 1700 < y < 7.19999999999999976e134

   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 b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

   8. Simplified 27.9%

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

   9. Taylor expanded in a around inf

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

       1. cube-mult N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

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

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

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

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

       6. unpow2 N/A

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

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

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

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

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

       9. *-commutative N/A

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

       10. cube-mult N/A

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

       11. unpow2 N/A

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

       12. associate-*l* N/A

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

       13. *-commutative N/A

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

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

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

       15. *-commutative N/A

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

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

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

       17. unpow2 N/A

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

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

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

       19. associate-*r/ N/A

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

       20. /-lowering-/.f64 N/A

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

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

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

       22. unpow2 N/A

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

       23. *-lowering-*.f64 55.5%

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

   11. Simplified 55.5%

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

   if 7.19999999999999976e134 < y

   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 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 68.2%

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

   10. Simplified 68.2%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{0 - a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e-92)
   (/ x (exp (* a b)))
   (if (<= b 1.45e+47) (/ x (exp (* y t))) (* x (exp (- 0.0 (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e-92) {
		tmp = x / exp((a * b));
	} else if (b <= 1.45e+47) {
		tmp = x / exp((y * t));
	} else {
		tmp = x * exp((0.0 - (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 (b <= (-1.4d-92)) then
        tmp = x / exp((a * b))
    else if (b <= 1.45d+47) then
        tmp = x / exp((y * t))
    else
        tmp = x * exp((0.0d0 - (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 (b <= -1.4e-92) {
		tmp = x / Math.exp((a * b));
	} else if (b <= 1.45e+47) {
		tmp = x / Math.exp((y * t));
	} else {
		tmp = x * Math.exp((0.0 - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e-92:
		tmp = x / math.exp((a * b))
	elif b <= 1.45e+47:
		tmp = x / math.exp((y * t))
	else:
		tmp = x * math.exp((0.0 - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e-92)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (b <= 1.45e+47)
		tmp = Float64(x / exp(Float64(y * t)));
	else
		tmp = Float64(x * exp(Float64(0.0 - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e-92)
		tmp = x / exp((a * b));
	elseif (b <= 1.45e+47)
		tmp = x / exp((y * t));
	else
		tmp = x * exp((0.0 - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e-92], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+47], N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e-92

   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 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 74.6%

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

   7. Simplified 74.6%

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

   if -1.4e-92 < b < 1.4499999999999999e47

   1. Initial program 92.7%

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

   3. Simplified 92.7%

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

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

   7. Simplified 72.2%

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

   if 1.4499999999999999e47 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 87.1%

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

   5. Simplified 87.1%

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

      1. sub0-neg N/A

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

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

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

      3. *-lowering-*.f64 87.1%

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

   7. Applied egg-rr 87.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{0 - a \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{+51}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))))
   (if (<= b -1.4e-91) t_1 (if (<= b 1e+51) (/ x (exp (* y t))) 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 (b <= -1.4e-91) {
		tmp = t_1;
	} else if (b <= 1e+51) {
		tmp = x / exp((y * t));
	} 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 (b <= (-1.4d-91)) then
        tmp = t_1
    else if (b <= 1d+51) then
        tmp = x / exp((y * t))
    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 (b <= -1.4e-91) {
		tmp = t_1;
	} else if (b <= 1e+51) {
		tmp = x / Math.exp((y * t));
	} 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 b <= -1.4e-91:
		tmp = t_1
	elif b <= 1e+51:
		tmp = x / math.exp((y * t))
	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 (b <= -1.4e-91)
		tmp = t_1;
	elseif (b <= 1e+51)
		tmp = Float64(x / exp(Float64(y * t)));
	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 (b <= -1.4e-91)
		tmp = t_1;
	elseif (b <= 1e+51)
		tmp = x / exp((y * t));
	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[b, -1.4e-91], t$95$1, If[LessEqual[b, 1e+51], N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4e-91 or 1e51 < b

   1. Initial program 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 80.1%

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

   7. Simplified 80.1%

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

   if -1.4e-91 < b < 1e51

   1. Initial program 92.7%

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

   3. Simplified 92.7%

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

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

   7. Simplified 72.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 55.2% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(b \cdot b\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot t\_1\right)}\\ \mathbf{elif}\;y \leq 620:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right) - a\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right) + \frac{t\_1}{a}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* b b))))
   (if (<= y -2.45e+179)
     (* x (+ 1.0 (* t (- (* 0.5 (* t (* y y))) y))))
     (if (<= y -3.3e-57)
       (/ x (* a (* a t_1)))
       (if (<= y 620.0)
         (* x (+ 1.0 (* b (- (* b (* a (* a 0.5))) a))))
         (if (<= y 7.2e+131)
           (*
            x
            (*
             a
             (* (* a a) (+ (* b (* (* b b) -0.16666666666666666)) (/ t_1 a)))))
           (/ x (+ 1.0 (* t (+ y (* t (* 0.5 (* y y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (b * b);
	double tmp;
	if (y <= -2.45e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -3.3e-57) {
		tmp = x / (a * (a * t_1));
	} else if (y <= 620.0) {
		tmp = x * (1.0 + (b * ((b * (a * (a * 0.5))) - a)));
	} else if (y <= 7.2e+131) {
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + (t_1 / a))));
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (b * b)
    if (y <= (-2.45d+179)) then
        tmp = x * (1.0d0 + (t * ((0.5d0 * (t * (y * y))) - y)))
    else if (y <= (-3.3d-57)) then
        tmp = x / (a * (a * t_1))
    else if (y <= 620.0d0) then
        tmp = x * (1.0d0 + (b * ((b * (a * (a * 0.5d0))) - a)))
    else if (y <= 7.2d+131) then
        tmp = x * (a * ((a * a) * ((b * ((b * b) * (-0.16666666666666666d0))) + (t_1 / a))))
    else
        tmp = x / (1.0d0 + (t * (y + (t * (0.5d0 * (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 t_1 = 0.5 * (b * b);
	double tmp;
	if (y <= -2.45e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -3.3e-57) {
		tmp = x / (a * (a * t_1));
	} else if (y <= 620.0) {
		tmp = x * (1.0 + (b * ((b * (a * (a * 0.5))) - a)));
	} else if (y <= 7.2e+131) {
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + (t_1 / a))));
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (b * b)
	tmp = 0
	if y <= -2.45e+179:
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)))
	elif y <= -3.3e-57:
		tmp = x / (a * (a * t_1))
	elif y <= 620.0:
		tmp = x * (1.0 + (b * ((b * (a * (a * 0.5))) - a)))
	elif y <= 7.2e+131:
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + (t_1 / a))))
	else:
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(b * b))
	tmp = 0.0
	if (y <= -2.45e+179)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(0.5 * Float64(t * Float64(y * y))) - y))));
	elseif (y <= -3.3e-57)
		tmp = Float64(x / Float64(a * Float64(a * t_1)));
	elseif (y <= 620.0)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(a * Float64(a * 0.5))) - a))));
	elseif (y <= 7.2e+131)
		tmp = Float64(x * Float64(a * Float64(Float64(a * a) * Float64(Float64(b * Float64(Float64(b * b) * -0.16666666666666666)) + Float64(t_1 / a)))));
	else
		tmp = Float64(x / Float64(1.0 + Float64(t * Float64(y + Float64(t * Float64(0.5 * Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (b * b);
	tmp = 0.0;
	if (y <= -2.45e+179)
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	elseif (y <= -3.3e-57)
		tmp = x / (a * (a * t_1));
	elseif (y <= 620.0)
		tmp = x * (1.0 + (b * ((b * (a * (a * 0.5))) - a)));
	elseif (y <= 7.2e+131)
		tmp = x * (a * ((a * a) * ((b * ((b * b) * -0.16666666666666666)) + (t_1 / a))));
	else
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e+179], N[(x * N[(1.0 + N[(t * N[(N[(0.5 * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-57], N[(x / N[(a * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 620.0], N[(x * N[(1.0 + N[(b * N[(N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+131], N[(x * N[(a * N[(N[(a * a), $MachinePrecision] * N[(N[(b * N[(N[(b * b), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(t * N[(y + N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4499999999999999e179

