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

Percentage Accurate: 96.6% → 99.6%

Time: 19.7s

Alternatives: 16

Speedup: 1.0×

• 20.4% 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 97.3%

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

   1. fma-def 97.3%

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

   2. sub-neg 97.3%

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

   3. log1p-def 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. Final simplification 99.6%

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

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 97.3%

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

2. Final simplification 97.3%

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

Alternative 3: 87.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-15} \lor \neg \left(y \leq 60000000000000\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.4e-15) (not (<= y 60000000000000.0)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* (- a) (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.4e-15) || !(y <= 60000000000000.0)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((-a * (z + 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 <= (-6.4d-15)) .or. (.not. (y <= 60000000000000.0d0))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((-a * (z + 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 <= -6.4e-15) || !(y <= 60000000000000.0)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((-a * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.4e-15) or not (y <= 60000000000000.0):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((-a * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.4e-15) || !(y <= 60000000000000.0))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.4e-15) || ~((y <= 60000000000000.0)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((-a * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.4e-15], N[Not[LessEqual[y, 60000000000000.0]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999999e-15 or 6e13 < y

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 95.5%

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

   if -6.3999999999999999e-15 < y < 6e13

   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. Taylor expanded in y around 0 86.1%

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

      1. sub-neg 86.1%

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

      2. neg-mul-1 86.1%

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

      3. log1p-def 90.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in z around 0 90.0%

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

      1. associate-*r* 90.0%

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

      2. associate-*r* 90.0%

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

      3. distribute-lft-out 90.0%

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

      4. neg-mul-1 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-15} \lor \neg \left(y \leq 60000000000000\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 4: 73.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -6200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+68} \lor \neg \left(y \leq 3.4 \cdot 10^{+156}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -6200.0)
     t_1
     (if (<= y 4.6e+21)
       (* x (exp (* a (- b))))
       (if (or (<= y 2.4e+68) (not (<= y 3.4e+156)))
         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 <= -6200.0) {
		tmp = t_1;
	} else if (y <= 4.6e+21) {
		tmp = x * exp((a * -b));
	} else if ((y <= 2.4e+68) || !(y <= 3.4e+156)) {
		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 <= (-6200.0d0)) then
        tmp = t_1
    else if (y <= 4.6d+21) then
        tmp = x * exp((a * -b))
    else if ((y <= 2.4d+68) .or. (.not. (y <= 3.4d+156))) 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 <= -6200.0) {
		tmp = t_1;
	} else if (y <= 4.6e+21) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 2.4e+68) || !(y <= 3.4e+156)) {
		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 <= -6200.0:
		tmp = t_1
	elif y <= 4.6e+21:
		tmp = x * math.exp((a * -b))
	elif (y <= 2.4e+68) or not (y <= 3.4e+156):
		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 <= -6200.0)
		tmp = t_1;
	elseif (y <= 4.6e+21)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 2.4e+68) || !(y <= 3.4e+156))
		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 <= -6200.0)
		tmp = t_1;
	elseif (y <= 4.6e+21)
		tmp = x * exp((a * -b));
	elseif ((y <= 2.4e+68) || ~((y <= 3.4e+156)))
		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, -6200.0], t$95$1, If[LessEqual[y, 4.6e+21], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.4e+68], N[Not[LessEqual[y, 3.4e+156]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6200 or 4.6e21 < y < 2.40000000000000008e68 or 3.4000000000000001e156 < 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. Taylor expanded in y around inf 97.2%

