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

Percentage Accurate: 96.6% → 99.6%

Time: 23.9s

Alternatives: 27

Speedup: 1.0×

• 41.6% 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: 96.6% 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: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (fma y (- (log z) t) (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(fma(y, (log(z) - t), (a * (log1p(-z) - b))));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(fma(y, Float64(log(z) - t), Float64(a * Float64(log1p(Float64(-z)) - b)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.0%

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

   1. fma-define 97.0%

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

   2. sub-neg 97.0%

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

   3. log1p-define 99.6%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)\right)} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 96.6% 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]

Derivation

1. Initial program 97.0%

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

Alternative 3: 91.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13.5 \lor \neg \left(y \leq 3.35 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -13.5) (not (<= y 3.35e-12)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (- (* a (- b)) (* y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -13.5) || !(y <= 3.35e-12)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp(((a * -b) - (y * 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 <= (-13.5d0)) .or. (.not. (y <= 3.35d-12))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp(((a * -b) - (y * 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 <= -13.5) || !(y <= 3.35e-12)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp(((a * -b) - (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -13.5) or not (y <= 3.35e-12):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp(((a * -b) - (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -13.5) || !(y <= 3.35e-12))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(a * Float64(-b)) - Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -13.5) || ~((y <= 3.35e-12)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp(((a * -b) - (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -13.5], N[Not[LessEqual[y, 3.35e-12]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(a * (-b)), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -13.5 or 3.3500000000000001e-12 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 90.7%

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

   if -13.5 < y < 3.3500000000000001e-12

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 93.9%

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

   4. Taylor expanded in t around inf 93.8%

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

      1. mul-1-neg 93.8%

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

   6. Simplified 93.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13.5 \lor \neg \left(y \leq 3.35 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right) - y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) - (a * 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 * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.0%

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

3. Taylor expanded in z around 0 95.7%

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

4. Final simplification 95.7%

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

Alternative 5: 76.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ t_2 := x \cdot {z}^{y}\\ t_3 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;y \leq -0.0095:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- a) (+ z b)))))
        (t_2 (* x (pow z y)))
        (t_3 (* x (exp (* y (- t))))))
   (if (<= y -0.0095)
     t_2
     (if (<= y 3.35e-12)
       t_1
       (if (<= y 1.18e+39)
         t_2
         (if (<= y 1.3e+47)
           t_3
           (if (<= y 7e+198) t_2 (if (<= y 7.2e+203) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-a * (z + b)));
	double t_2 = x * pow(z, y);
	double t_3 = x * exp((y * -t));
	double tmp;
	if (y <= -0.0095) {
		tmp = t_2;
	} else if (y <= 3.35e-12) {
		tmp = t_1;
	} else if (y <= 1.18e+39) {
		tmp = t_2;
	} else if (y <= 1.3e+47) {
		tmp = t_3;
	} else if (y <= 7e+198) {
		tmp = t_2;
	} else if (y <= 7.2e+203) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * exp((-a * (z + b)))
    t_2 = x * (z ** y)
    t_3 = x * exp((y * -t))
    if (y <= (-0.0095d0)) then
        tmp = t_2
    else if (y <= 3.35d-12) then
        tmp = t_1
    else if (y <= 1.18d+39) then
        tmp = t_2
    else if (y <= 1.3d+47) then
        tmp = t_3
    else if (y <= 7d+198) then
        tmp = t_2
    else if (y <= 7.2d+203) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((-a * (z + b)));
	double t_2 = x * Math.pow(z, y);
	double t_3 = x * Math.exp((y * -t));
	double tmp;
	if (y <= -0.0095) {
		tmp = t_2;
	} else if (y <= 3.35e-12) {
		tmp = t_1;
	} else if (y <= 1.18e+39) {
		tmp = t_2;
	} else if (y <= 1.3e+47) {
		tmp = t_3;
	} else if (y <= 7e+198) {
		tmp = t_2;
	} else if (y <= 7.2e+203) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-a * (z + b)))
	t_2 = x * math.pow(z, y)
	t_3 = x * math.exp((y * -t))
	tmp = 0
	if y <= -0.0095:
		tmp = t_2
	elif y <= 3.35e-12:
		tmp = t_1
	elif y <= 1.18e+39:
		tmp = t_2
	elif y <= 1.3e+47:
		tmp = t_3
	elif y <= 7e+198:
		tmp = t_2
	elif y <= 7.2e+203:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))))
	t_2 = Float64(x * (z ^ y))
	t_3 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (y <= -0.0095)
		tmp = t_2;
	elseif (y <= 3.35e-12)
		tmp = t_1;
	elseif (y <= 1.18e+39)
		tmp = t_2;
	elseif (y <= 1.3e+47)
		tmp = t_3;
	elseif (y <= 7e+198)
		tmp = t_2;
	elseif (y <= 7.2e+203)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-a * (z + b)));
	t_2 = x * (z ^ y);
	t_3 = x * exp((y * -t));
	tmp = 0.0;
	if (y <= -0.0095)
		tmp = t_2;
	elseif (y <= 3.35e-12)
		tmp = t_1;
	elseif (y <= 1.18e+39)
		tmp = t_2;
	elseif (y <= 1.3e+47)
		tmp = t_3;
	elseif (y <= 7e+198)
		tmp = t_2;
	elseif (y <= 7.2e+203)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0095], t$95$2, If[LessEqual[y, 3.35e-12], t$95$1, If[LessEqual[y, 1.18e+39], t$95$2, If[LessEqual[y, 1.3e+47], t$95$3, If[LessEqual[y, 7e+198], t$95$2, If[LessEqual[y, 7.2e+203], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00949999999999999976 or 3.3500000000000001e-12 < y < 1.17999999999999996e39 or 1.30000000000000002e47 < y < 7.00000000000000026e198

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 92.1%

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

   4. Taylor expanded in t around 0 69.5%

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

   if -0.00949999999999999976 < y < 3.3500000000000001e-12 or 7.00000000000000026e198 < y < 7.19999999999999964e203

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. sub-neg 84.1%

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

      2. log1p-define 89.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 89.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 89.7%

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

      1. associate-*r* 89.7%

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

      2. associate-*r* 89.7%

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

      3. distribute-lft-out 89.7%

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

      4. neg-mul-1 89.7%

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

   8. Simplified 89.7%

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

   if 1.17999999999999996e39 < y < 1.30000000000000002e47 or 7.19999999999999964e203 < 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 t around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-lft-neg-out 83.7%

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

      3. *-commutative 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0095:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+198}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+203}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+85} \lor \neg \left(y \leq 3.35 \cdot 10^{-12} \lor \neg \left(y \leq 9 \cdot 10^{+189}\right) \land y \leq 2.1 \cdot 10^{+241}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e+85)
         (not (or (<= y 3.35e-12) (and (not (<= y 9e+189)) (<= y 2.1e+241)))))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+85) || !((y <= 3.35e-12) || (!(y <= 9e+189) && (y <= 2.1e+241)))) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1d+85)) .or. (.not. (y <= 3.35d-12) .or. (.not. (y <= 9d+189)) .and. (y <= 2.1d+241))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+85) || !((y <= 3.35e-12) || (!(y <= 9e+189) && (y <= 2.1e+241)))) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e+85) or not ((y <= 3.35e-12) or (not (y <= 9e+189) and (y <= 2.1e+241))):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e+85) || !((y <= 3.35e-12) || (!(y <= 9e+189) && (y <= 2.1e+241))))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e+85) || ~(((y <= 3.35e-12) || (~((y <= 9e+189)) && (y <= 2.1e+241)))))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e+85], N[Not[Or[LessEqual[y, 3.35e-12], And[N[Not[LessEqual[y, 9e+189]], $MachinePrecision], LessEqual[y, 2.1e+241]]]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e85 or 3.3500000000000001e-12 < y < 8.99999999999999947e189 or 2.1e241 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf 91.6%

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

   4. Taylor expanded in t around 0 69.7%

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

   if -1e85 < y < 3.3500000000000001e-12 or 8.99999999999999947e189 < y < 2.1e241

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-out 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+85} \lor \neg \left(y \leq 3.35 \cdot 10^{-12} \lor \neg \left(y \leq 9 \cdot 10^{+189}\right) \land y \leq 2.1 \cdot 10^{+241}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -1.3)
     t_1
     (if (<= y 3.35e-12)
       (* x (exp (* a (- b))))
       (if (<= y 2.7e+39) t_1 (* x (exp (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -1.3) {
		tmp = t_1;
	} else if (y <= 3.35e-12) {
		tmp = x * exp((a * -b));
	} else if (y <= 2.7e+39) {
		tmp = t_1;
	} else {
		tmp = x * exp((y * -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) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-1.3d0)) then
        tmp = t_1
    else if (y <= 3.35d-12) then
        tmp = x * exp((a * -b))
    else if (y <= 2.7d+39) then
        tmp = t_1
    else
        tmp = x * exp((y * -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 t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.3) {
		tmp = t_1;
	} else if (y <= 3.35e-12) {
		tmp = x * Math.exp((a * -b));
	} else if (y <= 2.7e+39) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.3:
		tmp = t_1
	elif y <= 3.35e-12:
		tmp = x * math.exp((a * -b))
	elif y <= 2.7e+39:
		tmp = t_1
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.3)
		tmp = t_1;
	elseif (y <= 3.35e-12)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (y <= 2.7e+39)
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.3)
		tmp = t_1;
	elseif (y <= 3.35e-12)
		tmp = x * exp((a * -b));
	elseif (y <= 2.7e+39)
		tmp = t_1;
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3], t$95$1, If[LessEqual[y, 3.35e-12], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+39], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000004 or 3.3500000000000001e-12 < y < 2.70000000000000003e39

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 93.1%

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

   4. Taylor expanded in t around 0 68.2%

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

   if -1.30000000000000004 < y < 3.3500000000000001e-12

   1. Initial program 95.6%

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

   3. Taylor expanded in b around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-out 82.7%

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

   5. Simplified 82.7%

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

   if 2.70000000000000003e39 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-lft-neg-out 70.4%

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

      3. *-commutative 70.4%

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

   5. Simplified 70.4%

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

Alternative 8: 84.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((a * -b) - (y * t)))
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) - (y * t)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

3. Taylor expanded in z around 0 95.7%

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

4. Taylor expanded in t around inf 83.0%

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

   1. mul-1-neg 83.0%

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

6. Simplified 83.0%

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

7. Final simplification 83.0%

   \[\leadsto x \cdot e^{a \cdot \left(-b\right) - y \cdot t} \]
8. Add Preprocessing

Alternative 9: 54.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(t \cdot \left(\frac{1}{t} \cdot \frac{x}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.5e+123) (* y (* t (- (* (/ 1.0 t) (/ x y)) x))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+123) {
		tmp = y * (t * (((1.0 / t) * (x / y)) - x));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.5d+123)) then
        tmp = y * (t * (((1.0d0 / t) * (x / y)) - x))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+123) {
		tmp = y * (t * (((1.0 / t) * (x / y)) - x));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.5e+123:
		tmp = y * (t * (((1.0 / t) * (x / y)) - x))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.5e+123)
		tmp = Float64(y * Float64(t * Float64(Float64(Float64(1.0 / t) * Float64(x / y)) - x)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.5e+123)
		tmp = y * (t * (((1.0 / t) * (x / y)) - x));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.5e+123], N[(y * N[(t * N[(N[(N[(1.0 / t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999983e123

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. distribute-lft-neg-out 96.8%

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

      3. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in y around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. unsub-neg 43.7%

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

      3. associate-*r* 46.7%

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

   8. Simplified 46.7%

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

   9. Taylor expanded in y around inf 46.7%

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

   10. Taylor expanded in t around inf 46.6%

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

       1. *-un-lft-identity 46.6%

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

       2. times-frac 49.9%

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

   12. Applied egg-rr 49.9%

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

   if -4.49999999999999983e123 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 64.0%

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

   4. Taylor expanded in t around 0 55.2%

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

Alternative 10: 27.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - a \cdot b\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+195}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+265}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* a b)))))
   (if (<= a -2.7e-278)
     t_1
     (if (<= a 5.8e-184)
       (* x (* z (- a)))
       (if (<= a 1.85e-152)
         (* x (- 1.0 (* y t)))
         (if (<= a 1.65e-103)
           (* z (/ x z))
           (if (<= a 8.5e-83)
             (* y (/ x y))
             (if (<= a 9e+46)
               t_1
               (if (<= a 4.4e+143)
                 (* x (* y (- t)))
                 (if (<= a 1.35e+195)
                   (* t (* x (- y)))
                   (if (<= a 3.3e+265)
                     (* y (* x (- t)))
                     (* a (* x (- b))))))))))))))

