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

Percentage Accurate: 96.7% → 99.5%

Time: 18.5s

Alternatives: 15

Speedup: 1.0×

• 20.8% 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: 96.7% 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: 99.5% 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 97.7%

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

   1. fma-def 98.1%

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

   2. sub-neg 98.1%

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

   3. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 96.7% 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 97.7%

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

2. Final simplification 97.7%

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

Alternative 3: 87.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-23} \lor \neg \left(y \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e-23) (not (<= y 1.3e-42)))
   (* 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 <= -1.1e-23) || !(y <= 1.3e-42)) {
		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 <= (-1.1d-23)) .or. (.not. (y <= 1.3d-42))) 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 <= -1.1e-23) || !(y <= 1.3e-42)) {
		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 <= -1.1e-23) or not (y <= 1.3e-42):
		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 <= -1.1e-23) || !(y <= 1.3e-42))
		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 <= -1.1e-23) || ~((y <= 1.3e-42)))
		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, -1.1e-23], N[Not[LessEqual[y, 1.3e-42]], $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 < -1.1e-23 or 1.3e-42 < 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 y around inf 89.2%

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

   if -1.1e-23 < y < 1.3e-42

   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 0 87.4%

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

      1. sub-neg 87.4%

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

      2. neg-mul-1 87.4%

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

      3. log1p-def 90.0%

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

      4. neg-mul-1 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in z around 0 90.0%

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

      1. associate-*r* 90.0%

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

      2. neg-mul-1 90.0%

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

      3. associate-*r* 90.0%

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

      4. neg-mul-1 90.0%

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

      5. distribute-lft-out 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-23} \lor \neg \left(y \leq 1.3 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \end{array} \]

Alternative 4: 74.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -28000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00125:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+144} \lor \neg \left(y \leq 7 \cdot 10^{+223}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -28000000000000.0)
     t_1
     (if (<= y 0.00125)
       (* x (exp (* a (- b))))
       (if (or (<= y 3.2e+144) (not (<= y 7e+223)))
         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 <= -28000000000000.0) {
		tmp = t_1;
	} else if (y <= 0.00125) {
		tmp = x * exp((a * -b));
	} else if ((y <= 3.2e+144) || !(y <= 7e+223)) {
		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 <= (-28000000000000.0d0)) then
        tmp = t_1
    else if (y <= 0.00125d0) then
        tmp = x * exp((a * -b))
    else if ((y <= 3.2d+144) .or. (.not. (y <= 7d+223))) 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 <= -28000000000000.0) {
		tmp = t_1;
	} else if (y <= 0.00125) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 3.2e+144) || !(y <= 7e+223)) {
		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 <= -28000000000000.0:
		tmp = t_1
	elif y <= 0.00125:
		tmp = x * math.exp((a * -b))
	elif (y <= 3.2e+144) or not (y <= 7e+223):
		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 <= -28000000000000.0)
		tmp = t_1;
	elseif (y <= 0.00125)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 3.2e+144) || !(y <= 7e+223))
		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 <= -28000000000000.0)
		tmp = t_1;
	elseif (y <= 0.00125)
		tmp = x * exp((a * -b));
	elseif ((y <= 3.2e+144) || ~((y <= 7e+223)))
		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, -28000000000000.0], t$95$1, If[LessEqual[y, 0.00125], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.2e+144], N[Not[LessEqual[y, 7e+223]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e13 or 0.00125000000000000003 < y < 3.2000000000000001e144 or 7.0000000000000002e223 < y

   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 y around inf 88.9%

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

   3. Taylor expanded in t around 0 69.2%

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

   if -2.8e13 < y < 0.00125000000000000003

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

   4. Simplified 84.9%

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

   if 3.2000000000000001e144 < y < 7.0000000000000002e223

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   4. Simplified 84.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28000000000000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.00125:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+144} \lor \neg \left(y \leq 7 \cdot 10^{+223}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 5: 77.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+144} \lor \neg \left(y \leq 6 \cdot 10^{+225}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -3e+14)
     t_1
     (if (<= y 1.55)
       (* x (exp (* (- a) (+ z b))))
       (if (or (<= y 4.8e+144) (not (<= y 6e+225)))
         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 <= -3e+14) {
		tmp = t_1;
	} else if (y <= 1.55) {
		tmp = x * exp((-a * (z + b)));
	} else if ((y <= 4.8e+144) || !(y <= 6e+225)) {
		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 <= (-3d+14)) then
        tmp = t_1
    else if (y <= 1.55d0) then
        tmp = x * exp((-a * (z + b)))
    else if ((y <= 4.8d+144) .or. (.not. (y <= 6d+225))) 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 <= -3e+14) {
		tmp = t_1;
	} else if (y <= 1.55) {
		tmp = x * Math.exp((-a * (z + b)));
	} else if ((y <= 4.8e+144) || !(y <= 6e+225)) {
		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 <= -3e+14:
		tmp = t_1
	elif y <= 1.55:
		tmp = x * math.exp((-a * (z + b)))
	elif (y <= 4.8e+144) or not (y <= 6e+225):
		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 <= -3e+14)
		tmp = t_1;
	elseif (y <= 1.55)
		tmp = Float64(x * exp(Float64(Float64(-a) * Float64(z + b))));
	elseif ((y <= 4.8e+144) || !(y <= 6e+225))
		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 <= -3e+14)
		tmp = t_1;
	elseif (y <= 1.55)
		tmp = x * exp((-a * (z + b)));
	elseif ((y <= 4.8e+144) || ~((y <= 6e+225)))
		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, -3e+14], t$95$1, If[LessEqual[y, 1.55], N[(x * N[Exp[N[((-a) * N[(z + b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 4.8e+144], N[Not[LessEqual[y, 6e+225]], $MachinePrecision]], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e14 or 1.55000000000000004 < y < 4.8000000000000001e144 or 6.000000000000001e225 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 88.8%

