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

Percentage Accurate: 96.7% → 99.2%

Time: 22.3s

Alternatives: 22

Speedup: 1.5×

• 41.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% 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: 99.2% accurate, 1.5× speedup

Math

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

FPCore

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

Python

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

MATLAB

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

Derivation

1. Initial program 95.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in z around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 2: 83.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{if}\;y \leq -1.14 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 170000:\\ \;\;\;\;x \cdot e^{a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow (/ z (exp t)) y))))
   (if (<= y -1.14e+18)
     t_1
     (if (<= y 170000.0) (* x (exp (* a (- (log (- 1.0 z)) b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow((z / exp(t)), y);
	double tmp;
	if (y <= -1.14e+18) {
		tmp = t_1;
	} else if (y <= 170000.0) {
		tmp = x * exp((a * (log((1.0 - z)) - 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 * ((z / exp(t)) ** y)
    if (y <= (-1.14d+18)) then
        tmp = t_1
    else if (y <= 170000.0d0) then
        tmp = x * exp((a * (log((1.0d0 - z)) - b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow((z / Math.exp(t)), y);
	double tmp;
	if (y <= -1.14e+18) {
		tmp = t_1;
	} else if (y <= 170000.0) {
		tmp = x * Math.exp((a * (Math.log((1.0 - z)) - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow((z / math.exp(t)), y)
	tmp = 0
	if y <= -1.14e+18:
		tmp = t_1
	elif y <= 170000.0:
		tmp = x * math.exp((a * (math.log((1.0 - z)) - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (Float64(z / exp(t)) ^ y))
	tmp = 0.0
	if (y <= -1.14e+18)
		tmp = t_1;
	elseif (y <= 170000.0)
		tmp = Float64(x * exp(Float64(a * Float64(log(Float64(1.0 - z)) - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((z / exp(t)) ^ y);
	tmp = 0.0;
	if (y <= -1.14e+18)
		tmp = t_1;
	elseif (y <= 170000.0)
		tmp = x * exp((a * (log((1.0 - z)) - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.14e+18], t$95$1, If[LessEqual[y, 170000.0], N[(x * N[Exp[N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14e18 or 1.7e5 < y

   1. Initial program 99.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.14e18 < y < 1.7e5

   1. Initial program 92.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 140000:\\ \;\;\;\;x \cdot e^{0 - a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow (/ z (exp t)) y))))
   (if (<= y -1.45e+18)
     t_1
     (if (<= y 140000.0) (* x (exp (- 0.0 (* a b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow((z / exp(t)), y);
	double tmp;
	if (y <= -1.45e+18) {
		tmp = t_1;
	} else if (y <= 140000.0) {
		tmp = x * exp((0.0 - (a * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z / exp(t)) ** y)
    if (y <= (-1.45d+18)) then
        tmp = t_1
    else if (y <= 140000.0d0) then
        tmp = x * exp((0.0d0 - (a * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow((z / Math.exp(t)), y);
	double tmp;
	if (y <= -1.45e+18) {
		tmp = t_1;
	} else if (y <= 140000.0) {
		tmp = x * Math.exp((0.0 - (a * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow((z / math.exp(t)), y)
	tmp = 0
	if y <= -1.45e+18:
		tmp = t_1
	elif y <= 140000.0:
		tmp = x * math.exp((0.0 - (a * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (Float64(z / exp(t)) ^ y))
	tmp = 0.0
	if (y <= -1.45e+18)
		tmp = t_1;
	elseif (y <= 140000.0)
		tmp = Float64(x * exp(Float64(0.0 - Float64(a * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((z / exp(t)) ^ y);
	tmp = 0.0;
	if (y <= -1.45e+18)
		tmp = t_1;
	elseif (y <= 140000.0)
		tmp = x * exp((0.0 - (a * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+18], t$95$1, If[LessEqual[y, 140000.0], N[(x * N[Exp[N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e18 or 1.4e5 < y