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

   3. Taylor expanded in t around 0 78.4%

      \[\leadsto \color{blue}{x \cdot {z}^{y}} \]
   4. Step-by-step derivation

      1. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   if -6200 < y < 4.6e21

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-out 83.5%

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

   4. Simplified 83.5%

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

   if 2.40000000000000008e68 < y < 3.4000000000000001e156

   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. Taylor expanded in t around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-in 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6200:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+68} \lor \neg \left(y \leq 3.4 \cdot 10^{+156}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 5: 76.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -350:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+68} \lor \neg \left(y \leq 1.9 \cdot 10^{+160}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -350.0)
     t_1
     (if (<= y 1.18e+20)
       (* x (exp (* (- a) (+ z b))))
       (if (or (<= y 3.9e+68) (not (<= y 1.9e+160)))
         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 <= -350.0) {
		tmp = t_1;
	} else if (y <= 1.18e+20) {
		tmp = x * exp((-a * (z + b)));
	} else if ((y <= 3.9e+68) || !(y <= 1.9e+160)) {
		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 <= (-350.0d0)) then
        tmp = t_1
    else if (y <= 1.18d+20) then
        tmp = x * exp((-a * (z + b)))
    else if ((y <= 3.9d+68) .or. (.not. (y <= 1.9d+160))) 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 <= -350.0) {
		tmp = t_1;
	} else if (y <= 1.18e+20) {
		tmp = x * Math.exp((-a * (z + b)));
	} else if ((y <= 3.9e+68) || !(y <= 1.9e+160)) {
		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 <= -350.0:
		tmp = t_1
	elif y <= 1.18e+20:
		tmp = x * math.exp((-a * (z + b)))
	elif (y <= 3.9e+68) or not (y <= 1.9e+160):
		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 <= -350.0)
		tmp = t_1;
	elseif (y <= 1.18e+20)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	elseif ((y <= 3.9e+68) || !(y <= 1.9e+160))
		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 <= -350.0)
		tmp = t_1;
	elseif (y <= 1.18e+20)
		tmp = x * exp((-a * (z + b)));
	elseif ((y <= 3.9e+68) || ~((y <= 1.9e+160)))
		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, -350.0], t$95$1, If[LessEqual[y, 1.18e+20], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.9e+68], N[Not[LessEqual[y, 1.9e+160]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -350 or 1.18e20 < y < 3.90000000000000019e68 or 1.90000000000000006e160 < 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. Taylor expanded in y around inf 97.2%

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

   3. Taylor expanded in t around 0 78.4%

      \[\leadsto \color{blue}{x \cdot {z}^{y}} \]
   4. Step-by-step derivation

      1. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   if -350 < y < 1.18e20

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. neg-mul-1 84.3%

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

      3. log1p-def 88.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in z around 0 88.0%

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

      1. associate-*r* 88.0%

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

      2. associate-*r* 88.0%

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

      3. distribute-lft-out 88.0%

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

      4. neg-mul-1 88.0%

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

   7. Simplified 88.0%

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

   if 3.90000000000000019e68 < y < 1.90000000000000006e160

   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. Taylor expanded in t around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-in 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -350:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+68} \lor \neg \left(y \leq 1.9 \cdot 10^{+160}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 6: 74.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -20 \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -20.0) (not (<= y 2.15e+15)))
   (* 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 <= -20.0) || !(y <= 2.15e+15)) {
		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 <= (-20.0d0)) .or. (.not. (y <= 2.15d+15))) 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 <= -20.0) || !(y <= 2.15e+15)) {
		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 <= -20.0) or not (y <= 2.15e+15):
		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 <= -20.0) || !(y <= 2.15e+15))
		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 <= -20.0) || ~((y <= 2.15e+15)))
		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, -20.0], N[Not[LessEqual[y, 2.15e+15]], $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 < -20 or 2.15e15 < 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. Taylor expanded in y around inf 96.1%

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

   3. Taylor expanded in t around 0 73.4%

      \[\leadsto \color{blue}{x \cdot {z}^{y}} \]
   4. Step-by-step derivation

      1. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -20 < y < 2.15e15

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-out 83.5%

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

   4. Simplified 83.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -20 \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 7: 54.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3600:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3600.0) (* x (- 1.0 (* y t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3600.0) {
		tmp = x * (1.0 - (y * t));
	} 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 <= (-3600.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    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 <= -3600.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3600.0:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3600.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	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 <= -3600.0)
		tmp = x * (1.0 - (y * t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3600.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3600

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-rgt-neg-in 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in t around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. unsub-neg 35.8%

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

      3. *-commutative 35.8%

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

   7. Simplified 35.8%

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

   if -3600 < t

   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. Taylor expanded in y around inf 73.4%

