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

Percentage Accurate: 96.4% → 99.7%

Time: 24.7s

Alternatives: 15

Speedup: 1.0×

• 41.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.4% 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: 99.7% 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 95.8%

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

   1. fma-define 95.9%

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

   2. sub-neg 95.9%

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

   3. log1p-define 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 96.4% 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 95.8%

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

3. Final simplification 95.8%

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

Alternative 3: 72.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{y \cdot \log z}\\ \mathbf{if}\;y \leq -0.0096:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* y (log z))))))
   (if (<= y -0.0096)
     t_1
     (if (<= y 2.4e-11)
       (* x (exp (* a (- b))))
       (if (<= y 2.8e+145) t_1 (* x (exp (* t (- y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * log(z)));
	double tmp;
	if (y <= -0.0096) {
		tmp = t_1;
	} else if (y <= 2.4e-11) {
		tmp = x * exp((a * -b));
	} else if (y <= 2.8e+145) {
		tmp = t_1;
	} else {
		tmp = x * exp((t * -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 * exp((y * log(z)))
    if (y <= (-0.0096d0)) then
        tmp = t_1
    else if (y <= 2.4d-11) then
        tmp = x * exp((a * -b))
    else if (y <= 2.8d+145) then
        tmp = t_1
    else
        tmp = x * exp((t * -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 * Math.exp((y * Math.log(z)));
	double tmp;
	if (y <= -0.0096) {
		tmp = t_1;
	} else if (y <= 2.4e-11) {
		tmp = x * Math.exp((a * -b));
	} else if (y <= 2.8e+145) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((t * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * math.log(z)))
	tmp = 0
	if y <= -0.0096:
		tmp = t_1
	elif y <= 2.4e-11:
		tmp = x * math.exp((a * -b))
	elif y <= 2.8e+145:
		tmp = t_1
	else:
		tmp = x * math.exp((t * -y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * log(z))))
	tmp = 0.0
	if (y <= -0.0096)
		tmp = t_1;
	elseif (y <= 2.4e-11)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (y <= 2.8e+145)
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(t * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * log(z)));
	tmp = 0.0;
	if (y <= -0.0096)
		tmp = t_1;
	elseif (y <= 2.4e-11)
		tmp = x * exp((a * -b));
	elseif (y <= 2.8e+145)
		tmp = t_1;
	else
		tmp = x * exp((t * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0096], t$95$1, If[LessEqual[y, 2.4e-11], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+145], t$95$1, N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00959999999999999916 or 2.4000000000000001e-11 < y < 2.7999999999999999e145

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 85.3%

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

   4. Taylor expanded in t around 0 75.9%

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

   if -0.00959999999999999916 < y < 2.4000000000000001e-11

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-in 82.7%

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

   5. Simplified 82.7%

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

   if 2.7999999999999999e145 < y

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-lft-neg-out 78.3%

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

      3. *-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0096:\\ \;\;\;\;x \cdot e^{y \cdot \log z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+145}:\\ \;\;\;\;x \cdot e^{y \cdot \log z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-30} \lor \neg \left(y \leq 9.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.26e-30) (not (<= y 9.5e-34)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.26e-30) || !(y <= 9.5e-34)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (log1p(-z) - b)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.26e-30) || !(y <= 9.5e-34)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (Math.log1p(-z) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.26e-30) or not (y <= 9.5e-34):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (math.log1p(-z) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.26e-30) || !(y <= 9.5e-34))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(log1p(Float64(-z)) - b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.26e-30], N[Not[LessEqual[y, 9.5e-34]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.26e-30 or 9.49999999999999985e-34 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 87.3%

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

   if -1.26e-30 < y < 9.49999999999999985e-34

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 85.8%

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

      1. sub-neg 85.8%

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

      2. mul-1-neg 85.8%

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

      3. log1p-define 92.8%

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

      4. mul-1-neg 92.8%

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

   5. Simplified 92.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-30} \lor \neg \left(y \leq 9.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-30} \lor \neg \left(y \leq 9.2 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e-30) (not (<= y 9.2e-32)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e-30) || !(y <= 9.2e-32)) {
		tmp = x * exp((y * (log(z) - t)));
	} 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 <= (-4d-30)) .or. (.not. (y <= 9.2d-32))) then
        tmp = x * exp((y * (log(z) - t)))
    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 <= -4e-30) || !(y <= 9.2e-32)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e-30) or not (y <= 9.2e-32):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e-30) || !(y <= 9.2e-32))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	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 <= -4e-30) || ~((y <= 9.2e-32)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e-30], N[Not[LessEqual[y, 9.2e-32]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e-30 or 9.2000000000000002e-32 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 87.3%