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 (a <= -2.7e-278) {
		tmp = t_1;
	} else if (a <= 5.8e-184) {
		tmp = x * (z * -a);
	} else if (a <= 1.85e-152) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 1.65e-103) {
		tmp = z * (x / z);
	} else if (a <= 8.5e-83) {
		tmp = y * (x / y);
	} else if (a <= 9e+46) {
		tmp = t_1;
	} else if (a <= 4.4e+143) {
		tmp = x * (y * -t);
	} else if (a <= 1.35e+195) {
		tmp = t * (x * -y);
	} else if (a <= 3.3e+265) {
		tmp = y * (x * -t);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (a * b))
    if (a <= (-2.7d-278)) then
        tmp = t_1
    else if (a <= 5.8d-184) then
        tmp = x * (z * -a)
    else if (a <= 1.85d-152) then
        tmp = x * (1.0d0 - (y * t))
    else if (a <= 1.65d-103) then
        tmp = z * (x / z)
    else if (a <= 8.5d-83) then
        tmp = y * (x / y)
    else if (a <= 9d+46) then
        tmp = t_1
    else if (a <= 4.4d+143) then
        tmp = x * (y * -t)
    else if (a <= 1.35d+195) then
        tmp = t * (x * -y)
    else if (a <= 3.3d+265) then
        tmp = y * (x * -t)
    else
        tmp = a * (x * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (a * b));
	double tmp;
	if (a <= -2.7e-278) {
		tmp = t_1;
	} else if (a <= 5.8e-184) {
		tmp = x * (z * -a);
	} else if (a <= 1.85e-152) {
		tmp = x * (1.0 - (y * t));
	} else if (a <= 1.65e-103) {
		tmp = z * (x / z);
	} else if (a <= 8.5e-83) {
		tmp = y * (x / y);
	} else if (a <= 9e+46) {
		tmp = t_1;
	} else if (a <= 4.4e+143) {
		tmp = x * (y * -t);
	} else if (a <= 1.35e+195) {
		tmp = t * (x * -y);
	} else if (a <= 3.3e+265) {
		tmp = y * (x * -t);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (a * b))
	tmp = 0
	if a <= -2.7e-278:
		tmp = t_1
	elif a <= 5.8e-184:
		tmp = x * (z * -a)
	elif a <= 1.85e-152:
		tmp = x * (1.0 - (y * t))
	elif a <= 1.65e-103:
		tmp = z * (x / z)
	elif a <= 8.5e-83:
		tmp = y * (x / y)
	elif a <= 9e+46:
		tmp = t_1
	elif a <= 4.4e+143:
		tmp = x * (y * -t)
	elif a <= 1.35e+195:
		tmp = t * (x * -y)
	elif a <= 3.3e+265:
		tmp = y * (x * -t)
	else:
		tmp = a * (x * -b)
	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 (a <= -2.7e-278)
		tmp = t_1;
	elseif (a <= 5.8e-184)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (a <= 1.85e-152)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (a <= 1.65e-103)
		tmp = Float64(z * Float64(x / z));
	elseif (a <= 8.5e-83)
		tmp = Float64(y * Float64(x / y));
	elseif (a <= 9e+46)
		tmp = t_1;
	elseif (a <= 4.4e+143)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (a <= 1.35e+195)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (a <= 3.3e+265)
		tmp = Float64(y * Float64(x * Float64(-t)));
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	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 (a <= -2.7e-278)
		tmp = t_1;
	elseif (a <= 5.8e-184)
		tmp = x * (z * -a);
	elseif (a <= 1.85e-152)
		tmp = x * (1.0 - (y * t));
	elseif (a <= 1.65e-103)
		tmp = z * (x / z);
	elseif (a <= 8.5e-83)
		tmp = y * (x / y);
	elseif (a <= 9e+46)
		tmp = t_1;
	elseif (a <= 4.4e+143)
		tmp = x * (y * -t);
	elseif (a <= 1.35e+195)
		tmp = t * (x * -y);
	elseif (a <= 3.3e+265)
		tmp = y * (x * -t);
	else
		tmp = a * (x * -b);
	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[a, -2.7e-278], t$95$1, If[LessEqual[a, 5.8e-184], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-152], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-103], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-83], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+46], t$95$1, If[LessEqual[a, 4.4e+143], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+195], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+265], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -2.7000000000000001e-278 or 8.49999999999999938e-83 < a < 9.00000000000000019e46

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-out 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in a around 0 35.6%

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

      1. +-commutative 35.6%

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

      2. associate-*r* 35.6%

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

      3. neg-mul-1 35.6%

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

   8. Simplified 35.6%

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

   if -2.7000000000000001e-278 < a < 5.80000000000000028e-184

   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 y around 0 29.3%

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

      1. sub-neg 29.3%

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

      2. log1p-define 29.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 29.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 26.1%

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

   7. Taylor expanded in z around 0 26.1%

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

      1. associate-*r* 26.1%

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

      2. neg-mul-1 26.1%

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

   9. Simplified 26.1%

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

   10. Taylor expanded in a around inf 29.0%

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

       1. +-commutative 29.0%

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

       2. mul-1-neg 29.0%

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

       3. *-commutative 29.0%

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

       4. unsub-neg 29.0%

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

   12. Simplified 29.0%

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

   13. Taylor expanded in a around inf 39.1%

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

       1. mul-1-neg 39.1%

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

       2. *-commutative 39.1%

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

       3. associate-*r* 55.0%

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

       4. distribute-rgt-neg-in 55.0%

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

       5. distribute-rgt-neg-out 55.0%

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

   15. Simplified 55.0%

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

   if 5.80000000000000028e-184 < a < 1.8499999999999999e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-lft-neg-out 93.1%

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

      3. *-commutative 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. *-commutative 73.4%

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

   8. Simplified 73.4%

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

   if 1.8499999999999999e-152 < a < 1.64999999999999995e-103

   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 y around 0 40.3%

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

      1. sub-neg 40.3%

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

      2. log1p-define 40.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 40.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 23.0%

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

   7. Taylor expanded in z around 0 23.0%

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

      1. associate-*r* 23.0%

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

      2. neg-mul-1 23.0%

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

   9. Simplified 23.0%

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

   10. Taylor expanded in z around inf 47.8%

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

   11. Taylor expanded in a around 0 47.8%

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

   if 1.64999999999999995e-103 < a < 8.49999999999999938e-83

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-lft-neg-out 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 18.2%

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

      1. mul-1-neg 18.2%

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

      2. unsub-neg 18.2%

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

      3. associate-*r* 28.9%

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

   8. Simplified 28.9%

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

   9. Taylor expanded in y around inf 50.2%

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

   10. Taylor expanded in y around 0 61.1%

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

   if 9.00000000000000019e46 < a < 4.40000000000000028e143

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. distribute-lft-neg-out 56.6%

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

      3. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in y around 0 22.1%

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

      1. mul-1-neg 22.1%

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

      2. unsub-neg 22.1%

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

      3. associate-*r* 22.1%

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

   8. Simplified 22.1%

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

   9. Taylor expanded in t around inf 25.5%

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

       1. mul-1-neg 25.5%

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

       2. distribute-rgt-neg-in 25.5%

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

       3. *-commutative 25.5%

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

       4. distribute-lft-neg-in 25.5%

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

   11. Simplified 25.5%

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

       1. distribute-lft-neg-out 25.5%

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

       2. distribute-rgt-neg-out 25.5%

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

       3. *-commutative 25.5%

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

       4. associate-*l* 25.5%

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

       5. *-commutative 25.5%

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

       6. associate-*r* 36.6%

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

   13. Applied egg-rr 36.6%

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

   if 4.40000000000000028e143 < a < 1.3500000000000001e195

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-lft-neg-out 44.3%

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

      3. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in y around 0 16.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

      3. associate-*r* 16.6%

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

   8. Simplified 16.6%

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

   9. Taylor expanded in t around inf 30.6%

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

       1. mul-1-neg 30.6%

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

       2. distribute-rgt-neg-in 30.6%

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

       3. *-commutative 30.6%

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

       4. distribute-lft-neg-in 30.6%

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

   11. Simplified 30.6%

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

   if 1.3500000000000001e195 < a < 3.2999999999999998e265

   1. Initial program 85.2%

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

   3. Taylor expanded in t around inf 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-lft-neg-out 40.9%

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

      3. *-commutative 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in y around 0 18.5%

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

      1. mul-1-neg 18.5%

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

      2. unsub-neg 18.5%

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

      3. associate-*r* 18.6%

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

   8. Simplified 18.6%

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

   9. Taylor expanded in t around inf 40.7%

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

       1. associate-*r* 48.1%

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

       2. *-commutative 48.1%

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

       3. neg-mul-1 48.1%

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

       4. distribute-rgt-neg-in 48.1%

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

       5. distribute-rgt-neg-in 48.1%

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

   11. Simplified 48.1%

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

   if 3.2999999999999998e265 < a

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf 73.8%

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

      1. mul-1-neg 73.8%

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

      2. distribute-rgt-neg-out 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in a around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. associate-*r* 41.7%

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

      3. neg-mul-1 41.7%

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

   8. Simplified 41.7%

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

   9. Taylor expanded in a around inf 48.1%

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

       1. associate-*r* 48.1%

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

       2. mul-1-neg 48.1%

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

   11. Simplified 48.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot x\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+195}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+265}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.5% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(a \cdot \left(\frac{x}{z \cdot a} - x\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(t \cdot \left(\frac{\frac{x}{t}}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t (/ x (* y t))))))
   (if (<= x 1.7e-100)
     t_1
     (if (<= x 1.28e-24)
       (* a (* x (- b)))
       (if (<= x 4.4e-23)
         t_1
         (if (<= x 85000000.0)
           (* x (- 1.0 (* a b)))
           (if (<= x 3.7e+41)
             (* x (* z a))
             (if (<= x 4e+115)
               (* z (* a (- (/ x (* z a)) x)))
               (if (<= x 3.1e+191)
                 (* y (* t (- (/ (/ x t) y) x)))
                 (* t (- (/ x t) (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 1.28e-24) {
		tmp = a * (x * -b);
	} else if (x <= 4.4e-23) {
		tmp = t_1;
	} else if (x <= 85000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 3.7e+41) {
		tmp = x * (z * a);
	} else if (x <= 4e+115) {
		tmp = z * (a * ((x / (z * a)) - x));
	} else if (x <= 3.1e+191) {
		tmp = y * (t * (((x / t) / y) - x));
	} else {
		tmp = t * ((x / t) - (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t * (x / (y * t)))
    if (x <= 1.7d-100) then
        tmp = t_1
    else if (x <= 1.28d-24) then
        tmp = a * (x * -b)
    else if (x <= 4.4d-23) then
        tmp = t_1
    else if (x <= 85000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (x <= 3.7d+41) then
        tmp = x * (z * a)
    else if (x <= 4d+115) then
        tmp = z * (a * ((x / (z * a)) - x))
    else if (x <= 3.1d+191) then
        tmp = y * (t * (((x / t) / y) - x))
    else
        tmp = t * ((x / t) - (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 1.28e-24) {
		tmp = a * (x * -b);
	} else if (x <= 4.4e-23) {
		tmp = t_1;
	} else if (x <= 85000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 3.7e+41) {
		tmp = x * (z * a);
	} else if (x <= 4e+115) {
		tmp = z * (a * ((x / (z * a)) - x));
	} else if (x <= 3.1e+191) {
		tmp = y * (t * (((x / t) / y) - x));
	} else {
		tmp = t * ((x / t) - (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * (x / (y * t)))
	tmp = 0
	if x <= 1.7e-100:
		tmp = t_1
	elif x <= 1.28e-24:
		tmp = a * (x * -b)
	elif x <= 4.4e-23:
		tmp = t_1
	elif x <= 85000000.0:
		tmp = x * (1.0 - (a * b))
	elif x <= 3.7e+41:
		tmp = x * (z * a)
	elif x <= 4e+115:
		tmp = z * (a * ((x / (z * a)) - x))
	elif x <= 3.1e+191:
		tmp = y * (t * (((x / t) / y) - x))
	else:
		tmp = t * ((x / t) - (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * Float64(x / Float64(y * t))))
	tmp = 0.0
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 1.28e-24)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (x <= 4.4e-23)
		tmp = t_1;
	elseif (x <= 85000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (x <= 3.7e+41)
		tmp = Float64(x * Float64(z * a));
	elseif (x <= 4e+115)
		tmp = Float64(z * Float64(a * Float64(Float64(x / Float64(z * a)) - x)));
	elseif (x <= 3.1e+191)
		tmp = Float64(y * Float64(t * Float64(Float64(Float64(x / t) / y) - x)));
	else
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * (x / (y * t)));
	tmp = 0.0;
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 1.28e-24)
		tmp = a * (x * -b);
	elseif (x <= 4.4e-23)
		tmp = t_1;
	elseif (x <= 85000000.0)
		tmp = x * (1.0 - (a * b));
	elseif (x <= 3.7e+41)
		tmp = x * (z * a);
	elseif (x <= 4e+115)
		tmp = z * (a * ((x / (z * a)) - x));
	elseif (x <= 3.1e+191)
		tmp = y * (t * (((x / t) / y) - x));
	else
		tmp = t * ((x / t) - (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-100], t$95$1, If[LessEqual[x, 1.28e-24], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-23], t$95$1, If[LessEqual[x, 85000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+41], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+115], N[(z * N[(a * N[(N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+191], N[(y * N[(t * N[(N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < 1.69999999999999988e-100 or 1.28e-24 < x < 4.3999999999999999e-23