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

   3. Taylor expanded in t around 0 68.7%

      \[\leadsto \color{blue}{x \cdot {z}^{y}} \]
   4. Step-by-step derivation

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3600:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 8: 27.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \left(x \cdot a\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) (* x a))))
   (if (<= y -6.6e+190)
     (* x (* y (- t)))
     (if (<= y -4.1e+33)
       t_1
       (if (<= y -2.6e-75) (* (- b) (* x a)) (if (<= y 2.6e-45) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * (x * a);
	double tmp;
	if (y <= -6.6e+190) {
		tmp = x * (y * -t);
	} else if (y <= -4.1e+33) {
		tmp = t_1;
	} else if (y <= -2.6e-75) {
		tmp = -b * (x * a);
	} else if (y <= 2.6e-45) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * (x * a)
    if (y <= (-6.6d+190)) then
        tmp = x * (y * -t)
    else if (y <= (-4.1d+33)) then
        tmp = t_1
    else if (y <= (-2.6d-75)) then
        tmp = -b * (x * a)
    else if (y <= 2.6d-45) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * (x * a);
	double tmp;
	if (y <= -6.6e+190) {
		tmp = x * (y * -t);
	} else if (y <= -4.1e+33) {
		tmp = t_1;
	} else if (y <= -2.6e-75) {
		tmp = -b * (x * a);
	} else if (y <= 2.6e-45) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * (x * a)
	tmp = 0
	if y <= -6.6e+190:
		tmp = x * (y * -t)
	elif y <= -4.1e+33:
		tmp = t_1
	elif y <= -2.6e-75:
		tmp = -b * (x * a)
	elif y <= 2.6e-45:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * Float64(x * a))
	tmp = 0.0
	if (y <= -6.6e+190)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (y <= -4.1e+33)
		tmp = t_1;
	elseif (y <= -2.6e-75)
		tmp = Float64(Float64(-b) * Float64(x * a));
	elseif (y <= 2.6e-45)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * (x * a);
	tmp = 0.0;
	if (y <= -6.6e+190)
		tmp = x * (y * -t);
	elseif (y <= -4.1e+33)
		tmp = t_1;
	elseif (y <= -2.6e-75)
		tmp = -b * (x * a);
	elseif (y <= 2.6e-45)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+190], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e+33], t$95$1, If[LessEqual[y, -2.6e-75], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-45], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.6e190

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in t around 0 34.9%

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

      1. mul-1-neg 34.9%

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

      2. unsub-neg 34.9%

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

      3. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   8. Taylor expanded in y around inf 34.8%

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

      1. neg-mul-1 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 34.7%

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

      4. distribute-rgt-neg-in 34.7%

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

      5. distribute-rgt-neg-in 34.7%

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

   10. Simplified 34.7%

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

   if -6.6e190 < y < -4.09999999999999995e33 or 2.59999999999999987e-45 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 35.9%

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

      1. sub-neg 35.9%

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

      2. neg-mul-1 35.9%

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

      3. log1p-def 40.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in z around 0 40.3%

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

      1. associate-*r* 40.3%

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

      2. associate-*r* 40.3%

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

      3. distribute-lft-out 40.3%

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

      4. neg-mul-1 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in a around 0 9.4%

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

      1. mul-1-neg 9.4%

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

      2. unsub-neg 9.4%

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

      3. associate-*r* 11.9%

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

      4. *-commutative 11.9%

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

   10. Simplified 11.9%

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

   11. Taylor expanded in z around inf 26.1%

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

       1. mul-1-neg 26.1%

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

       2. associate-*r* 28.6%

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

       3. *-commutative 28.6%

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

       4. *-commutative 28.6%

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

       5. distribute-rgt-neg-in 28.6%

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

       6. distribute-rgt-neg-in 28.6%

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

   13. Simplified 28.6%

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

   if -4.09999999999999995e33 < y < -2.6e-75

   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. Taylor expanded in b around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. distribute-rgt-neg-out 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in a around 0 8.3%

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

      1. mul-1-neg 8.3%

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

      2. unsub-neg 8.3%

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

      3. *-commutative 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in a around inf 26.0%

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

      1. mul-1-neg 26.0%

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

      2. *-commutative 26.0%

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

      3. *-commutative 26.0%

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

      4. *-commutative 26.0%

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

      5. associate-*r* 25.9%

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

      6. distribute-rgt-neg-in 25.9%

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

      7. distribute-rgt-neg-in 25.9%

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

   10. Simplified 25.9%

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

   if -2.6e-75 < y < 2.59999999999999987e-45

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in y around 0 43.5%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+33}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 9: 27.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \left(x \cdot a\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) (* x a))))
   (if (<= y -4.9e+188)
     (* x (* y (- t)))
     (if (<= y -7.4e+35)
       t_1
       (if (<= y -8e-83) (* a (* x (- b))) (if (<= y 2.1e-46) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * (x * a);
	double tmp;
	if (y <= -4.9e+188) {
		tmp = x * (y * -t);
	} else if (y <= -7.4e+35) {
		tmp = t_1;
	} else if (y <= -8e-83) {
		tmp = a * (x * -b);
	} else if (y <= 2.1e-46) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * (x * a)
    if (y <= (-4.9d+188)) then
        tmp = x * (y * -t)
    else if (y <= (-7.4d+35)) then
        tmp = t_1
    else if (y <= (-8d-83)) then
        tmp = a * (x * -b)
    else if (y <= 2.1d-46) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * (x * a);
	double tmp;
	if (y <= -4.9e+188) {
		tmp = x * (y * -t);
	} else if (y <= -7.4e+35) {
		tmp = t_1;
	} else if (y <= -8e-83) {
		tmp = a * (x * -b);
	} else if (y <= 2.1e-46) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * (x * a)
	tmp = 0
	if y <= -4.9e+188:
		tmp = x * (y * -t)
	elif y <= -7.4e+35:
		tmp = t_1
	elif y <= -8e-83:
		tmp = a * (x * -b)
	elif y <= 2.1e-46:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * Float64(x * a))
	tmp = 0.0
	if (y <= -4.9e+188)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (y <= -7.4e+35)
		tmp = t_1;
	elseif (y <= -8e-83)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 2.1e-46)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * (x * a);
	tmp = 0.0;
	if (y <= -4.9e+188)
		tmp = x * (y * -t);
	elseif (y <= -7.4e+35)
		tmp = t_1;
	elseif (y <= -8e-83)
		tmp = a * (x * -b);
	elseif (y <= 2.1e-46)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+188], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.4e+35], t$95$1, If[LessEqual[y, -8e-83], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-46], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9e188