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

   if -4e-30 < y < 9.2000000000000002e-32

   1. Initial program 93.0%

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

   3. Taylor expanded in b around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-rgt-neg-in 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-30} \lor \neg \left(y \leq 9.2 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -110000000 \lor \neg \left(t \leq 1.2 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -110000000.0) (not (<= t 1.2e+47)))
   (* x (exp (* t (- y))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -110000000.0) || !(t <= 1.2e+47)) {
		tmp = x * exp((t * -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 ((t <= (-110000000.0d0)) .or. (.not. (t <= 1.2d+47))) then
        tmp = x * exp((t * -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 ((t <= -110000000.0) || !(t <= 1.2e+47)) {
		tmp = x * Math.exp((t * -y));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -110000000.0) or not (t <= 1.2e+47):
		tmp = x * math.exp((t * -y))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -110000000.0) || !(t <= 1.2e+47))
		tmp = Float64(x * exp(Float64(t * Float64(-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 ((t <= -110000000.0) || ~((t <= 1.2e+47)))
		tmp = x * exp((t * -y));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -110000000.0], N[Not[LessEqual[t, 1.2e+47]], $MachinePrecision]], N[(x * N[Exp[N[(t * (-y)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e8 or 1.20000000000000009e47 < t

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   if -1.1e8 < t < 1.20000000000000009e47

   1. Initial program 96.9%

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

   3. Taylor expanded in b around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-rgt-neg-in 66.3%

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

   5. Simplified 66.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -110000000 \lor \neg \left(t \leq 1.2 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot e^{t \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.5e+233) (* x (exp (* a (- b)))) (* (* x t) (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.5e+233) {
		tmp = x * exp((a * -b));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.5d+233) then
        tmp = x * exp((a * -b))
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.5e+233) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.5e+233:
		tmp = x * math.exp((a * -b))
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.5e+233)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.5e+233)
		tmp = x * exp((a * -b));
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.5e+233], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.50000000000000038e233

   1. Initial program 96.3%

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

   3. Taylor expanded in b around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-rgt-neg-in 62.2%

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

   5. Simplified 62.2%

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

   if 6.50000000000000038e233 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. distribute-lft-neg-out 79.7%

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

      3. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in y around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. unsub-neg 35.8%

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

      3. *-commutative 35.8%

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

   8. Simplified 35.8%

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

   9. Taylor expanded in t around inf 35.8%

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

       1. mul-1-neg 35.8%

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

       2. *-commutative 35.8%

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

       3. *-commutative 35.8%

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

       4. associate-*r* 63.5%

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

       5. distribute-rgt-neg-in 63.5%

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

       6. *-commutative 63.5%

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

   11. Simplified 63.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.2% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \left(x \cdot b\right)\right) + 0.5 \cdot \left(x \cdot \left(b \cdot \left(a \cdot \left(a \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+153)
   (* x (* t (- y)))
   (if (<= t 1.8e+106)
     (+ (- x (* a (* x b))) (* 0.5 (* x (* b (* a (* a b))))))
     (* t (* x (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+153) {
		tmp = x * (t * -y);
	} else if (t <= 1.8e+106) {
		tmp = (x - (a * (x * b))) + (0.5 * (x * (b * (a * (a * b)))));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.2d+153)) then
        tmp = x * (t * -y)
    else if (t <= 1.8d+106) then
        tmp = (x - (a * (x * b))) + (0.5d0 * (x * (b * (a * (a * b)))))
    else
        tmp = t * (x * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+153) {
		tmp = x * (t * -y);
	} else if (t <= 1.8e+106) {
		tmp = (x - (a * (x * b))) + (0.5 * (x * (b * (a * (a * b)))));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+153:
		tmp = x * (t * -y)
	elif t <= 1.8e+106:
		tmp = (x - (a * (x * b))) + (0.5 * (x * (b * (a * (a * b)))))
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+153)
		tmp = Float64(x * Float64(t * Float64(-y)));
	elseif (t <= 1.8e+106)
		tmp = Float64(Float64(x - Float64(a * Float64(x * b))) + Float64(0.5 * Float64(x * Float64(b * Float64(a * Float64(a * b))))));
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e+153)
		tmp = x * (t * -y);
	elseif (t <= 1.8e+106)
		tmp = (x - (a * (x * b))) + (0.5 * (x * (b * (a * (a * b)))));
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+153], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+106], N[(N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(b * N[(a * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000033e153