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

   3. Taylor expanded in t around 0 69.8%

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

   if -3e14 < y < 1.55000000000000004

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 85.0%

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

      1. sub-neg 85.0%

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

      2. neg-mul-1 85.0%

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

      3. log1p-def 88.2%

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

      4. neg-mul-1 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in z around 0 88.2%

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

      1. associate-*r* 88.2%

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

      2. neg-mul-1 88.2%

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

      3. associate-*r* 88.2%

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

      4. neg-mul-1 88.2%

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

      5. distribute-lft-out 88.2%

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

   7. Simplified 88.2%

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

   if 4.8000000000000001e144 < y < 6.000000000000001e225

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   4. Simplified 84.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.55:\\ \;\;\;\;x \cdot e^{\left(-a\right) \cdot \left(z + b\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+144} \lor \neg \left(y \leq 6 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 6: 55.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y \cdot t\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+286}:\\ \;\;\;\;\frac{x \cdot x}{x + x \cdot \left(y \cdot t\right)}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.44 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* y t)))))
   (if (<= t -1.25e+286)
     (/ (* x x) (+ x (* x (* y t))))
     (if (<= t -5.4e+200)
       t_1
       (if (<= t -1.44e+162)
         (* x (* a (- b)))
         (if (<= t -2.3e+73) t_1 (* x (pow z y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (y * t));
	double tmp;
	if (t <= -1.25e+286) {
		tmp = (x * x) / (x + (x * (y * t)));
	} else if (t <= -5.4e+200) {
		tmp = t_1;
	} else if (t <= -1.44e+162) {
		tmp = x * (a * -b);
	} else if (t <= -2.3e+73) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y * t))
    if (t <= (-1.25d+286)) then
        tmp = (x * x) / (x + (x * (y * t)))
    else if (t <= (-5.4d+200)) then
        tmp = t_1
    else if (t <= (-1.44d+162)) then
        tmp = x * (a * -b)
    else if (t <= (-2.3d+73)) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y * t));
	double tmp;
	if (t <= -1.25e+286) {
		tmp = (x * x) / (x + (x * (y * t)));
	} else if (t <= -5.4e+200) {
		tmp = t_1;
	} else if (t <= -1.44e+162) {
		tmp = x * (a * -b);
	} else if (t <= -2.3e+73) {
		tmp = t_1;
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (y * t))
	tmp = 0
	if t <= -1.25e+286:
		tmp = (x * x) / (x + (x * (y * t)))
	elif t <= -5.4e+200:
		tmp = t_1
	elif t <= -1.44e+162:
		tmp = x * (a * -b)
	elif t <= -2.3e+73:
		tmp = t_1
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(y * t)))
	tmp = 0.0
	if (t <= -1.25e+286)
		tmp = Float64(Float64(x * x) / Float64(x + Float64(x * Float64(y * t))));
	elseif (t <= -5.4e+200)
		tmp = t_1;
	elseif (t <= -1.44e+162)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (t <= -2.3e+73)
		tmp = t_1;
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (y * t));
	tmp = 0.0;
	if (t <= -1.25e+286)
		tmp = (x * x) / (x + (x * (y * t)));
	elseif (t <= -5.4e+200)
		tmp = t_1;
	elseif (t <= -1.44e+162)
		tmp = x * (a * -b);
	elseif (t <= -2.3e+73)
		tmp = t_1;
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+286], N[(N[(x * x), $MachinePrecision] / N[(x + N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e+200], t$95$1, If[LessEqual[t, -1.44e+162], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+73], t$95$1, N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2500000000000001e286

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. distribute-rgt-neg-out 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in y around 0 2.4%

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

      1. +-commutative 2.4%

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

      2. mul-1-neg 2.4%

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

      3. unsub-neg 2.4%

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

   7. Simplified 2.4%

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

      1. flip-- 1.6%

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

      2. *-commutative 1.6%

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

      3. *-commutative 1.6%

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

      4. *-commutative 1.6%

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

   9. Applied egg-rr 1.6%

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

       1. associate-*l* 1.6%

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

       2. *-commutative 1.6%

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

       3. associate-*r* 1.5%

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

       4. *-commutative 1.5%

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

       5. *-commutative 1.5%

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

       6. associate-*r* 1.5%

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

       7. *-commutative 1.5%

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

   11. Simplified 1.5%

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

   12. Taylor expanded in y around 0 63.1%

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

       1. unpow2 63.1%

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

   14. Simplified 63.1%

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

   if -1.2500000000000001e286 < t < -5.40000000000000031e200 or -1.43999999999999993e162 < t < -2.3e73