   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 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

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

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

   10. Simplified 63.9%

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

   11. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

       7. unpow2 N/A

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

       8. *-lowering-*.f64 67.2%

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

   13. Simplified 67.2%

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

   if -2.4499999999999999e179 < y < -3.2999999999999998e-57

   1. Initial program 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in a around 0

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in a around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

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

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

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

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

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

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

       12. unpow2 N/A

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

       13. *-lowering-*.f64 61.7%

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

   13. Simplified 61.7%

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

   if -3.2999999999999998e-57 < y < 620

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

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

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

      15. *-lowering-*.f64 60.3%

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

   8. Simplified 60.3%

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

   if 620 < y < 7.20000000000000063e131

   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 b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

   8. Simplified 27.9%

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

   9. Taylor expanded in a around inf

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

       1. cube-mult N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

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

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

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

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

       6. unpow2 N/A

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

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

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

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

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

       9. *-commutative N/A

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

       10. cube-mult N/A

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

       11. unpow2 N/A

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

       12. associate-*l* N/A

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

       13. *-commutative N/A

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

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

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

       15. *-commutative N/A

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

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

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

       17. unpow2 N/A

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

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

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

       19. associate-*r/ N/A

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

       20. /-lowering-/.f64 N/A

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

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

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

       22. unpow2 N/A

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

       23. *-lowering-*.f64 55.5%

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

   11. Simplified 55.5%

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

   if 7.20000000000000063e131 < y

   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 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 68.2%

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

   10. Simplified 68.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 620:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right) - a\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(a \cdot a\right) \cdot \left(b \cdot \left(\left(b \cdot b\right) \cdot -0.16666666666666666\right) + \frac{0.5 \cdot \left(b \cdot b\right)}{a}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(a \cdot 0.5\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot t\_1 - a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot \left(b \cdot b\right)\right) \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* a 0.5))))
   (if (<= y -3.9e+179)
     (* x (+ 1.0 (* t (- (* 0.5 (* t (* y y))) y))))
     (if (<= y -4.8e-57)
       (/ x (* a (* a (* 0.5 (* b b)))))
       (if (<= y 1.42e-12)
         (* x (+ 1.0 (* b (- (* b t_1) a))))
         (if (<= y 4.6e+134)
           (* (* x (* b b)) t_1)
           (/ x (+ 1.0 (* t (+ y (* t (* 0.5 (* y y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (a * 0.5);
	double tmp;
	if (y <= -3.9e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -4.8e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 1.42e-12) {
		tmp = x * (1.0 + (b * ((b * t_1) - a)));
	} else if (y <= 4.6e+134) {
		tmp = (x * (b * b)) * t_1;
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = a * (a * 0.5d0)
    if (y <= (-3.9d+179)) then
        tmp = x * (1.0d0 + (t * ((0.5d0 * (t * (y * y))) - y)))
    else if (y <= (-4.8d-57)) then
        tmp = x / (a * (a * (0.5d0 * (b * b))))
    else if (y <= 1.42d-12) then
        tmp = x * (1.0d0 + (b * ((b * t_1) - a)))
    else if (y <= 4.6d+134) then
        tmp = (x * (b * b)) * t_1
    else
        tmp = x / (1.0d0 + (t * (y + (t * (0.5d0 * (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 t_1 = a * (a * 0.5);
	double tmp;
	if (y <= -3.9e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -4.8e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 1.42e-12) {
		tmp = x * (1.0 + (b * ((b * t_1) - a)));
	} else if (y <= 4.6e+134) {
		tmp = (x * (b * b)) * t_1;
	} else {
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (a * 0.5)
	tmp = 0
	if y <= -3.9e+179:
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)))
	elif y <= -4.8e-57:
		tmp = x / (a * (a * (0.5 * (b * b))))
	elif y <= 1.42e-12:
		tmp = x * (1.0 + (b * ((b * t_1) - a)))
	elif y <= 4.6e+134:
		tmp = (x * (b * b)) * t_1
	else:
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(a * 0.5))
	tmp = 0.0
	if (y <= -3.9e+179)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(0.5 * Float64(t * Float64(y * y))) - y))));
	elseif (y <= -4.8e-57)
		tmp = Float64(x / Float64(a * Float64(a * Float64(0.5 * Float64(b * b)))));
	elseif (y <= 1.42e-12)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * t_1) - a))));
	elseif (y <= 4.6e+134)
		tmp = Float64(Float64(x * Float64(b * b)) * t_1);
	else
		tmp = Float64(x / Float64(1.0 + Float64(t * Float64(y + Float64(t * Float64(0.5 * Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (a * 0.5);
	tmp = 0.0;
	if (y <= -3.9e+179)
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	elseif (y <= -4.8e-57)
		tmp = x / (a * (a * (0.5 * (b * b))));
	elseif (y <= 1.42e-12)
		tmp = x * (1.0 + (b * ((b * t_1) - a)));
	elseif (y <= 4.6e+134)
		tmp = (x * (b * b)) * t_1;
	else
		tmp = x / (1.0 + (t * (y + (t * (0.5 * (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+179], N[(x * N[(1.0 + N[(t * N[(N[(0.5 * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-57], N[(x / N[(a * N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e-12], N[(x * N[(1.0 + N[(b * N[(N[(b * t$95$1), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+134], N[(N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision], N[(x / N[(1.0 + N[(t * N[(y + N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.89999999999999974e179