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-lft-neg-out 51.3%

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

      3. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in y around 0 25.1%

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

      1. mul-1-neg 25.1%

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

      2. unsub-neg 25.1%

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

      3. associate-*r* 25.8%

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

   8. Simplified 25.8%

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

   9. Taylor expanded in y around inf 26.8%

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

   10. Taylor expanded in t around inf 23.9%

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

   11. Taylor expanded in t around 0 29.8%

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

   if 1.69999999999999988e-100 < x < 1.28e-24

   1. Initial program 88.6%

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

   3. Taylor expanded in b around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. distribute-rgt-neg-out 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in a around 0 14.7%

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

      1. +-commutative 14.7%

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

      2. associate-*r* 14.7%

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

      3. neg-mul-1 14.7%

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

   8. Simplified 14.7%

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

   9. Taylor expanded in a around inf 21.0%

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

       1. associate-*r* 21.0%

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

       2. mul-1-neg 21.0%

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

   11. Simplified 21.0%

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

   if 4.3999999999999999e-23 < x < 8.5e7

   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 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-rgt-neg-out 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. associate-*r* 41.3%

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

      3. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

   if 8.5e7 < x < 3.69999999999999981e41

   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 y around 0 22.5%

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

      1. sub-neg 22.5%

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

      2. log1p-define 22.4%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 22.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.2%

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

   7. Taylor expanded in z around 0 10.2%

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

      1. associate-*r* 10.2%

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

      2. neg-mul-1 10.2%

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

   9. Simplified 10.2%

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

   10. Taylor expanded in z around inf 10.2%

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

   11. Taylor expanded in z around inf 2.7%

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

       1. associate-*r* 2.7%

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

       2. mul-1-neg 2.7%

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

   13. Simplified 2.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 1.5%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 2.9%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 2.9%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 1.4%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 2.9%

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

       6. pow1 2.9%

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

       7. *-commutative 2.9%

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

   15. Applied egg-rr 2.9%

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

       1. unpow1 2.9%

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

   17. Simplified 2.9%

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

   18. Taylor expanded in a around 0 2.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 2.9%

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

       2. associate-*l* 2.9%

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

       3. *-commutative 2.9%

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

   20. Simplified 2.9%

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

   if 3.69999999999999981e41 < x < 4.0000000000000001e115

   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 y around 0 71.2%

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

      1. sub-neg 71.2%

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

      2. log1p-define 77.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 77.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 16.8%

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

   7. Taylor expanded in z around 0 16.6%

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

      1. associate-*r* 16.6%

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

      2. neg-mul-1 16.6%

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

   9. Simplified 16.6%

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

   10. Taylor expanded in z around inf 28.5%

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

   11. Taylor expanded in a around inf 28.5%

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

       1. neg-mul-1 28.5%

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

       2. +-commutative 28.5%

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

       3. unsub-neg 28.5%

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

   13. Simplified 28.5%

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

   if 4.0000000000000001e115 < x < 3.09999999999999999e191

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-lft-neg-out 69.9%

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

      3. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. unsub-neg 45.6%

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

      3. associate-*r* 45.6%

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

   8. Simplified 45.6%

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

   9. Taylor expanded in y around inf 51.5%

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

   10. Taylor expanded in t around inf 51.4%

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

       1. associate-/r* 51.3%

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

   12. Simplified 51.3%

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

   if 3.09999999999999999e191 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-lft-neg-out 56.5%

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

      3. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. unsub-neg 41.7%

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

      3. associate-*r* 37.6%

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

   8. Simplified 37.6%

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

   9. Taylor expanded in t around inf 48.9%

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

       1. *-commutative 48.9%

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

   11. Simplified 48.9%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - y \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(a \cdot \left(\frac{x}{z \cdot a} - x\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(t \cdot \left(\frac{\frac{x}{t}}{y} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t (/ x (* y t))))))
   (if (<= x 1.7e-100)
     t_1
     (if (<= x 2.8e-24)
       (* a (* x (- b)))
       (if (<= x 3.6e-23)
         t_1
         (if (<= x 135000000.0)
           (* x (- 1.0 (* a b)))
           (if (<= x 4.3e+42)
             (* x (* z a))
             (if (<= x 2.8e+53)
               (* z (- (/ x z) (* x a)))
               (if (<= x 5e+146)
                 (* y (- (/ x y) (* x t)))
                 (* t (- (/ x t) (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = a * (x * -b);
	} else if (x <= 3.6e-23) {
		tmp = t_1;
	} else if (x <= 135000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 4.3e+42) {
		tmp = x * (z * a);
	} else if (x <= 2.8e+53) {
		tmp = z * ((x / z) - (x * a));
	} else if (x <= 5e+146) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = t * ((x / t) - (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t * (x / (y * t)))
    if (x <= 1.7d-100) then
        tmp = t_1
    else if (x <= 2.8d-24) then
        tmp = a * (x * -b)
    else if (x <= 3.6d-23) then
        tmp = t_1
    else if (x <= 135000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (x <= 4.3d+42) then
        tmp = x * (z * a)
    else if (x <= 2.8d+53) then
        tmp = z * ((x / z) - (x * a))
    else if (x <= 5d+146) then
        tmp = y * ((x / y) - (x * t))
    else
        tmp = t * ((x / t) - (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = a * (x * -b);
	} else if (x <= 3.6e-23) {
		tmp = t_1;
	} else if (x <= 135000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 4.3e+42) {
		tmp = x * (z * a);
	} else if (x <= 2.8e+53) {
		tmp = z * ((x / z) - (x * a));
	} else if (x <= 5e+146) {
		tmp = y * ((x / y) - (x * t));
	} else {
		tmp = t * ((x / t) - (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * (x / (y * t)))
	tmp = 0
	if x <= 1.7e-100:
		tmp = t_1
	elif x <= 2.8e-24:
		tmp = a * (x * -b)
	elif x <= 3.6e-23:
		tmp = t_1
	elif x <= 135000000.0:
		tmp = x * (1.0 - (a * b))
	elif x <= 4.3e+42:
		tmp = x * (z * a)
	elif x <= 2.8e+53:
		tmp = z * ((x / z) - (x * a))
	elif x <= 5e+146:
		tmp = y * ((x / y) - (x * t))
	else:
		tmp = t * ((x / t) - (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * Float64(x / Float64(y * t))))
	tmp = 0.0
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (x <= 3.6e-23)
		tmp = t_1;
	elseif (x <= 135000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (x <= 4.3e+42)
		tmp = Float64(x * Float64(z * a));
	elseif (x <= 2.8e+53)
		tmp = Float64(z * Float64(Float64(x / z) - Float64(x * a)));
	elseif (x <= 5e+146)
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * (x / (y * t)));
	tmp = 0.0;
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = a * (x * -b);
	elseif (x <= 3.6e-23)
		tmp = t_1;
	elseif (x <= 135000000.0)
		tmp = x * (1.0 - (a * b));
	elseif (x <= 4.3e+42)
		tmp = x * (z * a);
	elseif (x <= 2.8e+53)
		tmp = z * ((x / z) - (x * a));
	elseif (x <= 5e+146)
		tmp = y * ((x / y) - (x * t));
	else
		tmp = t * ((x / t) - (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-100], t$95$1, If[LessEqual[x, 2.8e-24], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-23], t$95$1, If[LessEqual[x, 135000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+42], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+53], N[(z * N[(N[(x / z), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+146], N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < 1.69999999999999988e-100 or 2.8000000000000002e-24 < x < 3.5999999999999998e-23

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-lft-neg-out 51.3%

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

      3. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in y around 0 25.1%

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

      1. mul-1-neg 25.1%

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

      2. unsub-neg 25.1%

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

      3. associate-*r* 25.8%

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

   8. Simplified 25.8%

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

   9. Taylor expanded in y around inf 26.8%

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

   10. Taylor expanded in t around inf 23.9%

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

   11. Taylor expanded in t around 0 29.8%

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

   if 1.69999999999999988e-100 < x < 2.8000000000000002e-24

   1. Initial program 88.6%

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

   3. Taylor expanded in b around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. distribute-rgt-neg-out 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in a around 0 14.7%

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

      1. +-commutative 14.7%

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

      2. associate-*r* 14.7%

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

      3. neg-mul-1 14.7%

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

   8. Simplified 14.7%

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

   9. Taylor expanded in a around inf 21.0%

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

       1. associate-*r* 21.0%

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

       2. mul-1-neg 21.0%

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

   11. Simplified 21.0%

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

   if 3.5999999999999998e-23 < x < 1.35e8

   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 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-rgt-neg-out 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. associate-*r* 41.3%

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

      3. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

   if 1.35e8 < x < 4.2999999999999998e42

   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 y around 0 22.5%

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

      1. sub-neg 22.5%

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

      2. log1p-define 22.4%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 22.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.2%

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

   7. Taylor expanded in z around 0 10.2%

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

      1. associate-*r* 10.2%

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

      2. neg-mul-1 10.2%

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

   9. Simplified 10.2%

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

   10. Taylor expanded in z around inf 10.2%

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

   11. Taylor expanded in z around inf 2.7%

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

       1. associate-*r* 2.7%

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

       2. mul-1-neg 2.7%

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

   13. Simplified 2.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 1.5%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 2.9%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 2.9%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 1.4%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 2.9%

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

       6. pow1 2.9%

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

       7. *-commutative 2.9%

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

   15. Applied egg-rr 2.9%

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

       1. unpow1 2.9%

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

   17. Simplified 2.9%

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

   18. Taylor expanded in a around 0 2.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 2.9%

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

       2. associate-*l* 2.9%

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

       3. *-commutative 2.9%

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

   20. Simplified 2.9%

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

   if 4.2999999999999998e42 < x < 2.8e53

   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 y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. log1p-define 100.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 100.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 3.5%

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

   7. Taylor expanded in z around 0 3.5%

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

      1. associate-*r* 3.5%

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

      2. neg-mul-1 3.5%

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

   9. Simplified 3.5%

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

   10. Taylor expanded in z around inf 3.5%

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

       1. +-commutative 3.5%

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

       2. mul-1-neg 3.5%

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

       3. unsub-neg 3.5%

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

   12. Applied egg-rr 3.5%

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

   if 2.8e53 < x < 4.9999999999999999e146

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-lft-neg-out 63.6%

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

      3. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in y around 0 28.9%

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

      1. mul-1-neg 28.9%

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

      2. unsub-neg 28.9%

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

      3. associate-*r* 27.6%

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

   8. Simplified 27.6%

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

   9. Taylor expanded in y around inf 35.6%

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

   if 4.9999999999999999e146 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-neg-out 57.1%