   1. Initial program 99.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.45e18 < y < 1.4e5

   1. Initial program 92.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 140000:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -1.05e+130)
     t_1
     (if (<= y -2.45e+59)
       (/ (/ (* x 2.0) (* a a)) (* b b))
       (if (<= y -2.3e+18)
         t_1
         (if (<= y 140000.0) (/ x (exp (* a b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -1.05e+130) {
		tmp = t_1;
	} else if (y <= -2.45e+59) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= -2.3e+18) {
		tmp = t_1;
	} else if (y <= 140000.0) {
		tmp = x / exp((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 * (z ** y)
    if (y <= (-1.05d+130)) then
        tmp = t_1
    else if (y <= (-2.45d+59)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= (-2.3d+18)) then
        tmp = t_1
    else if (y <= 140000.0d0) then
        tmp = x / exp((a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.05e+130) {
		tmp = t_1;
	} else if (y <= -2.45e+59) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= -2.3e+18) {
		tmp = t_1;
	} else if (y <= 140000.0) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.05e+130:
		tmp = t_1
	elif y <= -2.45e+59:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= -2.3e+18:
		tmp = t_1
	elif y <= 140000.0:
		tmp = x / math.exp((a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.05e+130)
		tmp = t_1;
	elseif (y <= -2.45e+59)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= -2.3e+18)
		tmp = t_1;
	elseif (y <= 140000.0)
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.05e+130)
		tmp = t_1;
	elseif (y <= -2.45e+59)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= -2.3e+18)
		tmp = t_1;
	elseif (y <= 140000.0)
		tmp = x / exp((a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+130], t$95$1, If[LessEqual[y, -2.45e+59], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e+18], t$95$1, If[LessEqual[y, 140000.0], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999995e130 or -2.45000000000000004e59 < y < -2.3e18 or 1.4e5 < y

   1. Initial program 99.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.04999999999999995e130 < y < -2.45000000000000004e59

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -2.3e18 < y < 1.4e5

   1. Initial program 92.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 59.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right) - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -2.1e+127)
     t_1
     (if (<= y -2.8e+59)
       (/ (/ (* x 2.0) (* a a)) (* b b))
       (if (<= y -5.6e-17)
         t_1
         (if (<= y 4.9e-11)
           (* x (+ 1.0 (* b (- (* 0.5 (* b (* a a))) a))))
           t_1))))))

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 <= -2.1e+127) {
		tmp = t_1;
	} else if (y <= -2.8e+59) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= -5.6e-17) {
		tmp = t_1;
	} else if (y <= 4.9e-11) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} 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 * (z ** y)
    if (y <= (-2.1d+127)) then
        tmp = t_1
    else if (y <= (-2.8d+59)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= (-5.6d-17)) then
        tmp = t_1
    else if (y <= 4.9d-11) then
        tmp = x * (1.0d0 + (b * ((0.5d0 * (b * (a * a))) - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -2.1e+127) {
		tmp = t_1;
	} else if (y <= -2.8e+59) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= -5.6e-17) {
		tmp = t_1;
	} else if (y <= 4.9e-11) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -2.1e+127:
		tmp = t_1
	elif y <= -2.8e+59:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= -5.6e-17:
		tmp = t_1
	elif y <= 4.9e-11:
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -2.1e+127)
		tmp = t_1;
	elseif (y <= -2.8e+59)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= -5.6e-17)
		tmp = t_1;
	elseif (y <= 4.9e-11)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(Float64(0.5 * Float64(b * Float64(a * a))) - a))));
	else
		tmp = t_1;
	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 <= -2.1e+127)
		tmp = t_1;
	elseif (y <= -2.8e+59)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= -5.6e-17)
		tmp = t_1;
	elseif (y <= 4.9e-11)
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	else
		tmp = t_1;
	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, -2.1e+127], t$95$1, If[LessEqual[y, -2.8e+59], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.6e-17], t$95$1, If[LessEqual[y, 4.9e-11], N[(x * N[(1.0 + N[(b * N[(N[(0.5 * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999992e127 or -2.7999999999999998e59 < y < -5.5999999999999998e-17 or 4.8999999999999999e-11 < y

   1. Initial program 99.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -2.09999999999999992e127 < y < -2.7999999999999998e59

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -5.5999999999999998e-17 < y < 4.8999999999999999e-11