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in t around 0 34.9%

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

      1. mul-1-neg 34.9%

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

      2. unsub-neg 34.9%

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

      3. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   8. Taylor expanded in y around inf 34.8%

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

      1. neg-mul-1 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 34.7%

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

      4. distribute-rgt-neg-in 34.7%

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

      5. distribute-rgt-neg-in 34.7%

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

   10. Simplified 34.7%

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

   if -4.9e188 < y < -7.4e35 or 2.09999999999999987e-46 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 35.9%

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

      1. sub-neg 35.9%

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

      2. neg-mul-1 35.9%

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

      3. log1p-def 40.3%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in z around 0 40.3%

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

      1. associate-*r* 40.3%

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

      2. associate-*r* 40.3%

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

      3. distribute-lft-out 40.3%

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

      4. neg-mul-1 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in a around 0 9.4%

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

      1. mul-1-neg 9.4%

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

      2. unsub-neg 9.4%

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

      3. associate-*r* 11.9%

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

      4. *-commutative 11.9%

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

   10. Simplified 11.9%

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

   11. Taylor expanded in z around inf 26.1%

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

       1. mul-1-neg 26.1%

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

       2. associate-*r* 28.6%

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

       3. *-commutative 28.6%

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

       4. *-commutative 28.6%

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

       5. distribute-rgt-neg-in 28.6%

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

       6. distribute-rgt-neg-in 28.6%

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

   13. Simplified 28.6%

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

   if -7.4e35 < y < -8.0000000000000003e-83

   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. Taylor expanded in b around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. distribute-rgt-neg-out 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in a around 0 8.3%

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

      1. mul-1-neg 8.3%

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

      2. unsub-neg 8.3%

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

      3. *-commutative 8.3%

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

   7. Simplified 8.3%

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

   8. Taylor expanded in a around inf 26.0%

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

      1. associate-*r* 26.0%

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

      2. neg-mul-1 26.0%

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

      3. *-commutative 26.0%

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

   10. Simplified 26.0%

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

   if -8.0000000000000003e-83 < y < 2.09999999999999987e-46

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in y around 0 43.5%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+35}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 10: 32.2% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.6e+112)
   (* t (* x (- y)))
   (if (<= y -3.5e-77)
     (* a (* z (- x)))
     (if (<= y 5.2e-45) (* x (- 1.0 (* a b))) (* (- z) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.6e+112) {
		tmp = t * (x * -y);
	} else if (y <= -3.5e-77) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = -z * (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 (y <= (-3.6d+112)) then
        tmp = t * (x * -y)
    else if (y <= (-3.5d-77)) then
        tmp = a * (z * -x)
    else if (y <= 5.2d-45) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = -z * (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 (y <= -3.6e+112) {
		tmp = t * (x * -y);
	} else if (y <= -3.5e-77) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = -z * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.6e+112:
		tmp = t * (x * -y)
	elif y <= -3.5e-77:
		tmp = a * (z * -x)
	elif y <= 5.2e-45:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = -z * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.6e+112)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= -3.5e-77)
		tmp = Float64(a * Float64(z * Float64(-x)));
	elseif (y <= 5.2e-45)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(Float64(-z) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.6e+112)
		tmp = t * (x * -y);
	elseif (y <= -3.5e-77)
		tmp = a * (z * -x);
	elseif (y <= 5.2e-45)
		tmp = x * (1.0 - (a * b));
	else
		tmp = -z * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.6e+112], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-77], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-45], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e112