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

      3. *-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

      3. associate-*r* 39.6%

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

   8. Simplified 39.6%

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

   9. Taylor expanded in t around inf 54.8%

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

       1. *-commutative 54.8%

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

   11. Simplified 54.8%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - y \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - x \cdot a\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(a \cdot \left(\frac{x}{z \cdot a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(-1 + \frac{1}{y \cdot t}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t (/ x (* y t))))))
   (if (<= x 1.7e-100)
     t_1
     (if (<= x 2.8e-24)
       (* a (* x (- b)))
       (if (<= x 4.2e-23)
         t_1
         (if (<= x 135000000.0)
           (* x (- 1.0 (* a b)))
           (if (<= x 4.4e+39)
             (* x (* z a))
             (if (<= x 2.3e+93)
               (* z (* a (- (/ x (* z a)) x)))
               (* t (* x (* y (+ -1.0 (/ 1.0 (* y t))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = a * (x * -b);
	} else if (x <= 4.2e-23) {
		tmp = t_1;
	} else if (x <= 135000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 4.4e+39) {
		tmp = x * (z * a);
	} else if (x <= 2.3e+93) {
		tmp = z * (a * ((x / (z * a)) - x));
	} else {
		tmp = t * (x * (y * (-1.0 + (1.0 / (y * 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) :: t_1
    real(8) :: tmp
    t_1 = y * (t * (x / (y * t)))
    if (x <= 1.7d-100) then
        tmp = t_1
    else if (x <= 2.8d-24) then
        tmp = a * (x * -b)
    else if (x <= 4.2d-23) then
        tmp = t_1
    else if (x <= 135000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (x <= 4.4d+39) then
        tmp = x * (z * a)
    else if (x <= 2.3d+93) then
        tmp = z * (a * ((x / (z * a)) - x))
    else
        tmp = t * (x * (y * ((-1.0d0) + (1.0d0 / (y * 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 t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 2.8e-24) {
		tmp = a * (x * -b);
	} else if (x <= 4.2e-23) {
		tmp = t_1;
	} else if (x <= 135000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 4.4e+39) {
		tmp = x * (z * a);
	} else if (x <= 2.3e+93) {
		tmp = z * (a * ((x / (z * a)) - x));
	} else {
		tmp = t * (x * (y * (-1.0 + (1.0 / (y * t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * (x / (y * t)))
	tmp = 0
	if x <= 1.7e-100:
		tmp = t_1
	elif x <= 2.8e-24:
		tmp = a * (x * -b)
	elif x <= 4.2e-23:
		tmp = t_1
	elif x <= 135000000.0:
		tmp = x * (1.0 - (a * b))
	elif x <= 4.4e+39:
		tmp = x * (z * a)
	elif x <= 2.3e+93:
		tmp = z * (a * ((x / (z * a)) - x))
	else:
		tmp = t * (x * (y * (-1.0 + (1.0 / (y * t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * Float64(x / Float64(y * t))))
	tmp = 0.0
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (x <= 4.2e-23)
		tmp = t_1;
	elseif (x <= 135000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (x <= 4.4e+39)
		tmp = Float64(x * Float64(z * a));
	elseif (x <= 2.3e+93)
		tmp = Float64(z * Float64(a * Float64(Float64(x / Float64(z * a)) - x)));
	else
		tmp = Float64(t * Float64(x * Float64(y * Float64(-1.0 + Float64(1.0 / Float64(y * t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * (x / (y * t)));
	tmp = 0.0;
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 2.8e-24)
		tmp = a * (x * -b);
	elseif (x <= 4.2e-23)
		tmp = t_1;
	elseif (x <= 135000000.0)
		tmp = x * (1.0 - (a * b));
	elseif (x <= 4.4e+39)
		tmp = x * (z * a);
	elseif (x <= 2.3e+93)
		tmp = z * (a * ((x / (z * a)) - x));
	else
		tmp = t * (x * (y * (-1.0 + (1.0 / (y * t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-100], t$95$1, If[LessEqual[x, 2.8e-24], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-23], t$95$1, If[LessEqual[x, 135000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+39], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+93], N[(z * N[(a * N[(N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * N[(y * N[(-1.0 + N[(1.0 / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < 1.69999999999999988e-100 or 2.8000000000000002e-24 < x < 4.2000000000000002e-23

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-lft-neg-out 51.3%

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

      3. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in y around 0 25.1%

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

      1. mul-1-neg 25.1%

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

      2. unsub-neg 25.1%

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

      3. associate-*r* 25.8%

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

   8. Simplified 25.8%

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

   9. Taylor expanded in y around inf 26.8%

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

   10. Taylor expanded in t around inf 23.9%

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

   11. Taylor expanded in t around 0 29.8%

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

   if 1.69999999999999988e-100 < x < 2.8000000000000002e-24

   1. Initial program 88.6%

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

   3. Taylor expanded in b around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. distribute-rgt-neg-out 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in a around 0 14.7%

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

      1. +-commutative 14.7%

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

      2. associate-*r* 14.7%

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

      3. neg-mul-1 14.7%

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

   8. Simplified 14.7%

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

   9. Taylor expanded in a around inf 21.0%

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

       1. associate-*r* 21.0%

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

       2. mul-1-neg 21.0%

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

   11. Simplified 21.0%

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

   if 4.2000000000000002e-23 < x < 1.35e8

   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 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-rgt-neg-out 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. associate-*r* 41.3%

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

      3. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

   if 1.35e8 < x < 4.4000000000000003e39

   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 y around 0 22.5%

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

      1. sub-neg 22.5%

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

      2. log1p-define 22.4%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 22.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.2%

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

   7. Taylor expanded in z around 0 10.2%

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

      1. associate-*r* 10.2%

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

      2. neg-mul-1 10.2%

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

   9. Simplified 10.2%

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

   10. Taylor expanded in z around inf 10.2%

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

   11. Taylor expanded in z around inf 2.7%

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

       1. associate-*r* 2.7%

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

       2. mul-1-neg 2.7%

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

   13. Simplified 2.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 1.5%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 2.9%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 2.9%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 1.4%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 2.9%

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

       6. pow1 2.9%

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

       7. *-commutative 2.9%

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

   15. Applied egg-rr 2.9%

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

       1. unpow1 2.9%

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

   17. Simplified 2.9%

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

   18. Taylor expanded in a around 0 2.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 2.9%

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

       2. associate-*l* 2.9%

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

       3. *-commutative 2.9%

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

   20. Simplified 2.9%

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

   if 4.4000000000000003e39 < x < 2.3000000000000002e93

   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 y around 0 66.9%

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

      1. sub-neg 66.9%

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

      2. log1p-define 66.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 66.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 14.2%

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

   7. Taylor expanded in z around 0 13.8%

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

      1. associate-*r* 13.8%

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

      2. neg-mul-1 13.8%

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

   9. Simplified 13.8%

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

   10. Taylor expanded in z around inf 22.6%

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

   11. Taylor expanded in a around inf 22.6%

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

       1. neg-mul-1 22.6%

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

       2. +-commutative 22.6%

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

       3. unsub-neg 22.6%

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

   13. Simplified 22.6%

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

   if 2.3000000000000002e93 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-lft-neg-out 62.2%

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

      3. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. unsub-neg 43.2%

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

      3. associate-*r* 38.9%

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

   8. Simplified 38.9%

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

   9. Taylor expanded in y around inf 38.8%

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

   10. Taylor expanded in t around inf 42.3%

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

   11. Taylor expanded in x around 0 53.4%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(a \cdot \left(\frac{x}{z \cdot a} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(-1 + \frac{1}{y \cdot t}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-216}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+45}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9.6e+153)
   (* x (* a (- b)))
   (if (<= a -3.2e+43)
     (/ y (/ y x))
     (if (<= a -3.7e-216)
       (- x (* y (* x t)))
       (if (<= a -1.65e-267)
         (/ (* x y) y)
         (if (<= a 1.02e-271)
           (* x (* z (- a)))
           (if (<= a 9.4e+45)
             (- x (* t (* x y)))
             (if (<= a 4.7e+203) (* x (* y (- t))) (* a (/ x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9.6e+153) {
		tmp = x * (a * -b);
	} else if (a <= -3.2e+43) {
		tmp = y / (y / x);
	} else if (a <= -3.7e-216) {
		tmp = x - (y * (x * t));
	} else if (a <= -1.65e-267) {
		tmp = (x * y) / y;
	} else if (a <= 1.02e-271) {
		tmp = x * (z * -a);
	} else if (a <= 9.4e+45) {
		tmp = x - (t * (x * y));
	} else if (a <= 4.7e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (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 (a <= (-9.6d+153)) then
        tmp = x * (a * -b)
    else if (a <= (-3.2d+43)) then
        tmp = y / (y / x)
    else if (a <= (-3.7d-216)) then
        tmp = x - (y * (x * t))
    else if (a <= (-1.65d-267)) then
        tmp = (x * y) / y
    else if (a <= 1.02d-271) then
        tmp = x * (z * -a)
    else if (a <= 9.4d+45) then
        tmp = x - (t * (x * y))
    else if (a <= 4.7d+203) then
        tmp = x * (y * -t)
    else
        tmp = a * (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 (a <= -9.6e+153) {
		tmp = x * (a * -b);
	} else if (a <= -3.2e+43) {
		tmp = y / (y / x);
	} else if (a <= -3.7e-216) {
		tmp = x - (y * (x * t));
	} else if (a <= -1.65e-267) {
		tmp = (x * y) / y;
	} else if (a <= 1.02e-271) {
		tmp = x * (z * -a);
	} else if (a <= 9.4e+45) {
		tmp = x - (t * (x * y));
	} else if (a <= 4.7e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9.6e+153:
		tmp = x * (a * -b)
	elif a <= -3.2e+43:
		tmp = y / (y / x)
	elif a <= -3.7e-216:
		tmp = x - (y * (x * t))
	elif a <= -1.65e-267:
		tmp = (x * y) / y
	elif a <= 1.02e-271:
		tmp = x * (z * -a)
	elif a <= 9.4e+45:
		tmp = x - (t * (x * y))
	elif a <= 4.7e+203:
		tmp = x * (y * -t)
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9.6e+153)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= -3.2e+43)
		tmp = Float64(y / Float64(y / x));
	elseif (a <= -3.7e-216)
		tmp = Float64(x - Float64(y * Float64(x * t)));
	elseif (a <= -1.65e-267)
		tmp = Float64(Float64(x * y) / y);
	elseif (a <= 1.02e-271)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (a <= 9.4e+45)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (a <= 4.7e+203)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9.6e+153)
		tmp = x * (a * -b);
	elseif (a <= -3.2e+43)
		tmp = y / (y / x);
	elseif (a <= -3.7e-216)
		tmp = x - (y * (x * t));
	elseif (a <= -1.65e-267)
		tmp = (x * y) / y;
	elseif (a <= 1.02e-271)
		tmp = x * (z * -a);
	elseif (a <= 9.4e+45)
		tmp = x - (t * (x * y));
	elseif (a <= 4.7e+203)
		tmp = x * (y * -t);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9.6e+153], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e+43], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-216], N[(x - N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-267], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[a, 1.02e-271], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e+45], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+203], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -9.5999999999999997e153

   1. Initial program 95.0%

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

   3. Taylor expanded in b around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-out 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in a around 0 35.3%

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

      1. +-commutative 35.3%

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

      2. associate-*r* 35.3%

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

      3. neg-mul-1 35.3%

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

   8. Simplified 35.3%

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

   9. Taylor expanded in a around inf 32.4%

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

       1. mul-1-neg 32.4%

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

       2. associate-*r* 34.8%

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

       3. distribute-lft-neg-in 34.8%

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

       4. *-commutative 34.8%

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

       5. distribute-rgt-neg-in 34.8%

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

   11. Simplified 34.8%

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

   if -9.5999999999999997e153 < a < -3.20000000000000014e43

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-lft-neg-out 36.2%

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

      3. *-commutative 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in y around 0 14.3%

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

      1. mul-1-neg 14.3%

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

      2. unsub-neg 14.3%

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

      3. associate-*r* 14.6%

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

   8. Simplified 14.6%

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

   9. Taylor expanded in y around inf 35.3%

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

   10. Taylor expanded in y around 0 41.1%

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

       1. clear-num 41.1%

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

       2. un-div-inv 41.1%

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

   12. Applied egg-rr 41.1%

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

   if -3.20000000000000014e43 < a < -3.69999999999999996e-216

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-lft-neg-out 61.9%

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

      3. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. unsub-neg 41.2%

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

      3. associate-*r* 42.8%

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

   8. Simplified 42.8%

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

   if -3.69999999999999996e-216 < a < -1.65000000000000002e-267

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. distribute-lft-neg-out 72.7%