   1. Initial program 92.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-300}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{e^{t \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))))
   (if (<= b -5.4e-45)
     t_1
     (if (<= b 1.32e-300)
       (* x (pow z y))
       (if (<= b 1.25e+96) (/ x (exp (* t y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((a * b));
	double tmp;
	if (b <= -5.4e-45) {
		tmp = t_1;
	} else if (b <= 1.32e-300) {
		tmp = x * pow(z, y);
	} else if (b <= 1.25e+96) {
		tmp = x / exp((t * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / exp((a * b))
    if (b <= (-5.4d-45)) then
        tmp = t_1
    else if (b <= 1.32d-300) then
        tmp = x * (z ** y)
    else if (b <= 1.25d+96) then
        tmp = x / exp((t * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((a * b));
	double tmp;
	if (b <= -5.4e-45) {
		tmp = t_1;
	} else if (b <= 1.32e-300) {
		tmp = x * Math.pow(z, y);
	} else if (b <= 1.25e+96) {
		tmp = x / Math.exp((t * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((a * b))
	tmp = 0
	if b <= -5.4e-45:
		tmp = t_1
	elif b <= 1.32e-300:
		tmp = x * math.pow(z, y)
	elif b <= 1.25e+96:
		tmp = x / math.exp((t * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(a * b)))
	tmp = 0.0
	if (b <= -5.4e-45)
		tmp = t_1;
	elseif (b <= 1.32e-300)
		tmp = Float64(x * (z ^ y));
	elseif (b <= 1.25e+96)
		tmp = Float64(x / exp(Float64(t * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((a * b));
	tmp = 0.0;
	if (b <= -5.4e-45)
		tmp = t_1;
	elseif (b <= 1.32e-300)
		tmp = x * (z ^ y);
	elseif (b <= 1.25e+96)
		tmp = x / exp((t * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e-45], t$95$1, If[LessEqual[b, 1.32e-300], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+96], N[(x / N[Exp[N[(t * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.3999999999999997e-45 or 1.2500000000000001e96 < b