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 92.7%

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

      1. mul-1-neg 92.7%

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

      2. distribute-lft-neg-out 92.7%

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

      3. *-commutative 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. unsub-neg 42.9%

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

      3. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in t around inf 46.4%

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

       1. associate-*r* 46.4%

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

       2. neg-mul-1 46.4%

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

       3. *-commutative 46.4%

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

       4. associate-*l* 56.7%

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

       5. *-commutative 56.7%

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

       6. *-commutative 56.7%

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

   11. Simplified 56.7%

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

   if -4.20000000000000033e153 < t < 1.8e106

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. distribute-rgt-neg-in 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in a around 0 34.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ 34.8%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right)} \]

      2. mul-1-neg 34.8%

         \[\leadsto \left(x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)}\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto \color{blue}{\left(x - a \cdot \left(b \cdot x\right)\right)} + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right) \]

      4. associate-*r* 36.7%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \color{blue}{\left(\left({a}^{2} \cdot {b}^{2}\right) \cdot x\right)} \]

      5. unpow2 36.7%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left(\left(\color{blue}{\left(a \cdot a\right)} \cdot {b}^{2}\right) \cdot x\right) \]

      6. unpow2 36.7%

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

      7. swap-sqr 38.1%

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

      8. unpow2 38.1%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left(\color{blue}{{\left(a \cdot b\right)}^{2}} \cdot x\right) \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left({\left(a \cdot b\right)}^{2} \cdot x\right)} \]
   9. Step-by-step derivation

      1. unpow2 38.1%

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

      2. associate-*r* 38.6%

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

   10. Applied egg-rr 38.6%

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

   if 1.8e106 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. distribute-lft-neg-out 86.8%

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

      3. *-commutative 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in y around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. unsub-neg 29.0%

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

      3. *-commutative 29.0%

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

   8. Simplified 29.0%

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

   9. Taylor expanded in t around inf 32.0%

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

       1. associate-*r* 32.0%

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

       2. neg-mul-1 32.0%

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

       3. *-commutative 32.0%

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

       4. associate-*l* 30.3%

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

       5. *-commutative 30.3%

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

       6. *-commutative 30.3%

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

   11. Simplified 30.3%

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

   12. Taylor expanded in x around 0 32.0%

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

       1. mul-1-neg 32.0%

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

       2. *-commutative 32.0%

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

       3. associate-*r* 30.3%

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

       4. distribute-lft-neg-in 30.3%

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

       5. associate-*r* 32.0%

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

   14. Simplified 32.0%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \left(x \cdot b\right)\right) + 0.5 \cdot \left(x \cdot \left(b \cdot \left(a \cdot \left(a \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.0% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \left(x \cdot b\right)\right) + 0.5 \cdot \left(x \cdot \left(a \cdot \left(b \cdot \left(a \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+153)
   (* x (* t (- y)))
   (if (<= t 5.6e+106)
     (+ (- x (* a (* x b))) (* 0.5 (* x (* a (* b (* a b))))))
     (* t (* x (- y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+153) {
		tmp = x * (t * -y);
	} else if (t <= 5.6e+106) {
		tmp = (x - (a * (x * b))) + (0.5 * (x * (a * (b * (a * b)))));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.2d+153)) then
        tmp = x * (t * -y)
    else if (t <= 5.6d+106) then
        tmp = (x - (a * (x * b))) + (0.5d0 * (x * (a * (b * (a * b)))))
    else
        tmp = t * (x * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+153) {
		tmp = x * (t * -y);
	} else if (t <= 5.6e+106) {
		tmp = (x - (a * (x * b))) + (0.5 * (x * (a * (b * (a * b)))));
	} else {
		tmp = t * (x * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e+153:
		tmp = x * (t * -y)
	elif t <= 5.6e+106:
		tmp = (x - (a * (x * b))) + (0.5 * (x * (a * (b * (a * b)))))
	else:
		tmp = t * (x * -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+153)
		tmp = Float64(x * Float64(t * Float64(-y)));
	elseif (t <= 5.6e+106)
		tmp = Float64(Float64(x - Float64(a * Float64(x * b))) + Float64(0.5 * Float64(x * Float64(a * Float64(b * Float64(a * b))))));
	else
		tmp = Float64(t * Float64(x * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e+153)
		tmp = x * (t * -y);
	elseif (t <= 5.6e+106)
		tmp = (x - (a * (x * b))) + (0.5 * (x * (a * (b * (a * b)))));
	else
		tmp = t * (x * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+153], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+106], N[(N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(a * N[(b * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000001e153