   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 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

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

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

   10. Simplified 63.9%

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

   11. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

       7. unpow2 N/A

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

       8. *-lowering-*.f64 67.2%

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

   13. Simplified 67.2%

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

   if -3.89999999999999974e179 < y < -4.80000000000000012e-57

   1. Initial program 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in a around 0

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in a around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

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

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

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

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

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

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

       12. unpow2 N/A

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

       13. *-lowering-*.f64 61.7%

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

   13. Simplified 61.7%

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

   if -4.80000000000000012e-57 < y < 1.42e-12

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

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

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

      15. *-lowering-*.f64 60.9%

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

   8. Simplified 60.9%

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

   if 1.42e-12 < y < 4.5999999999999996e134

   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 b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in a around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

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

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

      12. unpow2 N/A

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

      13. *-lowering-*.f64 23.1%

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

   8. Simplified 23.1%

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

   9. Taylor expanded in a around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

       4. *-commutative N/A

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

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

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

       6. unpow2 N/A

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

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

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

       8. *-commutative N/A

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

       9. unpow2 N/A

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

       10. associate-*l* N/A

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

       11. *-commutative N/A

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

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

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

       13. *-commutative N/A

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

       14. *-lowering-*.f64 53.7%

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

   11. Simplified 53.7%

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

   if 4.5999999999999996e134 < y

   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 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 68.2%

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

   10. Simplified 68.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right) - a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot \left(b \cdot b\right)\right) \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + t \cdot \left(y + t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.8% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 560:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(t\_1 - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a (* a 0.5)))))
   (if (<= y -2.55e+179)
     (* x (+ 1.0 (* t (- (* 0.5 (* t (* y y))) y))))
     (if (<= y -7.5e-57)
       (/ x (* a (* a (* 0.5 (* b b)))))
       (if (<= y 560.0) (* x (+ 1.0 (* b (- t_1 a)))) (* x (* b t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * (a * 0.5));
	double tmp;
	if (y <= -2.55e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -7.5e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 560.0) {
		tmp = x * (1.0 + (b * (t_1 - a)));
	} else {
		tmp = x * (b * 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 = b * (a * (a * 0.5d0))
    if (y <= (-2.55d+179)) then
        tmp = x * (1.0d0 + (t * ((0.5d0 * (t * (y * y))) - y)))
    else if (y <= (-7.5d-57)) then
        tmp = x / (a * (a * (0.5d0 * (b * b))))
    else if (y <= 560.0d0) then
        tmp = x * (1.0d0 + (b * (t_1 - a)))
    else
        tmp = x * (b * 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 = b * (a * (a * 0.5));
	double tmp;
	if (y <= -2.55e+179) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -7.5e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 560.0) {
		tmp = x * (1.0 + (b * (t_1 - a)));
	} else {
		tmp = x * (b * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a * (a * 0.5))
	tmp = 0
	if y <= -2.55e+179:
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)))
	elif y <= -7.5e-57:
		tmp = x / (a * (a * (0.5 * (b * b))))
	elif y <= 560.0:
		tmp = x * (1.0 + (b * (t_1 - a)))
	else:
		tmp = x * (b * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * Float64(a * 0.5)))
	tmp = 0.0
	if (y <= -2.55e+179)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(0.5 * Float64(t * Float64(y * y))) - y))));
	elseif (y <= -7.5e-57)
		tmp = Float64(x / Float64(a * Float64(a * Float64(0.5 * Float64(b * b)))));
	elseif (y <= 560.0)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(t_1 - a))));
	else
		tmp = Float64(x * Float64(b * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * (a * 0.5));
	tmp = 0.0;
	if (y <= -2.55e+179)
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	elseif (y <= -7.5e-57)
		tmp = x / (a * (a * (0.5 * (b * b))));
	elseif (y <= 560.0)
		tmp = x * (1.0 + (b * (t_1 - a)));
	else
		tmp = x * (b * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+179], N[(x * N[(1.0 + N[(t * N[(N[(0.5 * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-57], N[(x / N[(a * N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 560.0], N[(x * N[(1.0 + N[(b * N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5500000000000001e179

   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 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

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

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

   10. Simplified 63.9%

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

   11. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

       7. unpow2 N/A

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

       8. *-lowering-*.f64 67.2%

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

   13. Simplified 67.2%

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

   if -2.5500000000000001e179 < y < -7.49999999999999973e-57

   1. Initial program 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in a around 0

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in a around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

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

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

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

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

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

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

       12. unpow2 N/A

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

       13. *-lowering-*.f64 61.7%

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

   13. Simplified 61.7%

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

   if -7.49999999999999973e-57 < y < 560

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

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

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

      15. *-lowering-*.f64 60.3%

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

   8. Simplified 60.3%

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

   if 560 < y

   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 b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