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in t around 0 22.7%

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

      1. mul-1-neg 22.7%

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

      2. unsub-neg 22.7%

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

      3. *-commutative 22.7%

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

   7. Simplified 22.7%

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

   8. Taylor expanded in y around inf 25.0%

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

      1. neg-mul-1 25.0%

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

      2. *-commutative 25.0%

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

      3. associate-*r* 22.5%

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

      4. distribute-rgt-neg-in 22.5%

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

      5. distribute-rgt-neg-in 22.5%

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

   10. Simplified 22.5%

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

   11. Taylor expanded in x around 0 25.0%

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

       1. associate-*r* 25.0%

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

       2. neg-mul-1 25.0%

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

   13. Simplified 25.0%

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

   if -3.6e112 < y < -3.50000000000000013e-77

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   3. 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. neg-mul-1 48.4%

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

      3. log1p-def 50.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in z around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. associate-*r* 50.9%

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

      3. distribute-lft-out 50.9%

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

      4. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in a around 0 8.7%

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

      1. mul-1-neg 8.7%

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

      2. unsub-neg 8.7%

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

      3. associate-*r* 13.1%

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

      4. *-commutative 13.1%

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

   10. Simplified 13.1%

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

   11. Taylor expanded in z around inf 27.8%

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

       1. associate-*r* 27.8%

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

       2. neg-mul-1 27.8%

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

   13. Simplified 27.8%

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

   if -3.50000000000000013e-77 < y < 5.19999999999999973e-45

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. distribute-rgt-neg-out 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in a around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in x around 0 49.4%

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

   if 5.19999999999999973e-45 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 38.2%

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

      1. sub-neg 38.2%

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

      2. neg-mul-1 38.2%

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

      3. log1p-def 40.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r* 40.8%

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

      2. associate-*r* 40.8%

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

      3. distribute-lft-out 40.8%

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

      4. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 10.8%

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

      4. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 29.2%

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

       1. mul-1-neg 29.2%

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

       2. associate-*r* 31.7%

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

       3. *-commutative 31.7%

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

       4. *-commutative 31.7%

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

       5. distribute-rgt-neg-in 31.7%

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

       6. distribute-rgt-neg-in 31.7%

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

   13. Simplified 31.7%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 11: 31.3% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e+112)
   (* t (* x (- y)))
   (if (<= y -2.6e-75)
     (* a (* z (- x)))
     (if (<= y 5.2e-45) (- x (* a (* x b))) (* (- z) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t * (x * -y);
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -z * (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 (y <= (-1.7d+112)) then
        tmp = t * (x * -y)
    else if (y <= (-2.6d-75)) then
        tmp = a * (z * -x)
    else if (y <= 5.2d-45) then
        tmp = x - (a * (x * b))
    else
        tmp = -z * (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 (y <= -1.7e+112) {
		tmp = t * (x * -y);
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -z * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e+112:
		tmp = t * (x * -y)
	elif y <= -2.6e-75:
		tmp = a * (z * -x)
	elif y <= 5.2e-45:
		tmp = x - (a * (x * b))
	else:
		tmp = -z * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e+112)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= -2.6e-75)
		tmp = Float64(a * Float64(z * Float64(-x)));
	elseif (y <= 5.2e-45)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(Float64(-z) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e+112)
		tmp = t * (x * -y);
	elseif (y <= -2.6e-75)
		tmp = a * (z * -x);
	elseif (y <= 5.2e-45)
		tmp = x - (a * (x * b));
	else
		tmp = -z * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e+112], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-75], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-45], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999997e112

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in t around 0 22.7%

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

      1. mul-1-neg 22.7%

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

      2. unsub-neg 22.7%

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

      3. *-commutative 22.7%

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

   7. Simplified 22.7%

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

   8. Taylor expanded in y around inf 25.0%

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

      1. neg-mul-1 25.0%

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

      2. *-commutative 25.0%

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

      3. associate-*r* 22.5%

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

      4. distribute-rgt-neg-in 22.5%

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

      5. distribute-rgt-neg-in 22.5%

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

   10. Simplified 22.5%

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

   11. Taylor expanded in x around 0 25.0%

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

       1. associate-*r* 25.0%

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

       2. neg-mul-1 25.0%

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

   13. Simplified 25.0%

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

   if -1.69999999999999997e112 < y < -2.6e-75

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   3. 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. neg-mul-1 48.4%

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

      3. log1p-def 50.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in z around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. associate-*r* 50.9%