   1. Initial program 98.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -5.3999999999999997e-45 < b < 1.32e-300

   1. Initial program 90.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.32e-300 < b < 1.2500000000000001e96

   1. Initial program 96.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 45.6% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ t_2 := x \cdot \left(1 - a \cdot b\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \left(\left(y \cdot y\right) \cdot \left(t \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(b \cdot \left(\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))) (t_2 (* x (- 1.0 (* a b)))))
   (if (<= y -2.5e+116)
     (* (* x 0.5) (* (* y y) (* t t)))
     (if (<= y -2.85e-35)
       (* a (* a (* x (* (* b b) 0.5))))
       (if (<= y -1.3e-81)
         t_2
         (if (<= y -3.2e-109)
           (* x (* b (* (* b (* a 0.5)) a)))
           (if (<= y 1.55e-209)
             t_2
             (if (<= y 1.7e-128)
               t_1
               (if (<= y 7.8e+154)
                 (* x (* a (* (* b b) (* a 0.5))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double t_2 = x * (1.0 - (a * b));
	double tmp;
	if (y <= -2.5e+116) {
		tmp = (x * 0.5) * ((y * y) * (t * t));
	} else if (y <= -2.85e-35) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else if (y <= -1.3e-81) {
		tmp = t_2;
	} else if (y <= -3.2e-109) {
		tmp = x * (b * ((b * (a * 0.5)) * a));
	} else if (y <= 1.55e-209) {
		tmp = t_2;
	} else if (y <= 1.7e-128) {
		tmp = t_1;
	} else if (y <= 7.8e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (y * (x / (y * y)))
    t_2 = x * (1.0d0 - (a * b))
    if (y <= (-2.5d+116)) then
        tmp = (x * 0.5d0) * ((y * y) * (t * t))
    else if (y <= (-2.85d-35)) then
        tmp = a * (a * (x * ((b * b) * 0.5d0)))
    else if (y <= (-1.3d-81)) then
        tmp = t_2
    else if (y <= (-3.2d-109)) then
        tmp = x * (b * ((b * (a * 0.5d0)) * a))
    else if (y <= 1.55d-209) then
        tmp = t_2
    else if (y <= 1.7d-128) then
        tmp = t_1
    else if (y <= 7.8d+154) then
        tmp = x * (a * ((b * b) * (a * 0.5d0)))
    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 = y * (y * (x / (y * y)));
	double t_2 = x * (1.0 - (a * b));
	double tmp;
	if (y <= -2.5e+116) {
		tmp = (x * 0.5) * ((y * y) * (t * t));
	} else if (y <= -2.85e-35) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else if (y <= -1.3e-81) {
		tmp = t_2;
	} else if (y <= -3.2e-109) {
		tmp = x * (b * ((b * (a * 0.5)) * a));
	} else if (y <= 1.55e-209) {
		tmp = t_2;
	} else if (y <= 1.7e-128) {
		tmp = t_1;
	} else if (y <= 7.8e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	t_2 = x * (1.0 - (a * b))
	tmp = 0
	if y <= -2.5e+116:
		tmp = (x * 0.5) * ((y * y) * (t * t))
	elif y <= -2.85e-35:
		tmp = a * (a * (x * ((b * b) * 0.5)))
	elif y <= -1.3e-81:
		tmp = t_2
	elif y <= -3.2e-109:
		tmp = x * (b * ((b * (a * 0.5)) * a))
	elif y <= 1.55e-209:
		tmp = t_2
	elif y <= 1.7e-128:
		tmp = t_1
	elif y <= 7.8e+154:
		tmp = x * (a * ((b * b) * (a * 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	t_2 = Float64(x * Float64(1.0 - Float64(a * b)))
	tmp = 0.0
	if (y <= -2.5e+116)
		tmp = Float64(Float64(x * 0.5) * Float64(Float64(y * y) * Float64(t * t)));
	elseif (y <= -2.85e-35)
		tmp = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))));
	elseif (y <= -1.3e-81)
		tmp = t_2;
	elseif (y <= -3.2e-109)
		tmp = Float64(x * Float64(b * Float64(Float64(b * Float64(a * 0.5)) * a)));
	elseif (y <= 1.55e-209)
		tmp = t_2;
	elseif (y <= 1.7e-128)
		tmp = t_1;
	elseif (y <= 7.8e+154)
		tmp = Float64(x * Float64(a * Float64(Float64(b * b) * Float64(a * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	t_2 = x * (1.0 - (a * b));
	tmp = 0.0;
	if (y <= -2.5e+116)
		tmp = (x * 0.5) * ((y * y) * (t * t));
	elseif (y <= -2.85e-35)
		tmp = a * (a * (x * ((b * b) * 0.5)));
	elseif (y <= -1.3e-81)
		tmp = t_2;
	elseif (y <= -3.2e-109)
		tmp = x * (b * ((b * (a * 0.5)) * a));
	elseif (y <= 1.55e-209)
		tmp = t_2;
	elseif (y <= 1.7e-128)
		tmp = t_1;
	elseif (y <= 7.8e+154)
		tmp = x * (a * ((b * b) * (a * 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+116], N[(N[(x * 0.5), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.85e-35], N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-81], t$95$2, If[LessEqual[y, -3.2e-109], N[(x * N[(b * N[(N[(b * N[(a * 0.5), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-209], t$95$2, If[LessEqual[y, 1.7e-128], t$95$1, If[LessEqual[y, 7.8e+154], N[(x * N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.50000000000000013e116

   1. Initial program 97.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -2.50000000000000013e116 < y < -2.8500000000000001e-35

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -2.8500000000000001e-35 < y < -1.2999999999999999e-81 or -3.2000000000000002e-109 < y < 1.55e-209

   1. Initial program 94.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.2999999999999999e-81 < y < -3.2000000000000002e-109

   1. Initial program 87.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   15. Applied egg-rr 0

       \[\leadsto expr\]

   if 1.55e-209 < y < 1.69999999999999987e-128 or 7.8000000000000006e154 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 1.69999999999999987e-128 < y < 7.8000000000000006e154