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

      3. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. unsub-neg 45.0%

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

      3. associate-*r* 31.6%

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

   8. Simplified 31.6%

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

   9. Taylor expanded in y around inf 5.2%

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

   10. Taylor expanded in y around 0 4.7%

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

       1. associate-*r/ 58.1%

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

       2. *-commutative 58.1%

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

   12. Applied egg-rr 58.1%

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

   if -1.65000000000000002e-267 < a < 1.02e-271

   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 y around 0 31.5%

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

      1. sub-neg 31.5%

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

      2. log1p-define 31.5%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 31.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 28.6%

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

   7. Taylor expanded in z around 0 28.6%

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

      1. associate-*r* 28.6%

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

      2. neg-mul-1 28.6%

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

   9. Simplified 28.6%

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

   10. Taylor expanded in a around inf 31.0%

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

       1. +-commutative 31.0%

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

       2. mul-1-neg 31.0%

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

       3. *-commutative 31.0%

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

       4. unsub-neg 31.0%

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

   12. Simplified 31.0%

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

   13. Taylor expanded in a around inf 44.7%

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

       1. mul-1-neg 44.7%

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

       2. *-commutative 44.7%

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

       3. associate-*r* 49.1%

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

       4. distribute-rgt-neg-in 49.1%

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

       5. distribute-rgt-neg-out 49.1%

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

   15. Simplified 49.1%

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

   if 1.02e-271 < a < 9.40000000000000004e45

   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 t around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-lft-neg-out 61.0%

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

      3. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in y around 0 32.9%

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

      1. mul-1-neg 32.9%

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

      2. unsub-neg 32.9%

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

      3. associate-*r* 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in t around 0 32.9%

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

       1. *-commutative 32.9%

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

   11. Simplified 32.9%

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

   if 9.40000000000000004e45 < a < 4.70000000000000002e203

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-lft-neg-out 49.6%

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

      3. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in y around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. unsub-neg 18.1%

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

      3. associate-*r* 18.1%

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

   8. Simplified 18.1%

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

   9. Taylor expanded in t around inf 28.4%

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

       1. mul-1-neg 28.4%

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

       2. distribute-rgt-neg-in 28.4%

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

       3. *-commutative 28.4%

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

       4. distribute-lft-neg-in 28.4%

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

   11. Simplified 28.4%

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

       1. distribute-lft-neg-out 28.4%

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

       2. distribute-rgt-neg-out 28.4%

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

       3. *-commutative 28.4%

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

       4. associate-*l* 25.6%

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

       5. *-commutative 25.6%

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

       6. associate-*r* 31.2%

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

   13. Applied egg-rr 31.2%

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

   if 4.70000000000000002e203 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. sub-neg 74.7%

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

      2. log1p-define 92.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 92.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 4.2%

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

   7. Taylor expanded in z around 0 2.5%

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

      1. associate-*r* 2.5%

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

      2. neg-mul-1 2.5%

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

   9. Simplified 2.5%

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

   10. Taylor expanded in a around inf 16.5%

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

       1. +-commutative 16.5%

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

       2. mul-1-neg 16.5%

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

       3. *-commutative 16.5%

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

       4. unsub-neg 16.5%

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

   12. Simplified 16.5%

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

   13. Taylor expanded in a around 0 42.5%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-216}:\\ \;\;\;\;x - y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+45}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.2% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.2e-278)
   (* x (- 1.0 (* a b)))
   (if (<= a 4.2e-175)
     (* x (* z (- a)))
     (if (<= a 1.45e-169)
       x
       (if (<= a 3.2e-109)
         (* t (- (/ x t) (* x y)))
         (if (<= a 2.5e+47)
           (/ y (/ y x))
           (if (<= a 2.4e+203) (* x (* y (- t))) (* a (/ x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.2e-278) {
		tmp = x * (1.0 - (a * b));
	} else if (a <= 4.2e-175) {
		tmp = x * (z * -a);
	} else if (a <= 1.45e-169) {
		tmp = x;
	} else if (a <= 3.2e-109) {
		tmp = t * ((x / t) - (x * y));
	} else if (a <= 2.5e+47) {
		tmp = y / (y / x);
	} else if (a <= 2.4e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (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 (a <= (-7.2d-278)) then
        tmp = x * (1.0d0 - (a * b))
    else if (a <= 4.2d-175) then
        tmp = x * (z * -a)
    else if (a <= 1.45d-169) then
        tmp = x
    else if (a <= 3.2d-109) then
        tmp = t * ((x / t) - (x * y))
    else if (a <= 2.5d+47) then
        tmp = y / (y / x)
    else if (a <= 2.4d+203) then
        tmp = x * (y * -t)
    else
        tmp = a * (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 (a <= -7.2e-278) {
		tmp = x * (1.0 - (a * b));
	} else if (a <= 4.2e-175) {
		tmp = x * (z * -a);
	} else if (a <= 1.45e-169) {
		tmp = x;
	} else if (a <= 3.2e-109) {
		tmp = t * ((x / t) - (x * y));
	} else if (a <= 2.5e+47) {
		tmp = y / (y / x);
	} else if (a <= 2.4e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.2e-278:
		tmp = x * (1.0 - (a * b))
	elif a <= 4.2e-175:
		tmp = x * (z * -a)
	elif a <= 1.45e-169:
		tmp = x
	elif a <= 3.2e-109:
		tmp = t * ((x / t) - (x * y))
	elif a <= 2.5e+47:
		tmp = y / (y / x)
	elif a <= 2.4e+203:
		tmp = x * (y * -t)
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.2e-278)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (a <= 4.2e-175)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (a <= 1.45e-169)
		tmp = x;
	elseif (a <= 3.2e-109)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (a <= 2.5e+47)
		tmp = Float64(y / Float64(y / x));
	elseif (a <= 2.4e+203)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.2e-278)
		tmp = x * (1.0 - (a * b));
	elseif (a <= 4.2e-175)
		tmp = x * (z * -a);
	elseif (a <= 1.45e-169)
		tmp = x;
	elseif (a <= 3.2e-109)
		tmp = t * ((x / t) - (x * y));
	elseif (a <= 2.5e+47)
		tmp = y / (y / x);
	elseif (a <= 2.4e+203)
		tmp = x * (y * -t);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.2e-278], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-175], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-169], x, If[LessEqual[a, 3.2e-109], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+47], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+203], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -7.19999999999999993e-278

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-rgt-neg-out 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in a around 0 37.3%

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

      1. +-commutative 37.3%

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

      2. associate-*r* 37.3%

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

      3. neg-mul-1 37.3%

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

   8. Simplified 37.3%

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

   if -7.19999999999999993e-278 < a < 4.2e-175

   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 y around 0 29.3%

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

      1. sub-neg 29.3%

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

      2. log1p-define 29.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 29.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 26.1%

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

   7. Taylor expanded in z around 0 26.1%

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

      1. associate-*r* 26.1%

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

      2. neg-mul-1 26.1%

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

   9. Simplified 26.1%

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

   10. Taylor expanded in a around inf 29.0%

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

       1. +-commutative 29.0%

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

       2. mul-1-neg 29.0%

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

       3. *-commutative 29.0%

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

       4. unsub-neg 29.0%

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

   12. Simplified 29.0%

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

   13. Taylor expanded in a around inf 39.1%

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

       1. mul-1-neg 39.1%

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

       2. *-commutative 39.1%

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

       3. associate-*r* 55.0%

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

       4. distribute-rgt-neg-in 55.0%

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

       5. distribute-rgt-neg-out 55.0%

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

   15. Simplified 55.0%

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

   if 4.2e-175 < a < 1.4500000000000001e-169

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-lft-neg-out 65.3%

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

      3. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 65.3%

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

   if 1.4500000000000001e-169 < a < 3.2000000000000002e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-*r* 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in t around inf 62.8%

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

       1. *-commutative 62.8%

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

   11. Simplified 62.8%

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

   if 3.2000000000000002e-109 < a < 2.50000000000000011e47

   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 t around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-lft-neg-out 56.9%

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

      3. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y around 0 24.4%

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

      1. mul-1-neg 24.4%

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

      2. unsub-neg 24.4%

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

      3. associate-*r* 26.6%

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

   8. Simplified 26.6%

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

   9. Taylor expanded in y around inf 26.6%

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

   10. Taylor expanded in y around 0 29.2%

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

       1. clear-num 29.2%

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

       2. un-div-inv 29.2%

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

   12. Applied egg-rr 29.2%

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

   if 2.50000000000000011e47 < a < 2.4000000000000001e203

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. distribute-lft-neg-out 49.5%

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

      3. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in y around 0 19.1%

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

      1. mul-1-neg 19.1%

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

      2. unsub-neg 19.1%

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

      3. associate-*r* 19.1%

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

   8. Simplified 19.1%

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

   9. Taylor expanded in t around inf 30.0%

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

       1. mul-1-neg 30.0%

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

       2. distribute-rgt-neg-in 30.0%

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

       3. *-commutative 30.0%

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

       4. distribute-lft-neg-in 30.0%

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

   11. Simplified 30.0%

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

       1. distribute-lft-neg-out 30.0%

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

       2. distribute-rgt-neg-out 30.0%

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

       3. *-commutative 30.0%

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

       4. associate-*l* 27.1%

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

       5. *-commutative 27.1%

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

       6. associate-*r* 33.1%

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

   13. Applied egg-rr 33.1%

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

   if 2.4000000000000001e203 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. sub-neg 74.7%

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

      2. log1p-define 92.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 92.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 4.2%

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

   7. Taylor expanded in z around 0 2.5%

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

      1. associate-*r* 2.5%

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

      2. neg-mul-1 2.5%

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

   9. Simplified 2.5%

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

   10. Taylor expanded in a around inf 16.5%

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

       1. +-commutative 16.5%

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

       2. mul-1-neg 16.5%

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

       3. *-commutative 16.5%

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

       4. unsub-neg 16.5%

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

   12. Simplified 16.5%

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

   13. Taylor expanded in a around 0 42.5%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.5% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(x \cdot y\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t (* x y)))))
   (if (<= a -1e+154)
     (* x (* a (- b)))
     (if (<= a -3.9e+43)
       (/ y (/ y x))
       (if (<= a -7.6e-274)
         t_1
         (if (<= a 1.12e-259)
           (* x (* z (- a)))
           (if (<= a 1.6e+40)
             t_1
             (if (<= a 1.35e+203) (* x (* y (- t))) (* a (/ x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * (x * y));
	double tmp;
	if (a <= -1e+154) {
		tmp = x * (a * -b);
	} else if (a <= -3.9e+43) {
		tmp = y / (y / x);
	} else if (a <= -7.6e-274) {
		tmp = t_1;
	} else if (a <= 1.12e-259) {
		tmp = x * (z * -a);
	} else if (a <= 1.6e+40) {
		tmp = t_1;
	} else if (a <= 1.35e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (x * y))
    if (a <= (-1d+154)) then
        tmp = x * (a * -b)
    else if (a <= (-3.9d+43)) then
        tmp = y / (y / x)
    else if (a <= (-7.6d-274)) then
        tmp = t_1
    else if (a <= 1.12d-259) then
        tmp = x * (z * -a)
    else if (a <= 1.6d+40) then
        tmp = t_1
    else if (a <= 1.35d+203) then
        tmp = x * (y * -t)
    else
        tmp = a * (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 t_1 = x - (t * (x * y));
	double tmp;
	if (a <= -1e+154) {
		tmp = x * (a * -b);
	} else if (a <= -3.9e+43) {
		tmp = y / (y / x);
	} else if (a <= -7.6e-274) {
		tmp = t_1;
	} else if (a <= 1.12e-259) {
		tmp = x * (z * -a);
	} else if (a <= 1.6e+40) {
		tmp = t_1;
	} else if (a <= 1.35e+203) {
		tmp = x * (y * -t);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * (x * y))
	tmp = 0
	if a <= -1e+154:
		tmp = x * (a * -b)
	elif a <= -3.9e+43:
		tmp = y / (y / x)
	elif a <= -7.6e-274:
		tmp = t_1
	elif a <= 1.12e-259:
		tmp = x * (z * -a)
	elif a <= 1.6e+40:
		tmp = t_1
	elif a <= 1.35e+203:
		tmp = x * (y * -t)
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * Float64(x * y)))
	tmp = 0.0
	if (a <= -1e+154)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (a <= -3.9e+43)
		tmp = Float64(y / Float64(y / x));
	elseif (a <= -7.6e-274)
		tmp = t_1;
	elseif (a <= 1.12e-259)
		tmp = Float64(x * Float64(z * Float64(-a)));
	elseif (a <= 1.6e+40)
		tmp = t_1;
	elseif (a <= 1.35e+203)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (t * (x * y));
	tmp = 0.0;
	if (a <= -1e+154)
		tmp = x * (a * -b);
	elseif (a <= -3.9e+43)
		tmp = y / (y / x);
	elseif (a <= -7.6e-274)
		tmp = t_1;
	elseif (a <= 1.12e-259)
		tmp = x * (z * -a);
	elseif (a <= 1.6e+40)
		tmp = t_1;
	elseif (a <= 1.35e+203)
		tmp = x * (y * -t);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+154], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e+43], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.6e-274], t$95$1, If[LessEqual[a, 1.12e-259], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+40], t$95$1, If[LessEqual[a, 1.35e+203], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.00000000000000004e154