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

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

      12. unpow2 N/A

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

      13. *-lowering-*.f64 18.0%

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

   8. Simplified 18.0%

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

   9. Taylor expanded in a around inf

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

       1. unpow2 N/A

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

       2. associate-*r* N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

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

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

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

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

       9. *-commutative N/A

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

       10. unpow2 N/A

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

       11. associate-*l* N/A

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

       12. *-commutative N/A

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

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

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

       14. *-commutative N/A

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

       15. *-lowering-*.f64 50.4%

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

   11. Simplified 50.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 560:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right) - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+180}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 560:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(t\_1 - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a (* a 0.5)))))
   (if (<= y -8.2e+180)
     (* 0.5 (* t (* t (* y (* x y)))))
     (if (<= y -7.5e-57)
       (/ x (* a (* a (* 0.5 (* b b)))))
       (if (<= y 560.0) (* x (+ 1.0 (* b (- t_1 a)))) (* x (* b t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * (a * 0.5));
	double tmp;
	if (y <= -8.2e+180) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -7.5e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 560.0) {
		tmp = x * (1.0 + (b * (t_1 - a)));
	} else {
		tmp = x * (b * 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 = b * (a * (a * 0.5d0))
    if (y <= (-8.2d+180)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= (-7.5d-57)) then
        tmp = x / (a * (a * (0.5d0 * (b * b))))
    else if (y <= 560.0d0) then
        tmp = x * (1.0d0 + (b * (t_1 - a)))
    else
        tmp = x * (b * 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 = b * (a * (a * 0.5));
	double tmp;
	if (y <= -8.2e+180) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -7.5e-57) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 560.0) {
		tmp = x * (1.0 + (b * (t_1 - a)));
	} else {
		tmp = x * (b * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a * (a * 0.5))
	tmp = 0
	if y <= -8.2e+180:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= -7.5e-57:
		tmp = x / (a * (a * (0.5 * (b * b))))
	elif y <= 560.0:
		tmp = x * (1.0 + (b * (t_1 - a)))
	else:
		tmp = x * (b * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * Float64(a * 0.5)))
	tmp = 0.0
	if (y <= -8.2e+180)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= -7.5e-57)
		tmp = Float64(x / Float64(a * Float64(a * Float64(0.5 * Float64(b * b)))));
	elseif (y <= 560.0)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(t_1 - a))));
	else
		tmp = Float64(x * Float64(b * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * (a * 0.5));
	tmp = 0.0;
	if (y <= -8.2e+180)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= -7.5e-57)
		tmp = x / (a * (a * (0.5 * (b * b))));
	elseif (y <= 560.0)
		tmp = x * (1.0 + (b * (t_1 - a)));
	else
		tmp = x * (b * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+180], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-57], N[(x / N[(a * N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 560.0], N[(x * N[(1.0 + N[(b * N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.2e180

   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 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

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

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

   10. Simplified 63.9%

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

   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. *-lowering-*.f64 N/A

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

       2. associate-*r* N/A

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

       3. unpow2 N/A

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

       4. associate-*r* N/A

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

       5. associate-*r* N/A

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

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

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

       7. unpow2 N/A

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

       8. associate-*l* N/A

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

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

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

       10. associate-*r* N/A

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

       11. *-commutative N/A

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

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

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

       13. *-commutative N/A

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

       14. *-lowering-*.f64 46.7%

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

   13. Simplified 46.7%

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

   14. Taylor expanded in t around 0

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

       1. unpow2 N/A

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

       2. associate-*l* N/A

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

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

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

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

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

       5. *-commutative N/A

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

       6. unpow2 N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

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

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

       10. *-lowering-*.f64 64.2%

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

   16. Simplified 64.2%

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

   if -8.2e180 < y < -7.49999999999999973e-57

   1. Initial program 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in a around 0

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in a around inf

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

       1. *-commutative N/A

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

       2. unpow2 N/A

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

       3. associate-*l* N/A

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

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

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

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

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

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

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

       12. unpow2 N/A

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

       13. *-lowering-*.f64 61.7%

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

   13. Simplified 61.7%

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

   if -7.49999999999999973e-57 < y < 560

   1. Initial program 94.2%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

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

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

      15. *-lowering-*.f64 60.3%

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

   8. Simplified 60.3%

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

   if 560 < y

   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 b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-lowering-*.f64 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 18.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 18.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({a}^{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({a}^{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right) \cdot \color{blue}{b}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(a \cdot a\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       15. *-lowering-*.f64 50.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 50.4%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+180}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 560:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right) - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+179}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \mathbf{elif}\;y \leq 0.21:\\ \;\;\;\;x \cdot \left(1 + a \cdot \left(t\_1 - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 0.5 (* b b)))))
   (if (<= y -2.55e+179)
     (* 0.5 (* t (* t (* y (* x y)))))
     (if (<= y -2.15e-58)
       (/ x (* a t_1))
       (if (<= y 0.21)
         (* x (+ 1.0 (* a (- t_1 b))))
         (* x (* b (* b (* a (* a 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (0.5 * (b * b));
	double tmp;
	if (y <= -2.55e+179) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -2.15e-58) {
		tmp = x / (a * t_1);
	} else if (y <= 0.21) {
		tmp = x * (1.0 + (a * (t_1 - b)));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (0.5d0 * (b * b))
    if (y <= (-2.55d+179)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= (-2.15d-58)) then
        tmp = x / (a * t_1)
    else if (y <= 0.21d0) then
        tmp = x * (1.0d0 + (a * (t_1 - b)))
    else
        tmp = x * (b * (b * (a * (a * 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (0.5 * (b * b));
	double tmp;
	if (y <= -2.55e+179) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -2.15e-58) {
		tmp = x / (a * t_1);
	} else if (y <= 0.21) {
		tmp = x * (1.0 + (a * (t_1 - b)));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (0.5 * (b * b))
	tmp = 0
	if y <= -2.55e+179:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= -2.15e-58:
		tmp = x / (a * t_1)
	elif y <= 0.21:
		tmp = x * (1.0 + (a * (t_1 - b)))
	else:
		tmp = x * (b * (b * (a * (a * 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(0.5 * Float64(b * b)))
	tmp = 0.0
	if (y <= -2.55e+179)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= -2.15e-58)
		tmp = Float64(x / Float64(a * t_1));
	elseif (y <= 0.21)
		tmp = Float64(x * Float64(1.0 + Float64(a * Float64(t_1 - b))));
	else
		tmp = Float64(x * Float64(b * Float64(b * Float64(a * Float64(a * 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (0.5 * (b * b));
	tmp = 0.0;
	if (y <= -2.55e+179)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= -2.15e-58)
		tmp = x / (a * t_1);
	elseif (y <= 0.21)
		tmp = x * (1.0 + (a * (t_1 - b)));
	else
		tmp = x * (b * (b * (a * (a * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+179], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-58], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.21], N[(x * N[(1.0 + N[(a * N[(t$95$1 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5500000000000001e179

   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 76.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 76.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 63.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 46.7%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 46.7%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 64.2%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 64.2%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -2.5500000000000001e179 < y < -2.15e-58

   1. Initial program 92.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 40.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 40.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + \left(a \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \color{blue}{\left({b}^{2} \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \left(\frac{1}{2} \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \color{blue}{\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 25.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 25.5%

       \[\leadsto \frac{x}{\color{blue}{1 + a \cdot \left(b + a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left({a}^{2} \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(a \cdot a\right) \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(a \cdot \left(a \cdot {b}^{2}\right)\right) \cdot \frac{1}{2}\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{{b}^{2}}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(a \cdot \frac{1}{2}\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 62.7%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   13. Simplified 62.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -2.15e-58 < y < 0.209999999999999992