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 8: 55.1% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(1 + t \cdot \left(0.5 \cdot \left(t \cdot \left(y \cdot y\right)\right) - y\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right) - a\right)\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e+154)
   (* x (+ 1.0 (* t (- (* 0.5 (* t (* y y))) y))))
   (if (<= y -5.2e-17)
     (/ (/ (* x 2.0) (* a a)) (* b b))
     (if (<= y 1.1e-86)
       (* x (+ 1.0 (* b (- (* 0.5 (* b (* a a))) a))))
       (if (<= y 2.15e+155)
         (* a (* a (* x (* (* b b) 0.5))))
         (* y (* y (/ x (* y y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+154) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -5.2e-17) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.1e-86) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} else if (y <= 2.15e+155) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.35d+154)) then
        tmp = x * (1.0d0 + (t * ((0.5d0 * (t * (y * y))) - y)))
    else if (y <= (-5.2d-17)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= 1.1d-86) then
        tmp = x * (1.0d0 + (b * ((0.5d0 * (b * (a * a))) - a)))
    else if (y <= 2.15d+155) then
        tmp = a * (a * (x * ((b * b) * 0.5d0)))
    else
        tmp = y * (y * (x / (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+154) {
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	} else if (y <= -5.2e-17) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.1e-86) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} else if (y <= 2.15e+155) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e+154:
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)))
	elif y <= -5.2e-17:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= 1.1e-86:
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)))
	elif y <= 2.15e+155:
		tmp = a * (a * (x * ((b * b) * 0.5)))
	else:
		tmp = y * (y * (x / (y * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e+154)
		tmp = Float64(x * Float64(1.0 + Float64(t * Float64(Float64(0.5 * Float64(t * Float64(y * y))) - y))));
	elseif (y <= -5.2e-17)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= 1.1e-86)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(Float64(0.5 * Float64(b * Float64(a * a))) - a))));
	elseif (y <= 2.15e+155)
		tmp = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))));
	else
		tmp = Float64(y * Float64(y * Float64(x / Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.35e+154)
		tmp = x * (1.0 + (t * ((0.5 * (t * (y * y))) - y)));
	elseif (y <= -5.2e-17)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= 1.1e-86)
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	elseif (y <= 2.15e+155)
		tmp = a * (a * (x * ((b * b) * 0.5)));
	else
		tmp = y * (y * (x / (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e+154], N[(x * N[(1.0 + N[(t * N[(N[(0.5 * N[(t * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-17], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-86], N[(x * N[(1.0 + N[(b * N[(N[(0.5 * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+155], N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.35000000000000003e154

   1. Initial program 97.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.35000000000000003e154 < y < -5.20000000000000006e-17

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -5.20000000000000006e-17 < y < 1.1000000000000001e-86

   1. Initial program 93.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.1000000000000001e-86 < y < 2.1500000000000001e155

   1. Initial program 96.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 2.1500000000000001e155 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 46.5% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))))
   (if (<= y -1.85e-16)
     (/ (/ (* x 2.0) (* a a)) (* b b))
     (if (<= y 4.8e-213)
       (* x (- 1.0 (* a b)))
       (if (<= y 1.7e-128)
         t_1
         (if (<= y 3e+154) (* x (* a (* (* b b) (* a 0.5)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -1.85e-16) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 4.8e-213) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.7e-128) {
		tmp = t_1;
	} else if (y <= 3e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} 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 = y * (y * (x / (y * y)))
    if (y <= (-1.85d-16)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= 4.8d-213) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 1.7d-128) then
        tmp = t_1
    else if (y <= 3d+154) then
        tmp = x * (a * ((b * b) * (a * 0.5d0)))
    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 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -1.85e-16) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 4.8e-213) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.7e-128) {
		tmp = t_1;
	} else if (y <= 3e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -1.85e-16:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= 4.8e-213:
		tmp = x * (1.0 - (a * b))
	elif y <= 1.7e-128:
		tmp = t_1
	elif y <= 3e+154:
		tmp = x * (a * ((b * b) * (a * 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -1.85e-16)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= 4.8e-213)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 1.7e-128)
		tmp = t_1;
	elseif (y <= 3e+154)
		tmp = Float64(x * Float64(a * Float64(Float64(b * b) * Float64(a * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -1.85e-16)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= 4.8e-213)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 1.7e-128)
		tmp = t_1;
	elseif (y <= 3e+154)
		tmp = x * (a * ((b * b) * (a * 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-16], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-213], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-128], t$95$1, If[LessEqual[y, 3e+154], N[(x * N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e-16

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -1.85e-16 < y < 4.79999999999999991e-213

   1. Initial program 93.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 4.79999999999999991e-213 < y < 1.69999999999999987e-128 or 3.00000000000000026e154 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 1.69999999999999987e-128 < y < 3.00000000000000026e154