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

      3. distribute-lft-out 50.9%

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

      4. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in a around 0 8.7%

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

      1. mul-1-neg 8.7%

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

      2. unsub-neg 8.7%

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

      3. associate-*r* 13.1%

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

      4. *-commutative 13.1%

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

   10. Simplified 13.1%

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

   11. Taylor expanded in z around inf 27.8%

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

       1. associate-*r* 27.8%

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

       2. neg-mul-1 27.8%

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

   13. Simplified 27.8%

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

   if -2.6e-75 < y < 5.19999999999999973e-45

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. distribute-rgt-neg-out 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in a around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if 5.19999999999999973e-45 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 38.2%

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

      1. sub-neg 38.2%

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

      2. neg-mul-1 38.2%

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

      3. log1p-def 40.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r* 40.8%

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

      2. associate-*r* 40.8%

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

      3. distribute-lft-out 40.8%

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

      4. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 10.8%

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

      4. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 29.2%

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

       1. mul-1-neg 29.2%

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

       2. associate-*r* 31.7%

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

       3. *-commutative 31.7%

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

       4. *-commutative 31.7%

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

       5. distribute-rgt-neg-in 31.7%

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

       6. distribute-rgt-neg-in 31.7%

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

   13. Simplified 31.7%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 12: 31.2% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+112}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+112)
   (- x (* t (* x y)))
   (if (<= y -2.6e-75)
     (* a (* z (- x)))
     (if (<= y 5.2e-45) (- x (* a (* x b))) (* (- z) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+112) {
		tmp = x - (t * (x * y));
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -z * (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 (y <= (-1.05d+112)) then
        tmp = x - (t * (x * y))
    else if (y <= (-2.6d-75)) then
        tmp = a * (z * -x)
    else if (y <= 5.2d-45) then
        tmp = x - (a * (x * b))
    else
        tmp = -z * (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 (y <= -1.05e+112) {
		tmp = x - (t * (x * y));
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 5.2e-45) {
		tmp = x - (a * (x * b));
	} else {
		tmp = -z * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+112:
		tmp = x - (t * (x * y))
	elif y <= -2.6e-75:
		tmp = a * (z * -x)
	elif y <= 5.2e-45:
		tmp = x - (a * (x * b))
	else:
		tmp = -z * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+112)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= -2.6e-75)
		tmp = Float64(a * Float64(z * Float64(-x)));
	elseif (y <= 5.2e-45)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(Float64(-z) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+112)
		tmp = x - (t * (x * y));
	elseif (y <= -2.6e-75)
		tmp = a * (z * -x);
	elseif (y <= 5.2e-45)
		tmp = x - (a * (x * b));
	else
		tmp = -z * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+112], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-75], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-45], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0499999999999999e112

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in t around 0 25.1%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   6. 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. *-commutative 25.1%

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

   7. Simplified 25.1%

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

   if -1.0499999999999999e112 < y < -2.6e-75

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   3. 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. neg-mul-1 48.4%

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

      3. log1p-def 50.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in z around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. associate-*r* 50.9%

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

      3. distribute-lft-out 50.9%

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

      4. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in a around 0 8.7%

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

      1. mul-1-neg 8.7%

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

      2. unsub-neg 8.7%

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

      3. associate-*r* 13.1%

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

      4. *-commutative 13.1%

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

   10. Simplified 13.1%

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

   11. Taylor expanded in z around inf 27.8%

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

       1. associate-*r* 27.8%

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

       2. neg-mul-1 27.8%

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

   13. Simplified 27.8%

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

   if -2.6e-75 < y < 5.19999999999999973e-45

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. distribute-rgt-neg-out 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in a around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if 5.19999999999999973e-45 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 38.2%