   1. Initial program 94.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 83.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 57.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 57.2%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   if 0.209999999999999992 < y

   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 b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 17.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 17.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({a}^{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({a}^{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right) \cdot \color{blue}{b}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(a \cdot a\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       15. *-lowering-*.f64 49.7%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 49.7%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.7% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+181}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 980:\\ \;\;\;\;x \cdot \left(1 + a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e+181)
   (* 0.5 (* t (* t (* y (* x y)))))
   (if (<= y -7e-58)
     (/ x (* a (* a (* 0.5 (* b b)))))
     (if (<= y 980.0)
       (* x (+ 1.0 (* a (* (* b b) (* a 0.5)))))
       (* x (* b (* b (* a (* a 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e+181) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -7e-58) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 980.0) {
		tmp = x * (1.0 + (a * ((b * b) * (a * 0.5))));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	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 <= (-1.55d+181)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= (-7d-58)) then
        tmp = x / (a * (a * (0.5d0 * (b * b))))
    else if (y <= 980.0d0) then
        tmp = x * (1.0d0 + (a * ((b * b) * (a * 0.5d0))))
    else
        tmp = x * (b * (b * (a * (a * 0.5d0))))
    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 <= -1.55e+181) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -7e-58) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 980.0) {
		tmp = x * (1.0 + (a * ((b * b) * (a * 0.5))));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e+181:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= -7e-58:
		tmp = x / (a * (a * (0.5 * (b * b))))
	elif y <= 980.0:
		tmp = x * (1.0 + (a * ((b * b) * (a * 0.5))))
	else:
		tmp = x * (b * (b * (a * (a * 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e+181)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= -7e-58)
		tmp = Float64(x / Float64(a * Float64(a * Float64(0.5 * Float64(b * b)))));
	elseif (y <= 980.0)
		tmp = Float64(x * Float64(1.0 + Float64(a * Float64(Float64(b * b) * Float64(a * 0.5)))));
	else
		tmp = Float64(x * Float64(b * Float64(b * Float64(a * Float64(a * 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e+181)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= -7e-58)
		tmp = x / (a * (a * (0.5 * (b * b))));
	elseif (y <= 980.0)
		tmp = x * (1.0 + (a * ((b * b) * (a * 0.5))));
	else
		tmp = x * (b * (b * (a * (a * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e+181], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-58], N[(x / N[(a * N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 980.0], N[(x * N[(1.0 + N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.54999999999999995e181

   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 76.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 76.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 63.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 46.7%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 46.7%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 64.2%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 64.2%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -1.54999999999999995e181 < y < -6.9999999999999998e-58

   1. Initial program 92.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 40.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 40.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + \left(a \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \color{blue}{\left({b}^{2} \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \left(\frac{1}{2} \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \color{blue}{\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 25.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 25.5%

       \[\leadsto \frac{x}{\color{blue}{1 + a \cdot \left(b + a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left({a}^{2} \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(a \cdot a\right) \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(a \cdot \left(a \cdot {b}^{2}\right)\right) \cdot \frac{1}{2}\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{{b}^{2}}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(a \cdot \frac{1}{2}\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 62.7%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   13. Simplified 62.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -6.9999999999999998e-58 < y < 980

   1. Initial program 94.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 83.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 83.6%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 56.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left({b}^{2} \cdot \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot b\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(\color{blue}{\frac{1}{2}} \cdot a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 56.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 56.7%

       \[\leadsto x \cdot \left(1 + a \cdot \color{blue}{\left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\right) \]

   if 980 < y

   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 b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 39.1%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 18.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 18.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({a}^{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({a}^{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right) \cdot \color{blue}{b}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(a \cdot a\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       15. *-lowering-*.f64 50.4%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 50.4%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 47.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+179}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.6e+179)
   (* 0.5 (* t (* t (* y (* x y)))))
   (if (<= y -2e-58)
     (/ x (* a (* a (* 0.5 (* b b)))))
     (if (<= y 9e-15)
       (* x (- 1.0 (* a b)))
       (* x (* b (* b (* a (* a 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+179) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -2e-58) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 9e-15) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	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 <= (-2.6d+179)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= (-2d-58)) then
        tmp = x / (a * (a * (0.5d0 * (b * b))))
    else if (y <= 9d-15) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (b * (b * (a * (a * 0.5d0))))
    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 <= -2.6e+179) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= -2e-58) {
		tmp = x / (a * (a * (0.5 * (b * b))));
	} else if (y <= 9e-15) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.6e+179:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= -2e-58:
		tmp = x / (a * (a * (0.5 * (b * b))))
	elif y <= 9e-15:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (b * (b * (a * (a * 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.6e+179)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= -2e-58)
		tmp = Float64(x / Float64(a * Float64(a * Float64(0.5 * Float64(b * b)))));
	elseif (y <= 9e-15)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(b * Float64(b * Float64(a * Float64(a * 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.6e+179)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= -2e-58)
		tmp = x / (a * (a * (0.5 * (b * b))));
	elseif (y <= 9e-15)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (b * (b * (a * (a * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.6e+179], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-58], N[(x / N[(a * N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-15], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6000000000000002e179

   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 76.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 76.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 63.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 46.7%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 46.7%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 64.2%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 64.2%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -2.6000000000000002e179 < y < -2.0000000000000001e-58

   1. Initial program 92.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 40.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 40.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + \left(a \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \color{blue}{\left({b}^{2} \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(b + a \cdot \left(\frac{1}{2} \cdot \color{blue}{{b}^{2}}\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \color{blue}{\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 25.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 25.5%

       \[\leadsto \frac{x}{\color{blue}{1 + a \cdot \left(b + a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left({a}^{2} \cdot {b}^{2}\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(\left(a \cdot a\right) \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(a \cdot \left(a \cdot {b}^{2}\right)\right) \cdot \frac{1}{2}\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \color{blue}{\left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2}\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{{b}^{2}}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(\left(a \cdot \frac{1}{2}\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 62.7%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   13. Simplified 62.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -2.0000000000000001e-58 < y < 8.9999999999999995e-15

   1. Initial program 94.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 84.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 84.0%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 53.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 53.2%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 8.9999999999999995e-15 < y