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-out 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in y around 0 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in x around 0 52.6%

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

   if -5.40000000000000031e200 < t < -1.43999999999999993e162

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

      3. distribute-rgt-neg-in 36.3%

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

   4. Simplified 36.3%

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

   5. Taylor expanded in b around 0 19.9%

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

      1. mul-1-neg 19.9%

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

      2. unsub-neg 19.9%

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

      3. *-commutative 19.9%

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

   7. Simplified 19.9%

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

   8. Taylor expanded in b around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-*r* 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

   10. Simplified 83.6%

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

   if -2.3e73 < t

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 70.7%

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

   3. Taylor expanded in t around 0 61.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+286}:\\ \;\;\;\;\frac{x \cdot x}{x + x \cdot \left(y \cdot t\right)}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq -1.44 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 7: 74.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+14} \lor \neg \left(y \leq 0.0042\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.1e+14) (not (<= y 0.0042)))
   (* 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 <= -3.1e+14) || !(y <= 0.0042)) {
		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 <= (-3.1d+14)) .or. (.not. (y <= 0.0042d0))) 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 <= -3.1e+14) || !(y <= 0.0042)) {
		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 <= -3.1e+14) or not (y <= 0.0042):
		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 <= -3.1e+14) || !(y <= 0.0042))
		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 <= -3.1e+14) || ~((y <= 0.0042)))
		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, -3.1e+14], N[Not[LessEqual[y, 0.0042]], $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 < -3.1e14 or 0.00419999999999999974 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 89.7%

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

   3. Taylor expanded in t around 0 66.2%

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

   if -3.1e14 < y < 0.00419999999999999974

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

   4. Simplified 84.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+14} \lor \neg \left(y \leq 0.0042\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 8: 36.1% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot x}{x + x \cdot \left(y \cdot t\right)}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x x) (+ x (* x (* y t))))))
   (if (<= y -6e+111)
     (* (- t) (* x y))
     (if (<= y -1.2e-66)
       t_1
       (if (<= y 0.00013)
         (* x (- 1.0 (* a b)))
         (if (<= y 4.2e+103) (* x (* a (- b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * x) / (x + (x * (y * t)));
	double tmp;
	if (y <= -6e+111) {
		tmp = -t * (x * y);
	} else if (y <= -1.2e-66) {
		tmp = t_1;
	} else if (y <= 0.00013) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 4.2e+103) {
		tmp = x * (a * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * x) / (x + (x * (y * t)))
    if (y <= (-6d+111)) then
        tmp = -t * (x * y)
    else if (y <= (-1.2d-66)) then
        tmp = t_1
    else if (y <= 0.00013d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 4.2d+103) then
        tmp = x * (a * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * x) / (x + (x * (y * t)));
	double tmp;
	if (y <= -6e+111) {
		tmp = -t * (x * y);
	} else if (y <= -1.2e-66) {
		tmp = t_1;
	} else if (y <= 0.00013) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 4.2e+103) {
		tmp = x * (a * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * x) / (x + (x * (y * t)))
	tmp = 0
	if y <= -6e+111:
		tmp = -t * (x * y)
	elif y <= -1.2e-66:
		tmp = t_1
	elif y <= 0.00013:
		tmp = x * (1.0 - (a * b))
	elif y <= 4.2e+103:
		tmp = x * (a * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * x) / Float64(x + Float64(x * Float64(y * t))))
	tmp = 0.0
	if (y <= -6e+111)
		tmp = Float64(Float64(-t) * Float64(x * y));
	elseif (y <= -1.2e-66)
		tmp = t_1;
	elseif (y <= 0.00013)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 4.2e+103)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * x) / (x + (x * (y * t)));
	tmp = 0.0;
	if (y <= -6e+111)
		tmp = -t * (x * y);
	elseif (y <= -1.2e-66)
		tmp = t_1;
	elseif (y <= 0.00013)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 4.2e+103)
		tmp = x * (a * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] / N[(x + N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+111], N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-66], t$95$1, If[LessEqual[y, 0.00013], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+103], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e111

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. distribute-rgt-neg-out 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in y around 0 21.0%

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

      1. +-commutative 21.0%

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

      2. mul-1-neg 21.0%

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

      3. unsub-neg 21.0%

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

   7. Simplified 21.0%

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

   8. Taylor expanded in y around inf 20.5%

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

      1. *-commutative 20.5%

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

      2. neg-mul-1 20.5%

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

      3. distribute-rgt-neg-in 20.5%

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

      4. distribute-rgt-neg-in 20.5%

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

   10. Simplified 20.5%

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

   11. Taylor expanded in y around 0 20.5%

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

       1. mul-1-neg 20.5%

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

       2. *-commutative 20.5%

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

       3. associate-*r* 33.4%

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

       4. *-commutative 33.4%

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

       5. distribute-rgt-neg-in 33.4%

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

   13. Simplified 33.4%

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

   if -6e111 < y < -1.20000000000000013e-66 or 4.2000000000000003e103 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-rgt-neg-out 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in y around 0 13.8%