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 46.1% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)}\\ \mathbf{elif}\;y \leq 10^{-211}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))))
   (if (<= y -7.8e-16)
     (/ x (* 0.5 (* (* a b) (* a b))))
     (if (<= y 1e-211)
       (* x (- 1.0 (* a b)))
       (if (<= y 2.25e-128)
         t_1
         (if (<= y 1.7e+154) (* x (* a (* (* b b) (* a 0.5)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -7.8e-16) {
		tmp = x / (0.5 * ((a * b) * (a * b)));
	} else if (y <= 1e-211) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.25e-128) {
		tmp = t_1;
	} else if (y <= 1.7e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} 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 = y * (y * (x / (y * y)))
    if (y <= (-7.8d-16)) then
        tmp = x / (0.5d0 * ((a * b) * (a * b)))
    else if (y <= 1d-211) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 2.25d-128) then
        tmp = t_1
    else if (y <= 1.7d+154) then
        tmp = x * (a * ((b * b) * (a * 0.5d0)))
    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 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -7.8e-16) {
		tmp = x / (0.5 * ((a * b) * (a * b)));
	} else if (y <= 1e-211) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.25e-128) {
		tmp = t_1;
	} else if (y <= 1.7e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -7.8e-16:
		tmp = x / (0.5 * ((a * b) * (a * b)))
	elif y <= 1e-211:
		tmp = x * (1.0 - (a * b))
	elif y <= 2.25e-128:
		tmp = t_1
	elif y <= 1.7e+154:
		tmp = x * (a * ((b * b) * (a * 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -7.8e-16)
		tmp = Float64(x / Float64(0.5 * Float64(Float64(a * b) * Float64(a * b))));
	elseif (y <= 1e-211)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 2.25e-128)
		tmp = t_1;
	elseif (y <= 1.7e+154)
		tmp = Float64(x * Float64(a * Float64(Float64(b * b) * Float64(a * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -7.8e-16)
		tmp = x / (0.5 * ((a * b) * (a * b)));
	elseif (y <= 1e-211)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 2.25e-128)
		tmp = t_1;
	elseif (y <= 1.7e+154)
		tmp = x * (a * ((b * b) * (a * 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-16], N[(x / N[(0.5 * N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-211], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-128], t$95$1, If[LessEqual[y, 1.7e+154], N[(x * N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.79999999999999954e-16

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -7.79999999999999954e-16 < y < 1.00000000000000009e-211

   1. Initial program 93.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.00000000000000009e-211 < y < 2.25e-128 or 1.69999999999999987e154 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 2.25e-128 < y < 1.69999999999999987e154

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 45.2% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;\left(t \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) \cdot \left(0.5 \cdot y\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))))
   (if (<= y -2.6e+17)
     (* (* t (* t (* x y))) (* 0.5 y))
     (if (<= y 1.7e-209)
       (* x (- 1.0 (* a b)))
       (if (<= y 2.8e-128)
         t_1
         (if (<= y 1.9e+151) (* x (* a (* (* b b) (* a 0.5)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.6e+17) {
		tmp = (t * (t * (x * y))) * (0.5 * y);
	} else if (y <= 1.7e-209) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.8e-128) {
		tmp = t_1;
	} else if (y <= 1.9e+151) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} 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 = y * (y * (x / (y * y)))
    if (y <= (-2.6d+17)) then
        tmp = (t * (t * (x * y))) * (0.5d0 * y)
    else if (y <= 1.7d-209) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 2.8d-128) then
        tmp = t_1
    else if (y <= 1.9d+151) then
        tmp = x * (a * ((b * b) * (a * 0.5d0)))
    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 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.6e+17) {
		tmp = (t * (t * (x * y))) * (0.5 * y);
	} else if (y <= 1.7e-209) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 2.8e-128) {
		tmp = t_1;
	} else if (y <= 1.9e+151) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -2.6e+17:
		tmp = (t * (t * (x * y))) * (0.5 * y)
	elif y <= 1.7e-209:
		tmp = x * (1.0 - (a * b))
	elif y <= 2.8e-128:
		tmp = t_1
	elif y <= 1.9e+151:
		tmp = x * (a * ((b * b) * (a * 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -2.6e+17)
		tmp = Float64(Float64(t * Float64(t * Float64(x * y))) * Float64(0.5 * y));
	elseif (y <= 1.7e-209)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 2.8e-128)
		tmp = t_1;
	elseif (y <= 1.9e+151)
		tmp = Float64(x * Float64(a * Float64(Float64(b * b) * Float64(a * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -2.6e+17)
		tmp = (t * (t * (x * y))) * (0.5 * y);
	elseif (y <= 1.7e-209)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 2.8e-128)
		tmp = t_1;
	elseif (y <= 1.9e+151)
		tmp = x * (a * ((b * b) * (a * 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+17], N[(N[(t * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-209], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-128], t$95$1, If[LessEqual[y, 1.9e+151], N[(x * N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6e17