   1. Initial program 95.0%

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

   3. Taylor expanded in b around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-out 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in a around 0 35.3%

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

      1. +-commutative 35.3%

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

      2. associate-*r* 35.3%

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

      3. neg-mul-1 35.3%

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

   8. Simplified 35.3%

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

   9. Taylor expanded in a around inf 32.4%

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

       1. mul-1-neg 32.4%

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

       2. associate-*r* 34.8%

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

       3. distribute-lft-neg-in 34.8%

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

       4. *-commutative 34.8%

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

       5. distribute-rgt-neg-in 34.8%

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

   11. Simplified 34.8%

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

   if -1.00000000000000004e154 < a < -3.9000000000000001e43

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-lft-neg-out 36.2%

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

      3. *-commutative 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in y around 0 14.3%

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

      1. mul-1-neg 14.3%

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

      2. unsub-neg 14.3%

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

      3. associate-*r* 14.6%

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

   8. Simplified 14.6%

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

   9. Taylor expanded in y around inf 35.3%

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

   10. Taylor expanded in y around 0 41.1%

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

       1. clear-num 41.1%

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

       2. un-div-inv 41.1%

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

   12. Applied egg-rr 41.1%

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

   if -3.9000000000000001e43 < a < -7.59999999999999969e-274 or 1.1199999999999999e-259 < a < 1.5999999999999999e40

   1. Initial program 99.3%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-lft-neg-out 62.9%

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

      3. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

      3. associate-*r* 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around 0 37.3%

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

       1. *-commutative 37.3%

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

   11. Simplified 37.3%

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

   if -7.59999999999999969e-274 < a < 1.1199999999999999e-259

   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 y around 0 25.5%

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

      1. sub-neg 25.5%

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

      2. log1p-define 25.5%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 25.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 22.1%

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

   7. Taylor expanded in z around 0 22.1%

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

      1. associate-*r* 22.1%

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

      2. neg-mul-1 22.1%

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

   9. Simplified 22.1%

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

   10. Taylor expanded in a around inf 30.2%

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

       1. +-commutative 30.2%

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

       2. mul-1-neg 30.2%

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

       3. *-commutative 30.2%

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

       4. unsub-neg 30.2%

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

   12. Simplified 30.2%

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

   13. Taylor expanded in a around inf 51.6%

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

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-a \cdot \left(x \cdot z\right)} \]

       2. *-commutative 51.6%

          \[\leadsto -\color{blue}{\left(x \cdot z\right) \cdot a} \]

       3. associate-*r* 56.8%

          \[\leadsto -\color{blue}{x \cdot \left(z \cdot a\right)} \]

       4. distribute-rgt-neg-in 56.8%

          \[\leadsto \color{blue}{x \cdot \left(-z \cdot a\right)} \]

       5. distribute-rgt-neg-out 56.8%

          \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-a\right)\right)} \]

   15. Simplified 56.8%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(-a\right)\right)} \]

   if 1.5999999999999999e40 < a < 1.35e203

   1. Initial program 97.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 49.6%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 49.6%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 49.6%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 49.6%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.1%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 18.1%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 18.1%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 18.1%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 18.1%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in t around inf 28.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 28.4%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. distribute-rgt-neg-in 28.4%

          \[\leadsto \color{blue}{t \cdot \left(-x \cdot y\right)} \]

       3. *-commutative 28.4%

          \[\leadsto t \cdot \left(-\color{blue}{y \cdot x}\right) \]

       4. distribute-lft-neg-in 28.4%

          \[\leadsto t \cdot \color{blue}{\left(\left(-y\right) \cdot x\right)} \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{t \cdot \left(\left(-y\right) \cdot x\right)} \]
   12. Step-by-step derivation

       1. distribute-lft-neg-out 28.4%

          \[\leadsto t \cdot \color{blue}{\left(-y \cdot x\right)} \]

       2. distribute-rgt-neg-out 28.4%

          \[\leadsto \color{blue}{-t \cdot \left(y \cdot x\right)} \]

       3. *-commutative 28.4%

          \[\leadsto -t \cdot \color{blue}{\left(x \cdot y\right)} \]

       4. associate-*l* 25.6%

          \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot y} \]

       5. *-commutative 25.6%

          \[\leadsto -\color{blue}{y \cdot \left(t \cdot x\right)} \]

       6. associate-*r* 31.2%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

   13. Applied egg-rr 31.2%

       \[\leadsto \color{blue}{-\left(y \cdot t\right) \cdot x} \]

   if 1.35e203 < a

   1. Initial program 89.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 74.7%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 92.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 92.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 4.2%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 2.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 2.5%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 2.5%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 2.5%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 16.5%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 16.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 16.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 16.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 16.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 16.5%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 42.5%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-274}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 53000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(\frac{\frac{x}{t}}{y} - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* t (/ x (* y t))))))
   (if (<= x 1.7e-100)
     t_1
     (if (<= x 1.65e-24)
       (* a (* x (- b)))
       (if (<= x 3.5e-23)
         t_1
         (if (<= x 53000000.0)
           (* x (- 1.0 (* a b)))
           (if (<= x 1.35e+39)
             (* x (* z a))
             (* y (* t (- (/ (/ x t) y) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 1.65e-24) {
		tmp = a * (x * -b);
	} else if (x <= 3.5e-23) {
		tmp = t_1;
	} else if (x <= 53000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 1.35e+39) {
		tmp = x * (z * a);
	} else {
		tmp = y * (t * (((x / t) / y) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t * (x / (y * t)))
    if (x <= 1.7d-100) then
        tmp = t_1
    else if (x <= 1.65d-24) then
        tmp = a * (x * -b)
    else if (x <= 3.5d-23) then
        tmp = t_1
    else if (x <= 53000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (x <= 1.35d+39) then
        tmp = x * (z * a)
    else
        tmp = y * (t * (((x / t) / y) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (t * (x / (y * t)));
	double tmp;
	if (x <= 1.7e-100) {
		tmp = t_1;
	} else if (x <= 1.65e-24) {
		tmp = a * (x * -b);
	} else if (x <= 3.5e-23) {
		tmp = t_1;
	} else if (x <= 53000000.0) {
		tmp = x * (1.0 - (a * b));
	} else if (x <= 1.35e+39) {
		tmp = x * (z * a);
	} else {
		tmp = y * (t * (((x / t) / y) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (t * (x / (y * t)))
	tmp = 0
	if x <= 1.7e-100:
		tmp = t_1
	elif x <= 1.65e-24:
		tmp = a * (x * -b)
	elif x <= 3.5e-23:
		tmp = t_1
	elif x <= 53000000.0:
		tmp = x * (1.0 - (a * b))
	elif x <= 1.35e+39:
		tmp = x * (z * a)
	else:
		tmp = y * (t * (((x / t) / y) - x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * Float64(x / Float64(y * t))))
	tmp = 0.0
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 1.65e-24)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (x <= 3.5e-23)
		tmp = t_1;
	elseif (x <= 53000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (x <= 1.35e+39)
		tmp = Float64(x * Float64(z * a));
	else
		tmp = Float64(y * Float64(t * Float64(Float64(Float64(x / t) / y) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (t * (x / (y * t)));
	tmp = 0.0;
	if (x <= 1.7e-100)
		tmp = t_1;
	elseif (x <= 1.65e-24)
		tmp = a * (x * -b);
	elseif (x <= 3.5e-23)
		tmp = t_1;
	elseif (x <= 53000000.0)
		tmp = x * (1.0 - (a * b));
	elseif (x <= 1.35e+39)
		tmp = x * (z * a);
	else
		tmp = y * (t * (((x / t) / y) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(t * N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-100], t$95$1, If[LessEqual[x, 1.65e-24], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-23], t$95$1, If[LessEqual[x, 53000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+39], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * N[(N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < 1.69999999999999988e-100 or 1.64999999999999992e-24 < x < 3.49999999999999993e-23

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 51.3%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 51.3%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 51.3%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 25.1%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.1%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 25.1%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 25.8%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 25.8%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 26.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in t around inf 23.9%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(\frac{x}{t \cdot y} - x\right)\right)} \]

   11. Taylor expanded in t around 0 29.8%

       \[\leadsto y \cdot \left(t \cdot \color{blue}{\frac{x}{t \cdot y}}\right) \]

   if 1.69999999999999988e-100 < x < 1.64999999999999992e-24

   1. Initial program 88.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 48.8%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 48.8%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 48.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 14.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 14.7%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right) + 1\right)} \]

      2. associate-*r* 14.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot b} + 1\right) \]

      3. neg-mul-1 14.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot b + 1\right) \]

   8. Simplified 14.7%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot b + 1\right)} \]

   9. Taylor expanded in a around inf 21.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 21.0%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot x\right)} \]

       2. mul-1-neg 21.0%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot x\right) \]

   11. Simplified 21.0%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot x\right)} \]

   if 3.49999999999999993e-23 < x < 5.3e7

   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 61.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.1%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 61.1%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 61.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 41.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right) + 1\right)} \]

      2. associate-*r* 41.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot b} + 1\right) \]

      3. neg-mul-1 41.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot b + 1\right) \]

   8. Simplified 41.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot b + 1\right)} \]

   if 5.3e7 < x < 1.35000000000000002e39

   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 y around 0 22.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 22.5%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 22.4%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 22.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.2%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 10.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 10.2%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 10.2%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 10.2%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 10.2%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 2.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 2.7%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 2.7%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 2.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 1.5%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 2.9%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 2.9%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 1.4%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 2.9%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 2.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 2.9%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 2.9%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 2.9%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 2.9%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   18. Taylor expanded in a around 0 2.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 2.9%

          \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot a} \]

       2. associate-*l* 2.9%

          \[\leadsto \color{blue}{x \cdot \left(z \cdot a\right)} \]

       3. *-commutative 2.9%

          \[\leadsto x \cdot \color{blue}{\left(a \cdot z\right)} \]

   20. Simplified 2.9%

       \[\leadsto \color{blue}{x \cdot \left(a \cdot z\right)} \]

   if 1.35000000000000002e39 < x

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 37.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 37.4%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 33.5%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 35.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in t around inf 38.0%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(\frac{x}{t \cdot y} - x\right)\right)} \]
   11. Step-by-step derivation

       1. associate-/r* 39.8%

          \[\leadsto y \cdot \left(t \cdot \left(\color{blue}{\frac{\frac{x}{t}}{y}} - x\right)\right) \]

   12. Simplified 39.8%

       \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(\frac{\frac{x}{t}}{y} - x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{x}{y \cdot t}\right)\\ \mathbf{elif}\;x \leq 53000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(\frac{\frac{x}{t}}{y} - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.4e+105)
   (* x (* z a))
   (if (<= b -5.5e+57)
     (* y (/ x y))
     (if (<= b 9.5e-9)
       (* a (/ x a))
       (if (<= b 2.8e+116) (* t (* x (- y))) (* x (* z (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+105) {
		tmp = x * (z * a);
	} else if (b <= -5.5e+57) {
		tmp = y * (x / y);
	} else if (b <= 9.5e-9) {
		tmp = a * (x / a);
	} else if (b <= 2.8e+116) {
		tmp = t * (x * -y);
	} else {
		tmp = x * (z * -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 <= (-4.4d+105)) then
        tmp = x * (z * a)
    else if (b <= (-5.5d+57)) then
        tmp = y * (x / y)
    else if (b <= 9.5d-9) then
        tmp = a * (x / a)
    else if (b <= 2.8d+116) then
        tmp = t * (x * -y)
    else
        tmp = x * (z * -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 <= -4.4e+105) {
		tmp = x * (z * a);
	} else if (b <= -5.5e+57) {
		tmp = y * (x / y);
	} else if (b <= 9.5e-9) {
		tmp = a * (x / a);
	} else if (b <= 2.8e+116) {
		tmp = t * (x * -y);
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.4e+105:
		tmp = x * (z * a)
	elif b <= -5.5e+57:
		tmp = y * (x / y)
	elif b <= 9.5e-9:
		tmp = a * (x / a)
	elif b <= 2.8e+116:
		tmp = t * (x * -y)
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.4e+105)
		tmp = Float64(x * Float64(z * a));
	elseif (b <= -5.5e+57)
		tmp = Float64(y * Float64(x / y));
	elseif (b <= 9.5e-9)
		tmp = Float64(a * Float64(x / a));
	elseif (b <= 2.8e+116)
		tmp = Float64(t * Float64(x * Float64(-y)));
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.4e+105)
		tmp = x * (z * a);
	elseif (b <= -5.5e+57)
		tmp = y * (x / y);
	elseif (b <= 9.5e-9)
		tmp = a * (x / a);
	elseif (b <= 2.8e+116)
		tmp = t * (x * -y);
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.4e+105], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e+57], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-9], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+116], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.40000000000000014e105