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

      1. +-commutative 13.8%

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

      2. mul-1-neg 13.8%

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

      3. unsub-neg 13.8%

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

   7. Simplified 13.8%

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

      1. flip-- 17.3%

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

      2. *-commutative 17.3%

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

      3. *-commutative 17.3%

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

      4. *-commutative 17.3%

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

   9. Applied egg-rr 17.3%

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

       1. associate-*l* 18.5%

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

       2. *-commutative 18.5%

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

       3. associate-*r* 23.1%

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

       4. *-commutative 23.1%

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

       5. *-commutative 23.1%

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

       6. associate-*r* 14.5%

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

       7. *-commutative 14.5%

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

   11. Simplified 14.5%

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

   12. Taylor expanded in y around 0 35.4%

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

       1. unpow2 35.4%

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

   14. Simplified 35.4%

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

   if -1.20000000000000013e-66 < y < 1.29999999999999989e-4

   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 b around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-in 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in b around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

      3. *-commutative 50.7%

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

   7. Simplified 50.7%

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

   if 1.29999999999999989e-4 < y < 4.2000000000000003e103

   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 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. distribute-rgt-neg-in 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in b around 0 21.7%

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

      1. mul-1-neg 21.7%

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

      2. unsub-neg 21.7%

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

      3. *-commutative 21.7%

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

   7. Simplified 21.7%

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

   8. Taylor expanded in b around inf 35.5%

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

      1. mul-1-neg 35.5%

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

      2. associate-*r* 45.6%

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

      3. distribute-rgt-neg-in 45.6%

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

   10. Simplified 45.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot x}{x + x \cdot \left(y \cdot t\right)}\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{x + x \cdot \left(y \cdot t\right)}\\ \end{array} \]

Alternative 9: 27.6% accurate, 19.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) (* x y))))
   (if (<= y -6e+111)
     t_1
     (if (<= y -6.6e-41)
       (* a (* x (- b)))
       (if (<= y -5e-79)
         t_1
         (if (<= y 8.2e-115)
           x
           (if (<= y 8.8e+83) (* x (* a (- b))) (* x (* y (- t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * (x * y);
	double tmp;
	if (y <= -6e+111) {
		tmp = t_1;
	} else if (y <= -6.6e-41) {
		tmp = a * (x * -b);
	} else if (y <= -5e-79) {
		tmp = t_1;
	} else if (y <= 8.2e-115) {
		tmp = x;
	} else if (y <= 8.8e+83) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (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 = -t * (x * y)
    if (y <= (-6d+111)) then
        tmp = t_1
    else if (y <= (-6.6d-41)) then
        tmp = a * (x * -b)
    else if (y <= (-5d-79)) then
        tmp = t_1
    else if (y <= 8.2d-115) then
        tmp = x
    else if (y <= 8.8d+83) then
        tmp = x * (a * -b)
    else
        tmp = x * (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 = -t * (x * y);
	double tmp;
	if (y <= -6e+111) {
		tmp = t_1;
	} else if (y <= -6.6e-41) {
		tmp = a * (x * -b);
	} else if (y <= -5e-79) {
		tmp = t_1;
	} else if (y <= 8.2e-115) {
		tmp = x;
	} else if (y <= 8.8e+83) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * (x * y)
	tmp = 0
	if y <= -6e+111:
		tmp = t_1
	elif y <= -6.6e-41:
		tmp = a * (x * -b)
	elif y <= -5e-79:
		tmp = t_1
	elif y <= 8.2e-115:
		tmp = x
	elif y <= 8.8e+83:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * Float64(x * y))
	tmp = 0.0
	if (y <= -6e+111)
		tmp = t_1;
	elseif (y <= -6.6e-41)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= -5e-79)
		tmp = t_1;
	elseif (y <= 8.2e-115)
		tmp = x;
	elseif (y <= 8.8e+83)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * (x * y);
	tmp = 0.0;
	if (y <= -6e+111)
		tmp = t_1;
	elseif (y <= -6.6e-41)
		tmp = a * (x * -b);
	elseif (y <= -5e-79)
		tmp = t_1;
	elseif (y <= 8.2e-115)
		tmp = x;
	elseif (y <= 8.8e+83)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+111], t$95$1, If[LessEqual[y, -6.6e-41], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-79], t$95$1, If[LessEqual[y, 8.2e-115], x, If[LessEqual[y, 8.8e+83], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6e111 or -6.60000000000000047e-41 < y < -4.99999999999999999e-79

   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 t around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-rgt-neg-out 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in y around 0 19.0%

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

      1. +-commutative 19.0%

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

      2. mul-1-neg 19.0%

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

      3. unsub-neg 19.0%

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

   7. Simplified 19.0%

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

   8. Taylor expanded in y around inf 20.4%

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

      1. *-commutative 20.4%

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

      2. neg-mul-1 20.4%

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

      3. distribute-rgt-neg-in 20.4%

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

      4. distribute-rgt-neg-in 20.4%

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

   10. Simplified 20.4%

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

   11. Taylor expanded in y around 0 20.4%

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

       1. mul-1-neg 20.4%

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

       2. *-commutative 20.4%

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

       3. associate-*r* 35.5%

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

       4. *-commutative 35.5%

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

       5. distribute-rgt-neg-in 35.5%

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

   13. Simplified 35.5%

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

   if -6e111 < y < -6.60000000000000047e-41

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. *-commutative 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in b around 0 11.5%