   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 b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 40.4%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 18.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 18.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({a}^{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({a}^{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right) \cdot \color{blue}{b}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(a \cdot a\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       15. *-lowering-*.f64 49.8%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 49.8%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 31.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{+30}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+163}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e-30)
   (* x (- 1.0 (* a b)))
   (if (<= b 1.24e+30)
     (- x (* x (* y t)))
     (if (<= b 2.4e+163) (/ x (+ 1.0 (* a b))) (- x (* b (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e-30) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 1.24e+30) {
		tmp = x - (x * (y * t));
	} else if (b <= 2.4e+163) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d-30)) then
        tmp = x * (1.0d0 - (a * b))
    else if (b <= 1.24d+30) then
        tmp = x - (x * (y * t))
    else if (b <= 2.4d+163) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = x - (b * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e-30) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 1.24e+30) {
		tmp = x - (x * (y * t));
	} else if (b <= 2.4e+163) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e-30:
		tmp = x * (1.0 - (a * b))
	elif b <= 1.24e+30:
		tmp = x - (x * (y * t))
	elif b <= 2.4e+163:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = x - (b * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e-30)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (b <= 1.24e+30)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	elseif (b <= 2.4e+163)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(x - Float64(b * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e-30)
		tmp = x * (1.0 - (a * b));
	elseif (b <= 1.24e+30)
		tmp = x - (x * (y * t));
	elseif (b <= 2.4e+163)
		tmp = x / (1.0 + (a * b));
	else
		tmp = x - (b * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e-30], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.24e+30], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+163], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.24999999999999993e-30

   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 b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 74.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 74.7%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 28.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 28.4%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if -1.24999999999999993e-30 < b < 1.24e30

   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 70.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 70.4%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{t \cdot \left(x \cdot y\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(t \cdot \left(x \cdot y\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \left(y \cdot \color{blue}{x}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t \cdot y\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{x}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot t\right), x\right)\right) \]

      8. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, t\right), x\right)\right) \]

   10. Simplified 43.2%

       \[\leadsto \color{blue}{x - \left(y \cdot t\right) \cdot x} \]

   if 1.24e30 < b < 2.3999999999999999e163

   1. Initial program 99.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 79.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 79.9%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 39.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 39.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]

   if 2.3999999999999999e163 < b

   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 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 91.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 91.2%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 52.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 52.9%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 55.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   12. Applied egg-rr 55.8%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{+30}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+163}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.45e-33)
   (* 0.5 (* t (* t (* y (* x y)))))
   (if (<= y 1.12e-11)
     (* x (- 1.0 (* a b)))
     (* x (* b (* b (* a (* a 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e-33) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1.12e-11) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	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 <= (-1.45d-33)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= 1.12d-11) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (b * (b * (a * (a * 0.5d0))))
    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 <= -1.45e-33) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1.12e-11) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (b * (b * (a * (a * 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.45e-33:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= 1.12e-11:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (b * (b * (a * (a * 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.45e-33)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= 1.12e-11)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(b * Float64(b * Float64(a * Float64(a * 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.45e-33)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= 1.12e-11)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (b * (b * (a * (a * 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.45e-33], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-11], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(b * N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45000000000000001e-33

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 55.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 55.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 37.8%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 37.8%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 47.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 47.6%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -1.45000000000000001e-33 < y < 1.1200000000000001e-11

   1. Initial program 93.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 82.8%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 51.9%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 1.1200000000000001e-11 < y

   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 b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 40.4%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot b + \frac{1}{2} \cdot \left(a \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \color{blue}{-1 \cdot b}\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot \left(a \cdot {b}^{2}\right) - \color{blue}{b}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(\left(a \cdot {b}^{2}\right) \cdot \frac{1}{2} - b\right)\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left({b}^{2} \cdot \frac{1}{2}\right) - b\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right) - b\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot \left(\frac{1}{2} \cdot {b}^{2}\right)\right), \color{blue}{b}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), b\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 18.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), b\right)\right)\right)\right) \]

   8. Simplified 18.8%

      \[\leadsto x \cdot \color{blue}{\left(1 + a \cdot \left(a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right) - b\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left({a}^{2} \cdot \left(b \cdot \color{blue}{b}\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\left({a}^{2} \cdot b\right) \cdot \color{blue}{b}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right) \cdot \color{blue}{b}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left({a}^{2} \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\left(a \cdot a\right) \cdot \frac{1}{2}\right)\right)\right)\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{2}\right)}\right)\right)\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \left(\frac{1}{2} \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot a\right)}\right)\right)\right)\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

       15. *-lowering-*.f64 49.8%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\frac{1}{2}}\right)\right)\right)\right)\right) \]

   11. Simplified 49.8%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(a \cdot \left(a \cdot 0.5\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 44.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \left(x \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e-31)
   (* 0.5 (* t (* t (* y (* x y)))))
   (if (<= y 1e+14) (* x (- 1.0 (* a b))) (* 0.5 (* y (* x (* y (* t t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e-31) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1e+14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = 0.5 * (y * (x * (y * (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 <= (-1.55d-31)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= 1d+14) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = 0.5d0 * (y * (x * (y * (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 <= -1.55e-31) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1e+14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = 0.5 * (y * (x * (y * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e-31:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= 1e+14:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = 0.5 * (y * (x * (y * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e-31)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= 1e+14)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x * Float64(y * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e-31)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= 1e+14)
		tmp = x * (1.0 - (a * b));
	else
		tmp = 0.5 * (y * (x * (y * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e-31], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+14], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x * N[(y * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e-31

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 55.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 55.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 37.8%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 37.8%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 47.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 47.6%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -1.55e-31 < y < 1e14

   1. Initial program 93.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 82.1%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 51.1%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 1e14 < y

   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 62.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 62.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 24.3%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 32.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 32.6%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}, y\right)\right) \]
   15. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right), y\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(x \cdot \left(y \cdot {t}^{2}\right)\right), y\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot {t}^{2}\right)\right), y\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left({t}^{2}\right)\right)\right), y\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(t \cdot t\right)\right)\right), y\right)\right) \]

       6. *-lowering-*.f64 44.9%

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, t\right)\right)\right), y\right)\right) \]