   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 y around 0 86.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 86.9%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 86.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 86.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.5%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 9.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 9.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 9.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 9.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 9.7%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 21.9%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 21.9%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 21.9%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 21.9%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 16.1%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 37.3%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 37.3%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 11.7%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 27.8%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 27.8%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 27.8%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 27.8%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 27.8%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 27.8%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   18. Taylor expanded in a around 0 27.8%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot a} \]

       2. associate-*l* 27.8%

          \[\leadsto \color{blue}{x \cdot \left(z \cdot a\right)} \]

       3. *-commutative 27.8%

          \[\leadsto x \cdot \color{blue}{\left(a \cdot z\right)} \]

   20. Simplified 27.8%

       \[\leadsto \color{blue}{x \cdot \left(a \cdot z\right)} \]

   if -4.40000000000000014e105 < b < -5.5000000000000002e57

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 51.2%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 51.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 51.2%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 51.2%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 35.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.7%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 35.7%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 36.0%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 51.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 59.8%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]

   if -5.5000000000000002e57 < b < 9.5000000000000007e-9

   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 y around 0 49.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 49.0%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 59.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 59.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 26.4%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 24.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.2%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 24.2%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 24.2%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 27.6%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 27.6%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 27.6%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 27.6%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 27.6%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 27.6%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 33.5%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if 9.5000000000000007e-9 < b < 2.80000000000000004e116

   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 t around inf 59.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.1%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 36.1%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 36.1%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 30.8%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 30.8%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in t around inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.0%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. distribute-rgt-neg-in 38.0%

          \[\leadsto \color{blue}{t \cdot \left(-x \cdot y\right)} \]

       3. *-commutative 38.0%

          \[\leadsto t \cdot \left(-\color{blue}{y \cdot x}\right) \]

       4. distribute-lft-neg-in 38.0%

          \[\leadsto t \cdot \color{blue}{\left(\left(-y\right) \cdot x\right)} \]

   11. Simplified 38.0%

       \[\leadsto \color{blue}{t \cdot \left(\left(-y\right) \cdot x\right)} \]

   if 2.80000000000000004e116 < b

   1. Initial program 96.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 84.9%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 84.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 84.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 7.9%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 10.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 10.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 10.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 10.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 15.7%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 15.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 15.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 15.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 15.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 15.7%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around inf 24.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   14. Step-by-step derivation

       1. mul-1-neg 24.4%

          \[\leadsto \color{blue}{-a \cdot \left(x \cdot z\right)} \]

       2. *-commutative 24.4%

          \[\leadsto -\color{blue}{\left(x \cdot z\right) \cdot a} \]

       3. associate-*r* 24.6%

          \[\leadsto -\color{blue}{x \cdot \left(z \cdot a\right)} \]

       4. distribute-rgt-neg-in 24.6%

          \[\leadsto \color{blue}{x \cdot \left(-z \cdot a\right)} \]

       5. distribute-rgt-neg-out 24.6%

          \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-a\right)\right)} \]

   15. Simplified 24.6%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(-a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.6% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+84} \lor \neg \left(x \leq 3 \cdot 10^{+233}\right):\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.55e-76)
   (* a (/ x a))
   (if (<= x 7e-5)
     (* a (* x (- b)))
     (if (or (<= x 7.5e+84) (not (<= x 3e+233)))
       (* z (/ x z))
       (/ (* x y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.55e-76) {
		tmp = a * (x / a);
	} else if (x <= 7e-5) {
		tmp = a * (x * -b);
	} else if ((x <= 7.5e+84) || !(x <= 3e+233)) {
		tmp = z * (x / z);
	} else {
		tmp = (x * 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 (x <= 1.55d-76) then
        tmp = a * (x / a)
    else if (x <= 7d-5) then
        tmp = a * (x * -b)
    else if ((x <= 7.5d+84) .or. (.not. (x <= 3d+233))) then
        tmp = z * (x / z)
    else
        tmp = (x * 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 (x <= 1.55e-76) {
		tmp = a * (x / a);
	} else if (x <= 7e-5) {
		tmp = a * (x * -b);
	} else if ((x <= 7.5e+84) || !(x <= 3e+233)) {
		tmp = z * (x / z);
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.55e-76:
		tmp = a * (x / a)
	elif x <= 7e-5:
		tmp = a * (x * -b)
	elif (x <= 7.5e+84) or not (x <= 3e+233):
		tmp = z * (x / z)
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.55e-76)
		tmp = Float64(a * Float64(x / a));
	elseif (x <= 7e-5)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif ((x <= 7.5e+84) || !(x <= 3e+233))
		tmp = Float64(z * Float64(x / z));
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.55e-76)
		tmp = a * (x / a);
	elseif (x <= 7e-5)
		tmp = a * (x * -b);
	elseif ((x <= 7.5e+84) || ~((x <= 3e+233)))
		tmp = z * (x / z);
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.55e-76], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-5], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 7.5e+84], N[Not[LessEqual[x, 3e+233]], $MachinePrecision]], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.54999999999999985e-76

   1. Initial program 96.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 64.8%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 70.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 70.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 20.9%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 24.8%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 24.8%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 24.8%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 24.8%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 24.8%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 24.8%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 30.1%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if 1.54999999999999985e-76 < x < 6.9999999999999994e-5

   1. Initial program 87.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 33.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 33.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 9.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 9.0%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot b\right) + 1\right)} \]

      2. associate-*r* 9.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot b} + 1\right) \]

      3. neg-mul-1 9.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot b + 1\right) \]

   8. Simplified 9.0%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot b + 1\right)} \]

   9. Taylor expanded in a around inf 27.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 27.2%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot x\right)} \]

       2. mul-1-neg 27.2%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot x\right) \]

   11. Simplified 27.2%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(b \cdot x\right)} \]

   if 6.9999999999999994e-5 < x < 7.5000000000000001e84 or 3.00000000000000014e233 < x

   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 y around 0 62.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 62.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 62.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 62.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 21.1%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 23.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.5%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 23.5%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 23.5%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 30.3%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in a around 0 33.5%

       \[\leadsto z \cdot \color{blue}{\frac{x}{z}} \]

   if 7.5000000000000001e84 < x < 3.00000000000000014e233

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 65.5%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 65.5%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 65.5%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 65.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 44.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 44.6%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 41.2%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 41.2%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 41.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 21.0%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 37.8%

          \[\leadsto \color{blue}{\frac{y \cdot x}{y}} \]

       2. *-commutative 37.8%

          \[\leadsto \frac{\color{blue}{x \cdot y}}{y} \]

   12. Applied egg-rr 37.8%

       \[\leadsto \color{blue}{\frac{x \cdot y}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+84} \lor \neg \left(x \leq 3 \cdot 10^{+233}\right):\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.3% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+61} \lor \neg \left(b \leq 6.5 \cdot 10^{-150}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e+99)
   (* x (* z a))
   (if (or (<= b -1.12e+61) (not (<= b 6.5e-150)))
     (* y (/ x y))
     (* a (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e+99) {
		tmp = x * (z * a);
	} else if ((b <= -1.12e+61) || !(b <= 6.5e-150)) {
		tmp = y * (x / y);
	} else {
		tmp = a * (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 <= (-1.5d+99)) then
        tmp = x * (z * a)
    else if ((b <= (-1.12d+61)) .or. (.not. (b <= 6.5d-150))) then
        tmp = y * (x / y)
    else
        tmp = a * (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 <= -1.5e+99) {
		tmp = x * (z * a);
	} else if ((b <= -1.12e+61) || !(b <= 6.5e-150)) {
		tmp = y * (x / y);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.5e+99:
		tmp = x * (z * a)
	elif (b <= -1.12e+61) or not (b <= 6.5e-150):
		tmp = y * (x / y)
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5e+99)
		tmp = Float64(x * Float64(z * a));
	elseif ((b <= -1.12e+61) || !(b <= 6.5e-150))
		tmp = Float64(y * Float64(x / y));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.5e+99)
		tmp = x * (z * a);
	elseif ((b <= -1.12e+61) || ~((b <= 6.5e-150)))
		tmp = y * (x / y);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e+99], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.12e+61], N[Not[LessEqual[b, 6.5e-150]], $MachinePrecision]], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.50000000000000007e99

   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 y around 0 86.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 86.9%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 86.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 86.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.5%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 9.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 9.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 9.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 9.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 9.7%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 21.9%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 21.9%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 21.9%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 21.9%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 16.1%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 37.3%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 37.3%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 11.7%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 27.8%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 27.8%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 27.8%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 27.8%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 27.8%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 27.8%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   18. Taylor expanded in a around 0 27.8%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot a} \]

       2. associate-*l* 27.8%

          \[\leadsto \color{blue}{x \cdot \left(z \cdot a\right)} \]

       3. *-commutative 27.8%

          \[\leadsto x \cdot \color{blue}{\left(a \cdot z\right)} \]

   20. Simplified 27.8%

       \[\leadsto \color{blue}{x \cdot \left(a \cdot z\right)} \]

   if -1.50000000000000007e99 < b < -1.12e61 or 6.49999999999999997e-150 < b

   1. Initial program 98.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 50.4%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 50.4%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 50.4%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 50.4%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 26.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 26.0%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 26.0%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 25.3%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 25.3%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 29.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 29.0%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]

   if -1.12e61 < b < 6.49999999999999997e-150

   1. Initial program 94.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 45.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 45.8%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 57.6%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 57.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 27.8%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 24.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 24.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 24.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 30.1%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 30.1%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 30.1%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 30.1%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 30.1%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 30.1%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 36.2%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+61} \lor \neg \left(b \leq 6.5 \cdot 10^{-150}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.5% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.55e-76)
   (* a (/ x a))
   (if (<= x 7.2e-7) (* t (* x (- y))) (/ (* x y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.55e-76) {
		tmp = a * (x / a);
	} else if (x <= 7.2e-7) {
		tmp = t * (x * -y);
	} else {
		tmp = (x * 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 (x <= 1.55d-76) then
        tmp = a * (x / a)
    else if (x <= 7.2d-7) then
        tmp = t * (x * -y)
    else
        tmp = (x * 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 (x <= 1.55e-76) {
		tmp = a * (x / a);
	} else if (x <= 7.2e-7) {
		tmp = t * (x * -y);
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.55e-76:
		tmp = a * (x / a)
	elif x <= 7.2e-7:
		tmp = t * (x * -y)
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.55e-76)
		tmp = Float64(a * Float64(x / a));
	elseif (x <= 7.2e-7)
		tmp = Float64(t * Float64(x * Float64(-y)));
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.55e-76)
		tmp = a * (x / a);
	elseif (x <= 7.2e-7)
		tmp = t * (x * -y);
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.55e-76], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-7], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.54999999999999985e-76

   1. Initial program 96.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 64.8%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 70.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 70.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 20.9%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 24.8%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 24.8%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 24.8%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 24.8%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 24.8%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 24.8%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 30.1%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if 1.54999999999999985e-76 < x < 7.19999999999999989e-7

   1. Initial program 87.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 51.5%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 51.5%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 51.5%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 51.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 15.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 15.5%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 15.5%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 15.5%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 15.5%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in t around inf 27.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.7%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. distribute-rgt-neg-in 27.7%

          \[\leadsto \color{blue}{t \cdot \left(-x \cdot y\right)} \]

       3. *-commutative 27.7%

          \[\leadsto t \cdot \left(-\color{blue}{y \cdot x}\right) \]