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

      1. mul-1-neg 11.5%

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

      2. unsub-neg 11.5%

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

      3. *-commutative 11.5%

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

   7. Simplified 11.5%

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

   8. Taylor expanded in b around inf 27.9%

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

      1. associate-*r* 27.9%

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

      2. neg-mul-1 27.9%

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

   10. Simplified 27.9%

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

   if -4.99999999999999999e-79 < y < 8.1999999999999993e-115

   1. Initial program 96.8%

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

   2. Taylor expanded in b around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. distribute-rgt-neg-in 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in b around 0 40.3%

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

   if 8.1999999999999993e-115 < y < 8.79999999999999995e83

   1. Initial program 97.0%

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

   2. Taylor expanded in b around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. *-commutative 57.5%

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

      3. distribute-rgt-neg-in 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in b around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. unsub-neg 37.1%

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

      3. *-commutative 37.1%

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

   7. Simplified 37.1%

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

   8. Taylor expanded in b around inf 38.9%

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

      1. mul-1-neg 38.9%

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

      2. associate-*r* 45.3%

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

      3. distribute-rgt-neg-in 45.3%

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

   10. Simplified 45.3%

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

   if 8.79999999999999995e83 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-rgt-neg-out 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in y around 0 16.2%

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

      1. +-commutative 16.2%

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

      2. mul-1-neg 16.2%

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

      3. unsub-neg 16.2%

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

   7. Simplified 16.2%

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

   8. Taylor expanded in y around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. neg-mul-1 26.6%

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

      3. distribute-rgt-neg-in 26.6%

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

      4. distribute-rgt-neg-in 26.6%

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

   10. Simplified 26.6%

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

   11. Taylor expanded in y around 0 26.6%

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

       1. mul-1-neg 26.6%

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

       2. associate-*r* 28.5%

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

       3. *-commutative 28.5%

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

       4. distribute-rgt-neg-in 28.5%

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

       5. *-commutative 28.5%

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

       6. distribute-rgt-neg-in 28.5%

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

   13. Simplified 28.5%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-79}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 10: 33.2% accurate, 19.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) (* x y))))
   (if (<= y -4.5e+111)
     t_1
     (if (<= y -2.8e-39)
       (* a (* x (- b)))
       (if (<= y -6.8e-63)
         t_1
         (if (<= y 3.6e-7)
           (* x (- 1.0 (* a b)))
           (if (<= y 9.3e+86) (* x (* a (- b))) (* x (* y (- t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * (x * y);
	double tmp;
	if (y <= -4.5e+111) {
		tmp = t_1;
	} else if (y <= -2.8e-39) {
		tmp = a * (x * -b);
	} else if (y <= -6.8e-63) {
		tmp = t_1;
	} else if (y <= 3.6e-7) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 9.3e+86) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (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 = -t * (x * y)
    if (y <= (-4.5d+111)) then
        tmp = t_1
    else if (y <= (-2.8d-39)) then
        tmp = a * (x * -b)
    else if (y <= (-6.8d-63)) then
        tmp = t_1
    else if (y <= 3.6d-7) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 9.3d+86) then
        tmp = x * (a * -b)
    else
        tmp = x * (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 = -t * (x * y);
	double tmp;
	if (y <= -4.5e+111) {
		tmp = t_1;
	} else if (y <= -2.8e-39) {
		tmp = a * (x * -b);
	} else if (y <= -6.8e-63) {
		tmp = t_1;
	} else if (y <= 3.6e-7) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 9.3e+86) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * (x * y)
	tmp = 0
	if y <= -4.5e+111:
		tmp = t_1
	elif y <= -2.8e-39:
		tmp = a * (x * -b)
	elif y <= -6.8e-63:
		tmp = t_1
	elif y <= 3.6e-7:
		tmp = x * (1.0 - (a * b))
	elif y <= 9.3e+86:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * Float64(x * y))
	tmp = 0.0
	if (y <= -4.5e+111)
		tmp = t_1;
	elseif (y <= -2.8e-39)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= -6.8e-63)
		tmp = t_1;
	elseif (y <= 3.6e-7)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 9.3e+86)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * (x * y);
	tmp = 0.0;
	if (y <= -4.5e+111)
		tmp = t_1;
	elseif (y <= -2.8e-39)
		tmp = a * (x * -b);
	elseif (y <= -6.8e-63)
		tmp = t_1;
	elseif (y <= 3.6e-7)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 9.3e+86)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+111], t$95$1, If[LessEqual[y, -2.8e-39], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-63], t$95$1, If[LessEqual[y, 3.6e-7], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.3e+86], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.50000000000000001e111 or -2.8000000000000001e-39 < y < -6.79999999999999997e-63

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-rgt-neg-out 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in y around 0 19.6%