   16. Simplified 44.9%

       \[\leadsto 0.5 \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)} \cdot y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \left(x \cdot \left(y \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.7% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-35}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.6e-35)
   (* 0.5 (* t (* t (* y (* x y)))))
   (if (<= y 1e+14) (* x (- 1.0 (* a b))) (* 0.5 (* y (* t (* y (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e-35) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1e+14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = 0.5 * (y * (t * (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 <= (-5.6d-35)) then
        tmp = 0.5d0 * (t * (t * (y * (x * y))))
    else if (y <= 1d+14) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = 0.5d0 * (y * (t * (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 <= -5.6e-35) {
		tmp = 0.5 * (t * (t * (y * (x * y))));
	} else if (y <= 1e+14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = 0.5 * (y * (t * (y * (x * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.6e-35:
		tmp = 0.5 * (t * (t * (y * (x * y))))
	elif y <= 1e+14:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = 0.5 * (y * (t * (y * (x * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.6e-35)
		tmp = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))));
	elseif (y <= 1e+14)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(0.5 * Float64(y * Float64(t * Float64(y * Float64(x * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.6e-35)
		tmp = 0.5 * (t * (t * (y * (x * y))));
	elseif (y <= 1e+14)
		tmp = x * (1.0 - (a * b));
	else
		tmp = 0.5 * (y * (t * (y * (x * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.6e-35], N[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+14], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(t * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5999999999999999e-35

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 55.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 55.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 37.8%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 37.8%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 47.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 47.6%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -5.5999999999999999e-35 < y < 1e14

   1. Initial program 93.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 82.1%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 51.1%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 1e14 < y

   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 62.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 62.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 24.3%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 32.6%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 32.6%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-35}:\\ \;\;\;\;0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* t (* t (* y (* x y)))))))
   (if (<= y -1.32e-33) t_1 (if (<= y 1e+14) (* 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 = 0.5 * (t * (t * (y * (x * y))));
	double tmp;
	if (y <= -1.32e-33) {
		tmp = t_1;
	} else if (y <= 1e+14) {
		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 = 0.5d0 * (t * (t * (y * (x * y))))
    if (y <= (-1.32d-33)) then
        tmp = t_1
    else if (y <= 1d+14) 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 = 0.5 * (t * (t * (y * (x * y))));
	double tmp;
	if (y <= -1.32e-33) {
		tmp = t_1;
	} else if (y <= 1e+14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (t * (t * (y * (x * y))))
	tmp = 0
	if y <= -1.32e-33:
		tmp = t_1
	elif y <= 1e+14:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(t * Float64(t * Float64(y * Float64(x * y)))))
	tmp = 0.0
	if (y <= -1.32e-33)
		tmp = t_1;
	elseif (y <= 1e+14)
		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 = 0.5 * (t * (t * (y * (x * y))));
	tmp = 0.0;
	if (y <= -1.32e-33)
		tmp = t_1;
	elseif (y <= 1e+14)
		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[(0.5 * N[(t * N[(t * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e-33], t$95$1, If[LessEqual[y, 1e+14], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.31999999999999993e-33 or 1e14 < y

   1. Initial program 99.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 33.6%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{{y}^{2}}\right)\right) \]

       3. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot x\right) \cdot \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(\left({t}^{2} \cdot x\right) \cdot y\right) \cdot \color{blue}{y}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left({t}^{2} \cdot \left(x \cdot y\right)\right), \color{blue}{y}\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\left(t \cdot t\right) \cdot \left(x \cdot y\right)\right), y\right)\right) \]

       8. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(t \cdot \left(x \cdot y\right)\right)\right), y\right)\right) \]

       10. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(t \cdot x\right) \cdot y\right)\right), y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot \left(t \cdot x\right)\right)\right), y\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(t \cdot x\right)\right)\right), y\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), y\right)\right) \]

       14. *-lowering-*.f64 35.3%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), y\right)\right) \]

   13. Simplified 35.3%

       \[\leadsto \color{blue}{0.5 \cdot \left(\left(t \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) \cdot y\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)}\right) \]
   15. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(t \cdot t\right) \cdot \left(\color{blue}{x} \cdot {y}^{2}\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{\left(t \cdot \left(x \cdot {y}^{2}\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot {y}^{2}\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left({y}^{2} \cdot \color{blue}{x}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(\left(y \cdot y\right) \cdot x\right)\right)\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \color{blue}{\left(y \cdot x\right)}\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \left(y \cdot \left(x \cdot \color{blue}{y}\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 38.2%

           \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   16. Simplified 38.2%

       \[\leadsto 0.5 \cdot \color{blue}{\left(t \cdot \left(t \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   if -1.31999999999999993e-33 < y < 1e14

   1. Initial program 93.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 82.1%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 51.1%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - x \cdot b\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e-223)
   (* a (- (/ x a) (* x b)))
   (if (<= a 5.8e+175) (/ x (+ 1.0 (* y t))) (/ x (+ 1.0 (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e-223) {
		tmp = a * ((x / a) - (x * b));
	} else if (a <= 5.8e+175) {
		tmp = x / (1.0 + (y * t));
	} else {
		tmp = x / (1.0 + (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 <= (-8d-223)) then
        tmp = a * ((x / a) - (x * b))
    else if (a <= 5.8d+175) then
        tmp = x / (1.0d0 + (y * t))
    else
        tmp = x / (1.0d0 + (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 <= -8e-223) {
		tmp = a * ((x / a) - (x * b));
	} else if (a <= 5.8e+175) {
		tmp = x / (1.0 + (y * t));
	} else {
		tmp = x / (1.0 + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e-223:
		tmp = a * ((x / a) - (x * b))
	elif a <= 5.8e+175:
		tmp = x / (1.0 + (y * t))
	else:
		tmp = x / (1.0 + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e-223)
		tmp = Float64(a * Float64(Float64(x / a) - Float64(x * b)));
	elseif (a <= 5.8e+175)
		tmp = Float64(x / Float64(1.0 + Float64(y * t)));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8e-223)
		tmp = a * ((x / a) - (x * b));
	elseif (a <= 5.8e+175)
		tmp = x / (1.0 + (y * t));
	else
		tmp = x / (1.0 + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e-223], N[(a * N[(N[(x / a), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+175], N[(x / N[(1.0 + N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999998e-223

   1. Initial program 96.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 61.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 61.5%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 30.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 30.4%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - b \cdot x\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{x}{a} - b \cdot x\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(\frac{x}{a}\right), \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, a\right), \left(\color{blue}{b} \cdot x\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, a\right), \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       5. *-lowering-*.f64 35.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, a\right), \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 35.7%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - x \cdot b\right)} \]

   if -7.9999999999999998e-223 < a < 5.8e175

   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 68.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 68.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   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 42.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 42.9%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if 5.8e175 < a

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   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 82.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 82.1%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 45.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), 1\right)\right) \]