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 92.7%

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

      1. mul-1-neg 92.7%

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

      2. distribute-lft-neg-out 92.7%

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

      3. *-commutative 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. unsub-neg 42.9%

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

      3. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in t around inf 46.4%

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

       1. associate-*r* 46.4%

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

       2. neg-mul-1 46.4%

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

       3. *-commutative 46.4%

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

       4. associate-*l* 56.7%

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

       5. *-commutative 56.7%

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

       6. *-commutative 56.7%

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

   11. Simplified 56.7%

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

   if -3.2000000000000001e153 < t < 5.59999999999999986e106

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. distribute-rgt-neg-in 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in a around 0 34.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ 34.8%

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right)} \]

      2. mul-1-neg 34.8%

         \[\leadsto \left(x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)}\right) + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto \color{blue}{\left(x - a \cdot \left(b \cdot x\right)\right)} + 0.5 \cdot \left({a}^{2} \cdot \left({b}^{2} \cdot x\right)\right) \]

      4. associate-*r* 36.7%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \color{blue}{\left(\left({a}^{2} \cdot {b}^{2}\right) \cdot x\right)} \]

      5. unpow2 36.7%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left(\left(\color{blue}{\left(a \cdot a\right)} \cdot {b}^{2}\right) \cdot x\right) \]

      6. unpow2 36.7%

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

      7. swap-sqr 38.1%

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

      8. unpow2 38.1%

         \[\leadsto \left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left(\color{blue}{{\left(a \cdot b\right)}^{2}} \cdot x\right) \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(b \cdot x\right)\right) + 0.5 \cdot \left({\left(a \cdot b\right)}^{2} \cdot x\right)} \]
   9. Step-by-step derivation

      1. unpow2 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-*r* 39.1%

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

   10. Applied egg-rr 39.1%

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

   if 5.59999999999999986e106 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. distribute-lft-neg-out 86.8%

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

      3. *-commutative 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in y around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. unsub-neg 29.0%

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

      3. *-commutative 29.0%

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

   8. Simplified 29.0%

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

   9. Taylor expanded in t around inf 32.0%

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

       1. associate-*r* 32.0%

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

       2. neg-mul-1 32.0%

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

       3. *-commutative 32.0%

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

       4. associate-*l* 30.3%

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

       5. *-commutative 30.3%

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

       6. *-commutative 30.3%

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

   11. Simplified 30.3%

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

   12. Taylor expanded in x around 0 32.0%

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

       1. mul-1-neg 32.0%

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

       2. *-commutative 32.0%

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

       3. associate-*r* 30.3%

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

       4. distribute-lft-neg-in 30.3%

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

       5. associate-*r* 32.0%

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

   14. Simplified 32.0%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \left(x \cdot b\right)\right) + 0.5 \cdot \left(x \cdot \left(a \cdot \left(b \cdot \left(a \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e-69)
   (* t (* x (- y)))
   (if (<= y 2.5e+93) (* x (- 1.0 (* a b))) (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-69) {
		tmp = t * (x * -y);
	} else if (y <= 2.5e+93) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d-69)) then
        tmp = t * (x * -y)
    else if (y <= 2.5d+93) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-69) {
		tmp = t * (x * -y);
	} else if (y <= 2.5e+93) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e-69:
		tmp = t * (x * -y)
	elif y <= 2.5e+93:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e-69)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 2.5e+93)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e-69)
		tmp = t * (x * -y);
	elseif (y <= 2.5e+93)
		tmp = x * (1.0 - (a * b));
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e-69], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+93], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000004e-69

   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. Add Preprocessing

   3. Taylor expanded in t around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-lft-neg-out 53.4%

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

      3. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y around 0 24.4%

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

      1. mul-1-neg 24.4%

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

      2. unsub-neg 24.4%

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

      3. *-commutative 24.4%

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

   8. Simplified 24.4%

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

   9. Taylor expanded in t around inf 25.4%

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

       1. associate-*r* 25.4%

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

       2. neg-mul-1 25.4%

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

       3. *-commutative 25.4%

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

       4. associate-*l* 21.6%

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

       5. *-commutative 21.6%

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

       6. *-commutative 21.6%

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

   11. Simplified 21.6%

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

   12. Taylor expanded in x around 0 25.4%

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

       1. mul-1-neg 25.4%

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

       2. *-commutative 25.4%

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

       3. associate-*r* 21.6%

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

       4. distribute-lft-neg-in 21.6%

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

       5. associate-*r* 25.4%

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

   14. Simplified 25.4%

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

   if -1.70000000000000004e-69 < y < 2.5000000000000001e93

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. distribute-rgt-neg-in 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in a around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. unsub-neg 44.7%