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

      1. +-commutative 19.6%

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

      2. mul-1-neg 19.6%

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

      3. unsub-neg 19.6%

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

   7. Simplified 19.6%

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

   8. Taylor expanded in y around inf 19.1%

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

      1. *-commutative 19.1%

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

      2. neg-mul-1 19.1%

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

      3. distribute-rgt-neg-in 19.1%

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

      4. distribute-rgt-neg-in 19.1%

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

   10. Simplified 19.1%

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

   11. Taylor expanded in y around 0 19.1%

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

       1. mul-1-neg 19.1%

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

       2. *-commutative 19.1%

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

       3. associate-*r* 34.8%

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

       4. *-commutative 34.8%

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

       5. distribute-rgt-neg-in 34.8%

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

   13. Simplified 34.8%

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

   if -4.50000000000000001e111 < y < -2.8000000000000001e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. *-commutative 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in b around 0 11.5%

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

      1. mul-1-neg 11.5%

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

      2. unsub-neg 11.5%

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

      3. *-commutative 11.5%

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

   7. Simplified 11.5%

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

   8. Taylor expanded in b around inf 27.9%

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

      1. associate-*r* 27.9%

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

      2. neg-mul-1 27.9%

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

   10. Simplified 27.9%

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

   if -6.79999999999999997e-63 < y < 3.59999999999999994e-7

   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 b around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-in 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in b around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

      3. *-commutative 50.7%

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

   7. Simplified 50.7%

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

   if 3.59999999999999994e-7 < y < 9.30000000000000055e86

   1. Initial program 95.1%

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

   2. Taylor expanded in b around inf 37.2%

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

      1. mul-1-neg 37.2%

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

      2. *-commutative 37.2%

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

      3. distribute-rgt-neg-in 37.2%

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

   4. Simplified 37.2%

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

   5. Taylor expanded in b around 0 22.7%

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

      1. mul-1-neg 22.7%

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

      2. unsub-neg 22.7%

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

      3. *-commutative 22.7%

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

   7. Simplified 22.7%

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

   8. Taylor expanded in b around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. associate-*r* 47.8%

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

      3. distribute-rgt-neg-in 47.8%

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

   10. Simplified 47.8%

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

   if 9.30000000000000055e86 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-rgt-neg-out 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in y around 0 16.2%

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

      1. +-commutative 16.2%

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

      2. mul-1-neg 16.2%

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

      3. unsub-neg 16.2%

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

   7. Simplified 16.2%

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

   8. Taylor expanded in y around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. neg-mul-1 26.6%

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

      3. distribute-rgt-neg-in 26.6%

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

      4. distribute-rgt-neg-in 26.6%

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

   10. Simplified 26.6%

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

   11. Taylor expanded in y around 0 26.6%

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

       1. mul-1-neg 26.6%

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

       2. associate-*r* 28.5%

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

       3. *-commutative 28.5%

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

       4. distribute-rgt-neg-in 28.5%

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

       5. *-commutative 28.5%

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

       6. distribute-rgt-neg-in 28.5%

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

   13. Simplified 28.5%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;\left(-t\right) \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 11: 27.0% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* x (- b)))))
   (if (<= y -2.1e-15)
     t_1
     (if (<= y 1.16e-114)
       x
       (if (<= y 1.9e+144)
         t_1
         (if (<= y 8.5e+222) (* x (* y (- t))) (* y (* x (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * -b);
	double tmp;
	if (y <= -2.1e-15) {
		tmp = t_1;
	} else if (y <= 1.16e-114) {
		tmp = x;
	} else if (y <= 1.9e+144) {
		tmp = t_1;
	} else if (y <= 8.5e+222) {
		tmp = x * (y * -t);
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -b)
    if (y <= (-2.1d-15)) then
        tmp = t_1
    else if (y <= 1.16d-114) then
        tmp = x
    else if (y <= 1.9d+144) then
        tmp = t_1
    else if (y <= 8.5d+222) then
        tmp = x * (y * -t)
    else
        tmp = y * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x * -b);
	double tmp;
	if (y <= -2.1e-15) {
		tmp = t_1;
	} else if (y <= 1.16e-114) {
		tmp = x;
	} else if (y <= 1.9e+144) {
		tmp = t_1;
	} else if (y <= 8.5e+222) {
		tmp = x * (y * -t);
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (x * -b)
	tmp = 0
	if y <= -2.1e-15:
		tmp = t_1
	elif y <= 1.16e-114:
		tmp = x
	elif y <= 1.9e+144:
		tmp = t_1
	elif y <= 8.5e+222:
		tmp = x * (y * -t)
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(x * Float64(-b)))
	tmp = 0.0
	if (y <= -2.1e-15)
		tmp = t_1;
	elseif (y <= 1.16e-114)
		tmp = x;
	elseif (y <= 1.9e+144)
		tmp = t_1;
	elseif (y <= 8.5e+222)
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (x * -b);
	tmp = 0.0;
	if (y <= -2.1e-15)
		tmp = t_1;
	elseif (y <= 1.16e-114)
		tmp = x;
	elseif (y <= 1.9e+144)
		tmp = t_1;
	elseif (y <= 8.5e+222)
		tmp = x * (y * -t);
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-15], t$95$1, If[LessEqual[y, 1.16e-114], x, If[LessEqual[y, 1.9e+144], t$95$1, If[LessEqual[y, 8.5e+222], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.09999999999999981e-15 or 1.1599999999999999e-114 < y < 1.90000000000000013e144