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

      1. sub-neg 38.2%

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

      2. neg-mul-1 38.2%

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

      3. log1p-def 40.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r* 40.8%

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

      2. associate-*r* 40.8%

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

      3. distribute-lft-out 40.8%

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

      4. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 10.8%

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

      4. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 29.2%

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

       1. mul-1-neg 29.2%

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

       2. associate-*r* 31.7%

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

       3. *-commutative 31.7%

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

       4. *-commutative 31.7%

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

       5. distribute-rgt-neg-in 31.7%

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

       6. distribute-rgt-neg-in 31.7%

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

   13. Simplified 31.7%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+112}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 13: 27.9% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.7e+188)
   (* x (* y (- t)))
   (if (<= y -2.6e-75)
     (* a (* z (- x)))
     (if (<= y 2.9e-46) x (* (- z) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.7e+188) {
		tmp = x * (y * -t);
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 2.9e-46) {
		tmp = x;
	} else {
		tmp = -z * (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 (y <= (-2.7d+188)) then
        tmp = x * (y * -t)
    else if (y <= (-2.6d-75)) then
        tmp = a * (z * -x)
    else if (y <= 2.9d-46) then
        tmp = x
    else
        tmp = -z * (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 (y <= -2.7e+188) {
		tmp = x * (y * -t);
	} else if (y <= -2.6e-75) {
		tmp = a * (z * -x);
	} else if (y <= 2.9e-46) {
		tmp = x;
	} else {
		tmp = -z * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.7e+188:
		tmp = x * (y * -t)
	elif y <= -2.6e-75:
		tmp = a * (z * -x)
	elif y <= 2.9e-46:
		tmp = x
	else:
		tmp = -z * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.7e+188)
		tmp = Float64(x * Float64(y * Float64(-t)));
	elseif (y <= -2.6e-75)
		tmp = Float64(a * Float64(z * Float64(-x)));
	elseif (y <= 2.9e-46)
		tmp = x;
	else
		tmp = Float64(Float64(-z) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.7e+188)
		tmp = x * (y * -t);
	elseif (y <= -2.6e-75)
		tmp = a * (z * -x);
	elseif (y <= 2.9e-46)
		tmp = x;
	else
		tmp = -z * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.7e+188], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-75], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-46], x, N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e188

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-neg-in 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in t around 0 34.9%

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

      1. mul-1-neg 34.9%

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

      2. unsub-neg 34.9%

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

      3. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   8. Taylor expanded in y around inf 34.8%

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

      1. neg-mul-1 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 34.7%

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

      4. distribute-rgt-neg-in 34.7%

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

      5. distribute-rgt-neg-in 34.7%

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

   10. Simplified 34.7%

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

   if -2.7e188 < y < -2.6e-75

   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. Taylor expanded in y around 0 41.7%

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

      1. sub-neg 41.7%

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

      2. neg-mul-1 41.7%

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

      3. log1p-def 46.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in z around 0 46.8%

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

      1. associate-*r* 46.8%

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

      2. associate-*r* 46.8%

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

      3. distribute-lft-out 46.8%

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

      4. neg-mul-1 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in a around 0 7.1%

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

      1. mul-1-neg 7.1%

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

      2. unsub-neg 7.1%

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

      3. associate-*r* 13.5%

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

      4. *-commutative 13.5%

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

   10. Simplified 13.5%

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

   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. neg-mul-1 21.9%

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

   13. Simplified 21.9%

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

   if -2.6e-75 < y < 2.90000000000000005e-46

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in y around 0 43.5%

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

   if 2.90000000000000005e-46 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 38.2%

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

      1. sub-neg 38.2%

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

      2. neg-mul-1 38.2%

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

      3. log1p-def 40.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r* 40.8%

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

      2. associate-*r* 40.8%

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

      3. distribute-lft-out 40.8%

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

      4. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 10.8%

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

      4. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 29.2%

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

       1. mul-1-neg 29.2%

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

       2. associate-*r* 31.7%

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

       3. *-commutative 31.7%

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

       4. *-commutative 31.7%

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

       5. distribute-rgt-neg-in 31.7%

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

       6. distribute-rgt-neg-in 31.7%

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

   13. Simplified 31.7%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 14: 28.0% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e+112)
   (* t (* x (- y)))
   (if (<= y -1.05e-82)
     (* a (* z (- x)))
     (if (<= y 3.4e-46) x (* (- z) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+112) {
		tmp = t * (x * -y);
	} else if (y <= -1.05e-82) {
		tmp = a * (z * -x);
	} else if (y <= 3.4e-46) {
		tmp = x;
	} else {
		tmp = -z * (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 (y <= (-3.5d+112)) then
        tmp = t * (x * -y)
    else if (y <= (-1.05d-82)) then
        tmp = a * (z * -x)
    else if (y <= 3.4d-46) then
        tmp = x
    else
        tmp = -z * (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 (y <= -3.5e+112) {
		tmp = t * (x * -y);
	} else if (y <= -1.05e-82) {
		tmp = a * (z * -x);
	} else if (y <= 3.4e-46) {
		tmp = x;
	} else {
		tmp = -z * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e+112:
		tmp = t * (x * -y)
	elif y <= -1.05e-82:
		tmp = a * (z * -x)
	elif y <= 3.4e-46:
		tmp = x
	else:
		tmp = -z * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e+112)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= -1.05e-82)
		tmp = Float64(a * Float64(z * Float64(-x)));
	elseif (y <= 3.4e-46)
		tmp = x;
	else
		tmp = Float64(Float64(-z) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e+112)
		tmp = t * (x * -y);
	elseif (y <= -1.05e-82)
		tmp = a * (z * -x);
	elseif (y <= 3.4e-46)
		tmp = x;
	else
		tmp = -z * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e+112], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-82], N[(a * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-46], x, N[((-z) * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.49999999999999997e112