   1. Initial program 98.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if -2.6e17 < y < 1.69999999999999994e-209

   1. Initial program 93.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.69999999999999994e-209 < y < 2.7999999999999998e-128 or 1.9e151 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 2.7999999999999998e-128 < y < 1.9e151

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 44.4% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\left(b \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))))
   (if (<= y -9e-14)
     (* a (* a (* x (* (* b b) 0.5))))
     (if (<= y 1.05e-223)
       (* x (- 1.0 (* a b)))
       (if (<= y 5.4e-128)
         t_1
         (if (<= y 1.35e+154) (* x (* a (* (* b b) (* a 0.5)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -9e-14) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else if (y <= 1.05e-223) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 5.4e-128) {
		tmp = t_1;
	} else if (y <= 1.35e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} 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 = y * (y * (x / (y * y)))
    if (y <= (-9d-14)) then
        tmp = a * (a * (x * ((b * b) * 0.5d0)))
    else if (y <= 1.05d-223) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 5.4d-128) then
        tmp = t_1
    else if (y <= 1.35d+154) then
        tmp = x * (a * ((b * b) * (a * 0.5d0)))
    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 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -9e-14) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else if (y <= 1.05e-223) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 5.4e-128) {
		tmp = t_1;
	} else if (y <= 1.35e+154) {
		tmp = x * (a * ((b * b) * (a * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -9e-14:
		tmp = a * (a * (x * ((b * b) * 0.5)))
	elif y <= 1.05e-223:
		tmp = x * (1.0 - (a * b))
	elif y <= 5.4e-128:
		tmp = t_1
	elif y <= 1.35e+154:
		tmp = x * (a * ((b * b) * (a * 0.5)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -9e-14)
		tmp = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))));
	elseif (y <= 1.05e-223)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 5.4e-128)
		tmp = t_1;
	elseif (y <= 1.35e+154)
		tmp = Float64(x * Float64(a * Float64(Float64(b * b) * Float64(a * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -9e-14)
		tmp = a * (a * (x * ((b * b) * 0.5)));
	elseif (y <= 1.05e-223)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 5.4e-128)
		tmp = t_1;
	elseif (y <= 1.35e+154)
		tmp = x * (a * ((b * b) * (a * 0.5)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-14], N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-223], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-128], t$95$1, If[LessEqual[y, 1.35e+154], N[(x * N[(a * N[(N[(b * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999995e-14

   1. Initial program 98.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -8.9999999999999995e-14 < y < 1.04999999999999991e-223

   1. Initial program 93.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.04999999999999991e-223 < y < 5.40000000000000011e-128 or 1.35000000000000003e154 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 5.40000000000000011e-128 < y < 1.35000000000000003e154