   1. Initial program 98.3%

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

   2. Taylor expanded in b around inf 46.1%

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

      1. mul-1-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. distribute-rgt-neg-in 46.1%

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

   4. Simplified 46.1%

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

   5. Taylor expanded in b around 0 17.9%

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

      1. mul-1-neg 17.9%

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

      2. unsub-neg 17.9%

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

      3. *-commutative 17.9%

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

   7. Simplified 17.9%

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

   8. Taylor expanded in b around inf 27.6%

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

      1. associate-*r* 27.6%

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

      2. neg-mul-1 27.6%

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

   10. Simplified 27.6%

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

   if -2.09999999999999981e-15 < y < 1.1599999999999999e-114

   1. Initial program 97.1%

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

   2. Taylor expanded in b around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in b around 0 38.5%

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

   if 1.90000000000000013e144 < y < 8.4999999999999994e222

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in y around 0 23.8%

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

      1. +-commutative 23.8%

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

      2. mul-1-neg 23.8%

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

      3. unsub-neg 23.8%

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

   7. Simplified 23.8%

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

   8. Taylor expanded in y around inf 28.7%

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

      1. *-commutative 28.7%

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

      2. neg-mul-1 28.7%

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

      3. distribute-rgt-neg-in 28.7%

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

      4. distribute-rgt-neg-in 28.7%

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

   10. Simplified 28.7%

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

   11. Taylor expanded in y around 0 28.7%

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

       1. mul-1-neg 28.7%

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

       2. associate-*r* 43.5%

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

       3. *-commutative 43.5%

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

       4. distribute-rgt-neg-in 43.5%

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

       5. *-commutative 43.5%

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

       6. distribute-rgt-neg-in 43.5%

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

   13. Simplified 43.5%

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

   if 8.4999999999999994e222 < y

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. distribute-rgt-neg-out 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y around 0 14.0%

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

      1. +-commutative 14.0%

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

      2. mul-1-neg 14.0%

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

      3. unsub-neg 14.0%

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

   7. Simplified 14.0%

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

   8. Taylor expanded in y around inf 34.8%

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

      1. *-commutative 34.8%

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

      2. neg-mul-1 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

      4. distribute-rgt-neg-in 34.8%

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

   10. Simplified 34.8%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+144}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 12: 27.0% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.35e-9)
   (* a (* x (- b)))
   (if (<= y 9e-117)
     x
     (if (<= y 4.9e+87) (* x (* a (- b))) (* x (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.35e-9) {
		tmp = a * (x * -b);
	} else if (y <= 9e-117) {
		tmp = x;
	} else if (y <= 4.9e+87) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.35d-9)) then
        tmp = a * (x * -b)
    else if (y <= 9d-117) then
        tmp = x
    else if (y <= 4.9d+87) then
        tmp = x * (a * -b)
    else
        tmp = x * (y * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.35e-9) {
		tmp = a * (x * -b);
	} else if (y <= 9e-117) {
		tmp = x;
	} else if (y <= 4.9e+87) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.35e-9:
		tmp = a * (x * -b)
	elif y <= 9e-117:
		tmp = x
	elif y <= 4.9e+87:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.35e-9)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 9e-117)
		tmp = x;
	elseif (y <= 4.9e+87)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.35e-9)
		tmp = a * (x * -b);
	elseif (y <= 9e-117)
		tmp = x;
	elseif (y <= 4.9e+87)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.35e-9], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-117], x, If[LessEqual[y, 4.9e+87], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.34999999999999995e-9

   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 b around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. *-commutative 41.8%

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

      3. distribute-rgt-neg-in 41.8%

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

   4. Simplified 41.8%

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

   5. Taylor expanded in b around 0 11.2%

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

      1. mul-1-neg 11.2%

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

      2. unsub-neg 11.2%

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

      3. *-commutative 11.2%

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

   7. Simplified 11.2%

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

   8. Taylor expanded in b around inf 22.8%

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

      1. associate-*r* 22.8%

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

      2. neg-mul-1 22.8%

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

   10. Simplified 22.8%

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

   if -2.34999999999999995e-9 < y < 8.99999999999999939e-117

   1. Initial program 97.1%

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

   2. Taylor expanded in b around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in b around 0 38.5%

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

   if 8.99999999999999939e-117 < y < 4.89999999999999971e87

   1. Initial program 97.0%

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

   2. Taylor expanded in b around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. *-commutative 57.5%

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

      3. distribute-rgt-neg-in 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in b around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. unsub-neg 37.1%

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

      3. *-commutative 37.1%

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

   7. Simplified 37.1%

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

   8. Taylor expanded in b around inf 38.9%

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

      1. mul-1-neg 38.9%

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

      2. associate-*r* 45.3%

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

      3. distribute-rgt-neg-in 45.3%

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

   10. Simplified 45.3%

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

   if 4.89999999999999971e87 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-rgt-neg-out 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in y around 0 16.2%