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

   8. Simplified 44.7%

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

   if 2.5000000000000001e93 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. distribute-lft-neg-out 67.5%

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

      3. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in y around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. unsub-neg 25.7%

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

      3. *-commutative 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in t around inf 25.8%

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

       1. mul-1-neg 25.8%

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

       2. *-commutative 25.8%

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

       3. *-commutative 25.8%

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

       4. associate-*r* 36.9%

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

       5. distribute-rgt-neg-in 36.9%

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

       6. *-commutative 36.9%

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

   11. Simplified 36.9%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 25.8% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-76} \lor \neg \left(y \leq 3.2 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-76) (not (<= y 3.2e+109))) (* x (* t (- y))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-76) || !(y <= 3.2e+109)) {
		tmp = x * (t * -y);
	} 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 <= (-1.25d-76)) .or. (.not. (y <= 3.2d+109))) then
        tmp = x * (t * -y)
    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 <= -1.25e-76) || !(y <= 3.2e+109)) {
		tmp = x * (t * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e-76) or not (y <= 3.2e+109):
		tmp = x * (t * -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e-76) || !(y <= 3.2e+109))
		tmp = Float64(x * Float64(t * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e-76) || ~((y <= 3.2e+109)))
		tmp = x * (t * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e-76], N[Not[LessEqual[y, 3.2e+109]], $MachinePrecision]], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e-76 or 3.2000000000000001e109 < y

   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. Add Preprocessing

   3. Taylor expanded in t around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-lft-neg-out 60.0%

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

      3. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y around 0 25.9%

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

      1. mul-1-neg 25.9%

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

      2. unsub-neg 25.9%

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

      3. *-commutative 25.9%

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

   8. Simplified 25.9%

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

   9. Taylor expanded in t around inf 25.8%

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

       1. associate-*r* 25.8%

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

       2. neg-mul-1 25.8%

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

       3. *-commutative 25.8%

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

       4. associate-*l* 27.8%

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

       5. *-commutative 27.8%

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

       6. *-commutative 27.8%

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

   11. Simplified 27.8%

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

   if -1.2499999999999999e-76 < y < 3.2000000000000001e109

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-rgt-neg-in 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around 0 29.1%

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

4. Final simplification 28.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-76} \lor \neg \left(y \leq 3.2 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.0% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-71} \lor \neg \left(y \leq 160000\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.2e-71) (not (<= y 160000.0))) (* (* x t) (- y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.2e-71) || !(y <= 160000.0)) {
		tmp = (x * t) * -y;
	} 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 <= (-1.2d-71)) .or. (.not. (y <= 160000.0d0))) then
        tmp = (x * t) * -y
    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 <= -1.2e-71) || !(y <= 160000.0)) {
		tmp = (x * t) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.2e-71) or not (y <= 160000.0):
		tmp = (x * t) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.2e-71) || !(y <= 160000.0))
		tmp = Float64(Float64(x * t) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.2e-71) || ~((y <= 160000.0)))
		tmp = (x * t) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.2e-71], N[Not[LessEqual[y, 160000.0]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-71 or 1.6e5 < y