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in t around 0 22.7%

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

      1. mul-1-neg 22.7%

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

      2. unsub-neg 22.7%

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

      3. *-commutative 22.7%

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

   7. Simplified 22.7%

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

   8. Taylor expanded in y around inf 25.0%

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

      1. neg-mul-1 25.0%

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

      2. *-commutative 25.0%

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

      3. associate-*r* 22.5%

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

      4. distribute-rgt-neg-in 22.5%

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

      5. distribute-rgt-neg-in 22.5%

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

   10. Simplified 22.5%

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

   11. Taylor expanded in x around 0 25.0%

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

       1. associate-*r* 25.0%

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

       2. neg-mul-1 25.0%

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

   13. Simplified 25.0%

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

   if -3.49999999999999997e112 < y < -1.05e-82

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   3. 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. neg-mul-1 48.4%

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

      3. log1p-def 50.9%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in z around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. associate-*r* 50.9%

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

      3. distribute-lft-out 50.9%

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

      4. neg-mul-1 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in a around 0 8.7%

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

      1. mul-1-neg 8.7%

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

      2. unsub-neg 8.7%

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

      3. associate-*r* 13.1%

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

      4. *-commutative 13.1%

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

   10. Simplified 13.1%

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

   11. Taylor expanded in z around inf 27.8%

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

       1. associate-*r* 27.8%

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

       2. neg-mul-1 27.8%

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

   13. Simplified 27.8%

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

   if -1.05e-82 < y < 3.39999999999999996e-46

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in y around 0 43.5%

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

   if 3.39999999999999996e-46 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 38.2%

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

      1. sub-neg 38.2%

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

      2. neg-mul-1 38.2%

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

      3. log1p-def 40.8%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-1 \cdot z\right)} - b\right)} \]

      4. neg-mul-1 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r* 40.8%

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

      2. associate-*r* 40.8%

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

      3. distribute-lft-out 40.8%

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

      4. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 10.8%

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

      1. mul-1-neg 10.8%

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

      2. unsub-neg 10.8%

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

      3. associate-*r* 10.8%

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

      4. *-commutative 10.8%

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

   10. Simplified 10.8%

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

   11. Taylor expanded in z around inf 29.2%

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

       1. mul-1-neg 29.2%

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

       2. associate-*r* 31.7%

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

       3. *-commutative 31.7%

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

       4. *-commutative 31.7%

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

       5. distribute-rgt-neg-in 31.7%

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

       6. distribute-rgt-neg-in 31.7%

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

   13. Simplified 31.7%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(x \cdot a\right)\\ \end{array} \]

Alternative 15: 27.3% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-75} \lor \neg \left(y \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e-75) (not (<= y 4e-45))) (* (- b) (* x a)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e-75) || !(y <= 4e-45)) {
		tmp = -b * (x * a);
	} 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 <= (-2.6d-75)) .or. (.not. (y <= 4d-45))) then
        tmp = -b * (x * a)
    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 <= -2.6e-75) || !(y <= 4e-45)) {
		tmp = -b * (x * a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e-75) or not (y <= 4e-45):
		tmp = -b * (x * a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e-75) || !(y <= 4e-45))
		tmp = Float64(Float64(-b) * Float64(x * a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e-75) || ~((y <= 4e-45)))
		tmp = -b * (x * a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e-75], N[Not[LessEqual[y, 4e-45]], $MachinePrecision]], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-75 or 3.99999999999999994e-45 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in b around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. distribute-rgt-neg-out 37.1%

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

   4. Simplified 37.1%

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

   5. Taylor expanded in a around 0 9.5%

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

      1. mul-1-neg 9.5%

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

      2. unsub-neg 9.5%

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

      3. *-commutative 9.5%

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

   7. Simplified 9.5%

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

   8. Taylor expanded in a around inf 21.3%

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

      1. mul-1-neg 21.3%

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

      2. *-commutative 21.3%

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

      3. *-commutative 21.3%

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

      4. *-commutative 21.3%

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

      5. associate-*r* 21.3%

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

      6. distribute-rgt-neg-in 21.3%

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

      7. distribute-rgt-neg-in 21.3%

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

   10. Simplified 21.3%

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

   if -2.6e-75 < y < 3.99999999999999994e-45

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in y around 0 43.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-75} \lor \neg \left(y \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 19.7% 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 97.3%

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

2. Taylor expanded in y around inf 75.9%

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

3. Taylor expanded in y around 0 20.4%

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

4. Final simplification 20.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(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))))))