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

      1. +-commutative 16.2%

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

      2. mul-1-neg 16.2%

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

      3. unsub-neg 16.2%

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

   7. Simplified 16.2%

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

   8. Taylor expanded in y around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. neg-mul-1 26.6%

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

      3. distribute-rgt-neg-in 26.6%

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

      4. distribute-rgt-neg-in 26.6%

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

   10. Simplified 26.6%

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

   11. Taylor expanded in y around 0 26.6%

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

       1. mul-1-neg 26.6%

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

       2. associate-*r* 28.5%

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

       3. *-commutative 28.5%

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

       4. distribute-rgt-neg-in 28.5%

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

       5. *-commutative 28.5%

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

       6. distribute-rgt-neg-in 28.5%

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

   13. Simplified 28.5%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 13: 27.9% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-10} \lor \neg \left(y \leq 2.2 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e-10) (not (<= y 2.2e-32))) (* x (* y (- t))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e-10) || !(y <= 2.2e-32)) {
		tmp = x * (y * -t);
	} 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 <= (-8.5d-10)) .or. (.not. (y <= 2.2d-32))) then
        tmp = x * (y * -t)
    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 <= -8.5e-10) || !(y <= 2.2e-32)) {
		tmp = x * (y * -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e-10) or not (y <= 2.2e-32):
		tmp = x * (y * -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e-10) || !(y <= 2.2e-32))
		tmp = Float64(x * Float64(y * Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e-10) || ~((y <= 2.2e-32)))
		tmp = x * (y * -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e-10], N[Not[LessEqual[y, 2.2e-32]], $MachinePrecision]], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e-10 or 2.2e-32 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-rgt-neg-out 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in y around 0 16.5%

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

      1. +-commutative 16.5%

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

      2. mul-1-neg 16.5%

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

      3. unsub-neg 16.5%

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

   7. Simplified 16.5%

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

   8. Taylor expanded in y around inf 20.5%

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

      1. *-commutative 20.5%

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

      2. neg-mul-1 20.5%

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

      3. distribute-rgt-neg-in 20.5%

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

      4. distribute-rgt-neg-in 20.5%

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

   10. Simplified 20.5%

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

   11. Taylor expanded in y around 0 20.5%

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

       1. mul-1-neg 20.5%

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

       2. associate-*r* 22.3%

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

       3. *-commutative 22.3%

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

       4. distribute-rgt-neg-in 22.3%

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

       5. *-commutative 22.3%

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

       6. distribute-rgt-neg-in 22.3%

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

   13. Simplified 22.3%

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

   if -8.4999999999999996e-10 < y < 2.2e-32

   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 b around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-in 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in b around 0 36.8%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-10} \lor \neg \left(y \leq 2.2 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 24.9% accurate, 34.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00027 \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.00027) (not (<= y 0.0034))) (* a (* x b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.00027) || !(y <= 0.0034)) {
		tmp = a * (x * b);
	} 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 <= (-0.00027d0)) .or. (.not. (y <= 0.0034d0))) then
        tmp = a * (x * b)
    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 <= -0.00027) || !(y <= 0.0034)) {
		tmp = a * (x * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.00027) or not (y <= 0.0034):
		tmp = a * (x * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.00027) || !(y <= 0.0034))
		tmp = Float64(a * Float64(x * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.00027) || ~((y <= 0.0034)))
		tmp = a * (x * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.00027], N[Not[LessEqual[y, 0.0034]], $MachinePrecision]], N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000003e-4 or 0.00339999999999999981 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. *-commutative 39.9%

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

      3. distribute-rgt-neg-in 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in b around 0 9.7%

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

      1. mul-1-neg 9.7%

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

      2. unsub-neg 9.7%

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

      3. *-commutative 9.7%

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

   7. Simplified 9.7%

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

   8. Taylor expanded in b around inf 23.7%

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

      1. mul-1-neg 23.7%

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

      2. associate-*r* 21.7%

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

      3. distribute-rgt-neg-in 21.7%

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

   10. Simplified 21.7%

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

       1. expm1-log1p-u 17.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(a \cdot b\right) \cdot \left(-x\right)\right)\right)} \]

       2. expm1-udef 29.2%

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

       3. *-commutative 29.2%

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

       4. add-sqr-sqrt 14.1%

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

       5. sqrt-unprod 26.1%

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

       6. sqr-neg 26.1%

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

       7. sqrt-prod 12.2%

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

       8. add-sqr-sqrt 26.2%

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

       9. *-commutative 26.2%

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

   12. Applied egg-rr 26.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(b \cdot a\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 14.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(b \cdot a\right)\right)\right)} \]

       2. expm1-log1p 15.2%

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

       3. associate-*r* 19.1%

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

       4. *-commutative 19.1%

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

       5. *-commutative 19.1%

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

   14. Simplified 19.1%

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

   if -2.70000000000000003e-4 < y < 0.00339999999999999981

   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 b around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. *-commutative 85.2%

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

      3. distribute-rgt-neg-in 85.2%

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

   4. Simplified 85.2%

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

   5. Taylor expanded in b around 0 35.9%

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

4. Final simplification 26.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00027 \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 19.8% 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 97.7%

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

2. Taylor expanded in b around inf 60.8%

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

   1. mul-1-neg 60.8%

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

   2. *-commutative 60.8%

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

   3. distribute-rgt-neg-in 60.8%

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

4. Simplified 60.8%

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

5. Taylor expanded in b around 0 18.7%

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

6. Final simplification 18.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(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))))))