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-lft-neg-out 57.4%

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

      3. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around 0 23.6%

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

      1. mul-1-neg 23.6%

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

      2. unsub-neg 23.6%

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

      3. *-commutative 23.6%

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

   8. Simplified 23.6%

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

   9. Taylor expanded in t around inf 24.3%

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

       1. mul-1-neg 24.3%

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

       2. *-commutative 24.3%

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

       3. *-commutative 24.3%

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

       4. associate-*r* 28.1%

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

       5. distribute-rgt-neg-in 28.1%

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

       6. *-commutative 28.1%

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

   11. Simplified 28.1%

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

   if -1.2e-71 < y < 1.6e5

   1. Initial program 93.9%

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

   3. Taylor expanded in b around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in a around 0 32.3%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-71} \lor \neg \left(y \leq 160000\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.7% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.45e-71)
   (* t (* x (- y)))
   (if (<= y 160000.0) x (* (* x t) (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e-71) {
		tmp = t * (x * -y);
	} else if (y <= 160000.0) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.45d-71)) then
        tmp = t * (x * -y)
    else if (y <= 160000.0d0) then
        tmp = x
    else
        tmp = (x * t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e-71) {
		tmp = t * (x * -y);
	} else if (y <= 160000.0) {
		tmp = x;
	} else {
		tmp = (x * t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.45e-71:
		tmp = t * (x * -y)
	elif y <= 160000.0:
		tmp = x
	else:
		tmp = (x * t) * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.45e-71)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 160000.0)
		tmp = x;
	else
		tmp = Float64(Float64(x * t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.45e-71)
		tmp = t * (x * -y);
	elseif (y <= 160000.0)
		tmp = x;
	else
		tmp = (x * t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.45e-71], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160000.0], x, N[(N[(x * t), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e-71

   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. Add Preprocessing

   3. Taylor expanded in t around inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. distribute-lft-neg-out 54.0%

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

      3. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. unsub-neg 24.1%

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

      3. *-commutative 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in t around inf 25.2%

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

       1. associate-*r* 25.2%

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

       2. neg-mul-1 25.2%

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

       3. *-commutative 25.2%

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

       4. associate-*l* 21.5%

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

       5. *-commutative 21.5%

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

       6. *-commutative 21.5%

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

   11. Simplified 21.5%

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

   12. Taylor expanded in x around 0 25.2%

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

       1. mul-1-neg 25.2%

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

       2. *-commutative 25.2%

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

       3. associate-*r* 21.5%

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

       4. distribute-lft-neg-in 21.5%

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

       5. associate-*r* 25.2%

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

   14. Simplified 25.2%

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

   if -1.4499999999999999e-71 < y < 1.6e5

   1. Initial program 93.9%

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

   3. Taylor expanded in b around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in a around 0 32.3%

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

   if 1.6e5 < y

   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. Add Preprocessing

   3. Taylor expanded in t around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-neg-out 61.4%

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

      3. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around 0 23.1%

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

      1. mul-1-neg 23.1%

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

      2. unsub-neg 23.1%

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

      3. *-commutative 23.1%

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

   8. Simplified 23.1%

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

   9. Taylor expanded in t around inf 23.2%

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

       1. mul-1-neg 23.2%

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

       2. *-commutative 23.2%

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

       3. *-commutative 23.2%

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

       4. associate-*r* 34.4%

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

       5. distribute-rgt-neg-in 34.4%

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

       6. *-commutative 34.4%

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

   11. Simplified 34.4%

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

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 20.8% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a 6.5e+67) x (* t (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6.5e+67) {
		tmp = x;
	} else {
		tmp = t * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 6.5d+67) then
        tmp = x
    else
        tmp = t * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6.5e+67) {
		tmp = x;
	} else {
		tmp = t * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 6.5e+67:
		tmp = x
	else:
		tmp = t * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 6.5e+67)
		tmp = x;
	else
		tmp = Float64(t * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 6.5e+67)
		tmp = x;
	else
		tmp = t * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 6.5e+67], x, N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.4999999999999995e67

   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. Add Preprocessing

   3. Taylor expanded in b around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-rgt-neg-in 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in a around 0 19.5%

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

   if 6.4999999999999995e67 < a

   1. Initial program 88.9%

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

   3. Taylor expanded in t around inf 40.7%

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

      1. mul-1-neg 40.7%

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

      2. distribute-lft-neg-out 40.7%

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

      3. *-commutative 40.7%

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

   5. Simplified 40.7%

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

      1. pow1 40.7%

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

      2. exp-prod 44.3%

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

      3. add-sqr-sqrt 18.3%

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

      4. sqrt-unprod 17.3%

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

      5. sqr-neg 17.3%

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

      6. sqrt-unprod 9.4%

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

      7. add-sqr-sqrt 15.2%

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

   7. Applied egg-rr 15.2%

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

      1. unpow1 15.2%

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

      2. exp-prod 9.7%

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

      3. *-commutative 9.7%

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

      4. exp-prod 9.6%

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

   9. Simplified 9.6%

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

   10. Taylor expanded in t around 0 4.1%

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

   11. Taylor expanded in t around inf 15.0%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 18.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 19.1% accurate, 315.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.8%

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

3. Taylor expanded in b around inf 59.8%

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

   1. mul-1-neg 59.8%

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

   2. distribute-rgt-neg-in 59.8%

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

5. Simplified 59.8%

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

6. Taylor expanded in a around 0 16.4%

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

7. Final simplification 16.4%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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))))))