       4. distribute-lft-neg-in 27.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(-y\right) \cdot x\right)} \]

   11. Simplified 27.7%

       \[\leadsto \color{blue}{t \cdot \left(\left(-y\right) \cdot x\right)} \]

   if 7.19999999999999989e-7 < x

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 36.1%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 36.1%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 36.1%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 32.8%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 34.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 23.7%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 31.5%

          \[\leadsto \color{blue}{\frac{y \cdot x}{y}} \]

       2. *-commutative 31.5%

          \[\leadsto \frac{\color{blue}{x \cdot y}}{y} \]

   12. Applied egg-rr 31.5%

       \[\leadsto \color{blue}{\frac{x \cdot y}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.2% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+107} \lor \neg \left(y \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+107) (not (<= y 5e-7))) (* a (* x z)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+107) || !(y <= 5e-7)) {
		tmp = a * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d+107)) .or. (.not. (y <= 5d-7))) then
        tmp = a * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+107) || !(y <= 5e-7)) {
		tmp = a * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e+107) or not (y <= 5e-7):
		tmp = a * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+107) || !(y <= 5e-7))
		tmp = Float64(a * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e+107) || ~((y <= 5e-7)))
		tmp = a * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+107], N[Not[LessEqual[y, 5e-7]], $MachinePrecision]], N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999998e107 or 4.99999999999999977e-7 < y

   1. Initial program 99.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 40.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 40.4%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 47.2%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 47.2%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 6.8%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 5.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 5.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 5.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 5.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 14.0%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 24.5%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 24.5%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 24.5%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 24.5%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 11.3%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 42.9%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 42.9%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 13.5%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 22.2%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 22.2%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 22.2%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 22.2%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 22.2%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 22.2%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   if -3.5999999999999998e107 < y < 4.99999999999999977e-7

   1. Initial program 95.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 45.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 45.7%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 45.7%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 45.7%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 28.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+107} \lor \neg \left(y \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.1% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.1e-90)
   (* a (/ x a))
   (if (<= x 2.05e+41) (* a (* x z)) (/ (* x y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.1e-90) {
		tmp = a * (x / a);
	} else if (x <= 2.05e+41) {
		tmp = a * (x * z);
	} else {
		tmp = (x * 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 (x <= 1.1d-90) then
        tmp = a * (x / a)
    else if (x <= 2.05d+41) then
        tmp = a * (x * z)
    else
        tmp = (x * 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 (x <= 1.1e-90) {
		tmp = a * (x / a);
	} else if (x <= 2.05e+41) {
		tmp = a * (x * z);
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.1e-90:
		tmp = a * (x / a)
	elif x <= 2.05e+41:
		tmp = a * (x * z)
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.1e-90)
		tmp = Float64(a * Float64(x / a));
	elseif (x <= 2.05e+41)
		tmp = Float64(a * Float64(x * z));
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.1e-90)
		tmp = a * (x / a);
	elseif (x <= 2.05e+41)
		tmp = a * (x * z);
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.1e-90], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+41], N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.09999999999999993e-90

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 64.9%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 69.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 69.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 20.8%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 23.7%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 23.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 23.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 23.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 23.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 23.7%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 29.2%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if 1.09999999999999993e-90 < x < 2.0500000000000002e41

   1. Initial program 93.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 48.4%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 58.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 58.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 17.4%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 14.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 14.2%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 14.2%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 14.2%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 14.1%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 19.2%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 19.2%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 19.2%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 19.2%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 7.9%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 25.4%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 25.4%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 11.6%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 18.9%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 18.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 18.9%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 18.9%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 18.9%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 18.9%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   if 2.0500000000000002e41 < x

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 59.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 59.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 59.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 37.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 37.4%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 33.5%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{x - \left(t \cdot x\right) \cdot y} \]

   9. Taylor expanded in y around inf 35.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 22.9%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 31.9%

          \[\leadsto \color{blue}{\frac{y \cdot x}{y}} \]

       2. *-commutative 31.9%

          \[\leadsto \frac{\color{blue}{x \cdot y}}{y} \]

   12. Applied egg-rr 31.9%

       \[\leadsto \color{blue}{\frac{x \cdot y}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.1 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 26.7% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.7 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 3.7e-91)
   (* a (/ x a))
   (if (<= x 4.3e+42) (* a (* x z)) (* z (/ x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.7e-91) {
		tmp = a * (x / a);
	} else if (x <= 4.3e+42) {
		tmp = a * (x * z);
	} else {
		tmp = z * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 3.7d-91) then
        tmp = a * (x / a)
    else if (x <= 4.3d+42) then
        tmp = a * (x * z)
    else
        tmp = z * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.7e-91) {
		tmp = a * (x / a);
	} else if (x <= 4.3e+42) {
		tmp = a * (x * z);
	} else {
		tmp = z * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 3.7e-91:
		tmp = a * (x / a)
	elif x <= 4.3e+42:
		tmp = a * (x * z)
	else:
		tmp = z * (x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 3.7e-91)
		tmp = Float64(a * Float64(x / a));
	elseif (x <= 4.3e+42)
		tmp = Float64(a * Float64(x * z));
	else
		tmp = Float64(z * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 3.7e-91)
		tmp = a * (x / a);
	elseif (x <= 4.3e+42)
		tmp = a * (x * z);
	else
		tmp = z * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 3.7e-91], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+42], N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.7000000000000002e-91

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.9%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 64.9%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 69.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 69.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 20.8%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 23.7%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 23.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 23.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 23.7%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 23.7%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 23.7%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 29.2%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if 3.7000000000000002e-91 < x < 4.2999999999999998e42

   1. Initial program 93.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 48.4%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 58.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 58.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 17.4%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 14.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 14.2%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 14.2%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 14.2%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 14.1%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 19.2%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 19.2%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 19.2%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 19.2%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 7.9%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 25.4%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 25.4%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 11.6%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 18.9%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 18.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 18.9%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 18.9%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 18.9%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 18.9%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   if 4.2999999999999998e42 < x

   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 y around 0 61.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 61.1%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 66.5%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 66.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 23.3%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 22.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 22.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 22.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 22.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 27.0%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in a around 0 29.5%

       \[\leadsto z \cdot \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.7 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 24.9% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.32e+91) (* x (* z a)) (if (<= b -1.45e+20) x (* a (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.32e+91) {
		tmp = x * (z * a);
	} else if (b <= -1.45e+20) {
		tmp = x;
	} else {
		tmp = a * (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 <= (-1.32d+91)) then
        tmp = x * (z * a)
    else if (b <= (-1.45d+20)) then
        tmp = x
    else
        tmp = a * (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 <= -1.32e+91) {
		tmp = x * (z * a);
	} else if (b <= -1.45e+20) {
		tmp = x;
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.32e+91:
		tmp = x * (z * a)
	elif b <= -1.45e+20:
		tmp = x
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.32e+91)
		tmp = Float64(x * Float64(z * a));
	elseif (b <= -1.45e+20)
		tmp = x;
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.32e+91)
		tmp = x * (z * a);
	elseif (b <= -1.45e+20)
		tmp = x;
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.32e+91], N[(x * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e+20], x, N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.32000000000000003e91

   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 y around 0 85.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 85.3%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 85.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 85.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.3%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 9.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 9.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 9.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 9.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 9.5%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 23.3%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 23.3%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 23.3%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 23.3%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 15.4%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 38.0%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 38.0%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 13.6%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 28.9%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 28.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 28.9%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 28.9%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 28.9%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 28.9%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   18. Taylor expanded in a around 0 28.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot z\right)} \]
   19. Step-by-step derivation

       1. *-commutative 28.9%

          \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot a} \]

       2. associate-*l* 29.0%

          \[\leadsto \color{blue}{x \cdot \left(z \cdot a\right)} \]

       3. *-commutative 29.0%

          \[\leadsto x \cdot \color{blue}{\left(a \cdot z\right)} \]

   20. Simplified 29.0%

       \[\leadsto \color{blue}{x \cdot \left(a \cdot z\right)} \]

   if -1.32000000000000003e91 < b < -1.45e20

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 71.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 71.2%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 71.2%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 39.2%

      \[\leadsto \color{blue}{x} \]

   if -1.45e20 < b

   1. Initial program 96.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 56.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 56.5%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 63.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 63.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 21.6%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 24.5%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 24.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 24.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 24.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 24.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 24.5%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 28.3%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 24.9% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.7e+83) (* a (* x z)) (if (<= b -9.2e+19) x (* a (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.7e+83) {
		tmp = a * (x * z);
	} else if (b <= -9.2e+19) {
		tmp = x;
	} else {
		tmp = a * (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 <= (-4.7d+83)) then
        tmp = a * (x * z)
    else if (b <= (-9.2d+19)) then
        tmp = x
    else
        tmp = a * (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 <= -4.7e+83) {
		tmp = a * (x * z);
	} else if (b <= -9.2e+19) {
		tmp = x;
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.7e+83:
		tmp = a * (x * z)
	elif b <= -9.2e+19:
		tmp = x
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.7e+83)
		tmp = Float64(a * Float64(x * z));
	elseif (b <= -9.2e+19)
		tmp = x;
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.7e+83)
		tmp = a * (x * z);
	elseif (b <= -9.2e+19)
		tmp = x;
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.7e+83], N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e+19], x, N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.6999999999999999e83

   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 y around 0 85.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 85.3%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 85.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 85.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 10.3%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 9.6%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 9.6%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 9.6%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 9.6%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in z around inf 9.5%

       \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{x}{z}\right)} \]

   11. Taylor expanded in z around inf 23.3%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 23.3%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

       2. mul-1-neg 23.3%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   13. Simplified 23.3%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot z\right)} \]
   14. Step-by-step derivation

       1. add-sqr-sqrt 15.4%

          \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot z\right) \]

       2. sqrt-unprod 38.0%

          \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot z\right) \]

       3. sqr-neg 38.0%

          \[\leadsto \sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot z\right) \]

       4. sqrt-unprod 13.6%

          \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot z\right) \]

       5. add-sqr-sqrt 28.9%

          \[\leadsto \color{blue}{a} \cdot \left(x \cdot z\right) \]

       6. pow1 28.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot z\right)\right)}^{1}} \]

       7. *-commutative 28.9%

          \[\leadsto {\left(a \cdot \color{blue}{\left(z \cdot x\right)}\right)}^{1} \]

   15. Applied egg-rr 28.9%

       \[\leadsto \color{blue}{{\left(a \cdot \left(z \cdot x\right)\right)}^{1}} \]
   16. Step-by-step derivation

       1. unpow1 28.9%

          \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   17. Simplified 28.9%

       \[\leadsto \color{blue}{a \cdot \left(z \cdot x\right)} \]

   if -4.6999999999999999e83 < b < -9.2e19

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 71.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 71.2%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 71.2%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 39.2%

      \[\leadsto \color{blue}{x} \]

   if -9.2e19 < b

   1. Initial program 96.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 56.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 56.5%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 63.7%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 63.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 21.6%

      \[\leadsto x \cdot \color{blue}{{\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 20.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.9%

         \[\leadsto x + \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot z\right)} \]

      2. neg-mul-1 20.9%

         \[\leadsto x + \color{blue}{\left(-a\right)} \cdot \left(x \cdot z\right) \]

   9. Simplified 20.9%

      \[\leadsto \color{blue}{x + \left(-a\right) \cdot \left(x \cdot z\right)} \]

   10. Taylor expanded in a around inf 24.5%

       \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot z\right) + \frac{x}{a}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 24.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} + -1 \cdot \left(x \cdot z\right)\right)} \]

       2. mul-1-neg 24.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \color{blue}{\left(-x \cdot z\right)}\right) \]

       3. *-commutative 24.5%

          \[\leadsto a \cdot \left(\frac{x}{a} + \left(-\color{blue}{z \cdot x}\right)\right) \]

       4. unsub-neg 24.5%

          \[\leadsto a \cdot \color{blue}{\left(\frac{x}{a} - z \cdot x\right)} \]

   12. Simplified 24.5%

       \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - z \cdot x\right)} \]

   13. Taylor expanded in a around 0 28.3%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 19.9% 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 97.0%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in t around inf 53.0%

   \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
4. Step-by-step derivation

   1. mul-1-neg 53.0%

      \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

   2. distribute-lft-neg-out 53.0%

      \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

   3. *-commutative 53.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

5. Simplified 53.0%

   \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

6. Taylor expanded in y around 0 19.0%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(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))))))