   10. Simplified 45.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot b + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - x \cdot b\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{1 + y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - a \cdot b\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+71}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* a b)))))
   (if (<= b -1.42e-30) t_1 (if (<= b 8e+71) (- x (* x (* y t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (a * b));
	double tmp;
	if (b <= -1.42e-30) {
		tmp = t_1;
	} else if (b <= 8e+71) {
		tmp = x - (x * (y * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (a * b))
    if (b <= (-1.42d-30)) then
        tmp = t_1
    else if (b <= 8d+71) then
        tmp = x - (x * (y * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (a * b));
	double tmp;
	if (b <= -1.42e-30) {
		tmp = t_1;
	} else if (b <= 8e+71) {
		tmp = x - (x * (y * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (a * b))
	tmp = 0
	if b <= -1.42e-30:
		tmp = t_1
	elif b <= 8e+71:
		tmp = x - (x * (y * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(a * b)))
	tmp = 0.0
	if (b <= -1.42e-30)
		tmp = t_1;
	elseif (b <= 8e+71)
		tmp = Float64(x - Float64(x * Float64(y * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (a * b));
	tmp = 0.0;
	if (b <= -1.42e-30)
		tmp = t_1;
	elseif (b <= 8e+71)
		tmp = x - (x * (y * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e-30], t$95$1, If[LessEqual[b, 8e+71], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.42e-30 or 8.0000000000000003e71 < b

   1. Initial program 99.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 81.4%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 34.5%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if -1.42e-30 < b < 8.0000000000000003e71

   1. Initial program 93.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 69.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 69.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{t \cdot \left(x \cdot y\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(t \cdot \left(x \cdot y\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \left(y \cdot \color{blue}{x}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t \cdot y\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{x}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot t\right), x\right)\right) \]

      8. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, t\right), x\right)\right) \]

   10. Simplified 42.6%

       \[\leadsto \color{blue}{x - \left(y \cdot t\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+71}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 0.28:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.8e+64)
   (- x (* y (* x t)))
   (if (<= y 0.28) (* x (- 1.0 (* a b))) (* x (- 0.0 (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.8e+64) {
		tmp = x - (y * (x * t));
	} else if (y <= 0.28) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (0.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.8d+64)) then
        tmp = x - (y * (x * t))
    else if (y <= 0.28d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (0.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.8e+64) {
		tmp = x - (y * (x * t));
	} else if (y <= 0.28) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (0.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.8e+64:
		tmp = x - (y * (x * t))
	elif y <= 0.28:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (0.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.8e+64)
		tmp = Float64(x - Float64(y * Float64(x * t)));
	elseif (y <= 0.28)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(0.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.8e+64)
		tmp = x - (y * (x * t));
	elseif (y <= 0.28)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (0.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.8e+64], N[(x - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.28], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999996e64

   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 62.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 62.4%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{x + t \cdot \left(\left(t \cdot 0.5\right) \cdot \left(x \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   11. Taylor expanded in t around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{t \cdot \left(x \cdot y\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(t \cdot \left(x \cdot y\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t \cdot x\right) \cdot \color{blue}{y}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\left(t \cdot x\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t \cdot x\right)}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \left(x \cdot \color{blue}{t}\right)\right)\right) \]

       8. *-lowering-*.f64 26.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   13. Simplified 26.5%

       \[\leadsto \color{blue}{x - y \cdot \left(x \cdot t\right)} \]

   if -7.7999999999999996e64 < y < 0.28000000000000003

   1. Initial program 93.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 45.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 45.7%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 0.28000000000000003 < y

   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 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 40.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 40.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 12.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 12.2%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto -1 \cdot \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{x} \]

       3. *-commutative N/A

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(a \cdot b\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{a \cdot b}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       8. *-lowering-*.f64 29.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 29.1%

       \[\leadsto \color{blue}{x \cdot \left(0 - a \cdot b\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 26.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0 - a \cdot b\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 560:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 0.0 (* a b)))))
   (if (<= y -7.6e-78) t_1 (if (<= y 560.0) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (y <= -7.6e-78) {
		tmp = t_1;
	} else if (y <= 560.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (0.0d0 - (a * b))
    if (y <= (-7.6d-78)) then
        tmp = t_1
    else if (y <= 560.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (y <= -7.6e-78) {
		tmp = t_1;
	} else if (y <= 560.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.0 - (a * b))
	tmp = 0
	if y <= -7.6e-78:
		tmp = t_1
	elif y <= 560.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(0.0 - Float64(a * b)))
	tmp = 0.0
	if (y <= -7.6e-78)
		tmp = t_1;
	elseif (y <= 560.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (0.0 - (a * b));
	tmp = 0.0;
	if (y <= -7.6e-78)
		tmp = t_1;
	elseif (y <= 560.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e-78], t$95$1, If[LessEqual[y, 560.0], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999998e-78 or 560 < 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 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 39.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 39.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 13.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 13.5%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto -1 \cdot \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{x} \]

       3. *-commutative N/A

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(a \cdot b\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{a \cdot b}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       8. *-lowering-*.f64 23.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 23.6%

       \[\leadsto \color{blue}{x \cdot \left(0 - a \cdot b\right)} \]

   if -7.5999999999999998e-78 < y < 560

   1. Initial program 94.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 83.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 83.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x} \]
   9. Step-by-step derivation

   10. Simplified 38.3%

       \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 31.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.185:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 0.185) (* x (- 1.0 (* a b))) (* x (- 0.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 0.185) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (0.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 0.185d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (0.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 0.185) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (0.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 0.185:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (0.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 0.185)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(0.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 0.185)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (0.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 0.185], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.185

   1. Initial program 95.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - a \cdot b\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot b\right)\right)\right)\right) \]

      4. *-lowering-*.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, b\right)\right)\right)\right) \]

   5. Simplified 65.8%

      \[\leadsto x \cdot e^{\color{blue}{0 - a \cdot b}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(a \cdot b\right)\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{a \cdot b}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 37.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot b\right)} \]

   if 0.185 < y

   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 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 40.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 40.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   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 12.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 12.2%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto -1 \cdot \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(-1 \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{x} \]

       3. *-commutative N/A

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(a \cdot b\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{a \cdot b}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       8. *-lowering-*.f64 29.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 29.1%

       \[\leadsto \color{blue}{x \cdot \left(0 - a \cdot b\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 19.3% 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 96.5%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

3. Simplified 96.5%

   \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
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 59.1%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

7. Simplified 59.1%

   \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

8. Taylor expanded in a around 0

   \[\leadsto \color{blue}{x} \]
9. Step-by-step derivation

10. Simplified 19.3%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(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))))))