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 44.6% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ t_2 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* a (* x (* (* b b) 0.5)))))
        (t_2 (* y (* y (/ x (* y y))))))
   (if (<= y -2.7e-15)
     t_1
     (if (<= y 1.45e-209)
       (* x (- 1.0 (* a b)))
       (if (<= y 1.35e-128) t_2 (if (<= y 5.6e+153) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (a * (x * ((b * b) * 0.5)));
	double t_2 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.7e-15) {
		tmp = t_1;
	} else if (y <= 1.45e-209) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.35e-128) {
		tmp = t_2;
	} else if (y <= 5.6e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (a * (x * ((b * b) * 0.5d0)))
    t_2 = y * (y * (x / (y * y)))
    if (y <= (-2.7d-15)) then
        tmp = t_1
    else if (y <= 1.45d-209) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 1.35d-128) then
        tmp = t_2
    else if (y <= 5.6d+153) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (a * (x * ((b * b) * 0.5)));
	double t_2 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.7e-15) {
		tmp = t_1;
	} else if (y <= 1.45e-209) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 1.35e-128) {
		tmp = t_2;
	} else if (y <= 5.6e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (a * (x * ((b * b) * 0.5)))
	t_2 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -2.7e-15:
		tmp = t_1
	elif y <= 1.45e-209:
		tmp = x * (1.0 - (a * b))
	elif y <= 1.35e-128:
		tmp = t_2
	elif y <= 5.6e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))))
	t_2 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -2.7e-15)
		tmp = t_1;
	elseif (y <= 1.45e-209)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 1.35e-128)
		tmp = t_2;
	elseif (y <= 5.6e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (a * (x * ((b * b) * 0.5)));
	t_2 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -2.7e-15)
		tmp = t_1;
	elseif (y <= 1.45e-209)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 1.35e-128)
		tmp = t_2;
	elseif (y <= 5.6e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-15], t$95$1, If[LessEqual[y, 1.45e-209], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-128], t$95$2, If[LessEqual[y, 5.6e+153], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000009e-15 or 1.35000000000000003e-128 < y < 5.5999999999999997e153

   1. Initial program 96.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -2.70000000000000009e-15 < y < 1.45000000000000013e-209

   1. Initial program 93.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.45000000000000013e-209 < y < 1.35000000000000003e-128 or 5.5999999999999997e153 < y

   1. Initial program 95.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 38.7% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(\frac{x}{b} - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* y (/ x (* y y))))))
   (if (<= y -2.1e+59)
     t_1
     (if (<= y 8.5e-217)
       (* x (- 1.0 (* a b)))
       (if (<= y 3.9e-142)
         t_1
         (if (<= y 8.2e+116) (* b (- (/ x b) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.1e+59) {
		tmp = t_1;
	} else if (y <= 8.5e-217) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 3.9e-142) {
		tmp = t_1;
	} else if (y <= 8.2e+116) {
		tmp = b * ((x / b) - (x * a));
	} 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 = y * (y * (x / (y * y)))
    if (y <= (-2.1d+59)) then
        tmp = t_1
    else if (y <= 8.5d-217) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 3.9d-142) then
        tmp = t_1
    else if (y <= 8.2d+116) then
        tmp = b * ((x / b) - (x * a))
    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 = y * (y * (x / (y * y)));
	double tmp;
	if (y <= -2.1e+59) {
		tmp = t_1;
	} else if (y <= 8.5e-217) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 3.9e-142) {
		tmp = t_1;
	} else if (y <= 8.2e+116) {
		tmp = b * ((x / b) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (y * (x / (y * y)))
	tmp = 0
	if y <= -2.1e+59:
		tmp = t_1
	elif y <= 8.5e-217:
		tmp = x * (1.0 - (a * b))
	elif y <= 3.9e-142:
		tmp = t_1
	elif y <= 8.2e+116:
		tmp = b * ((x / b) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(y * Float64(x / Float64(y * y))))
	tmp = 0.0
	if (y <= -2.1e+59)
		tmp = t_1;
	elseif (y <= 8.5e-217)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 3.9e-142)
		tmp = t_1;
	elseif (y <= 8.2e+116)
		tmp = Float64(b * Float64(Float64(x / b) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (y * (x / (y * y)));
	tmp = 0.0;
	if (y <= -2.1e+59)
		tmp = t_1;
	elseif (y <= 8.5e-217)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 3.9e-142)
		tmp = t_1;
	elseif (y <= 8.2e+116)
		tmp = b * ((x / b) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+59], t$95$1, If[LessEqual[y, 8.5e-217], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-142], t$95$1, If[LessEqual[y, 8.2e+116], N[(b * N[(N[(x / b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999984e59 or 8.4999999999999994e-217 < y < 3.9000000000000003e-142 or 8.1999999999999996e116 < y

   1. Initial program 97.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if -2.09999999999999984e59 < y < 8.4999999999999994e-217

   1. Initial program 95.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 3.9000000000000003e-142 < y < 8.1999999999999996e116

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 + b \cdot \left(0.5 \cdot \left(b \cdot \left(a \cdot a\right)\right) - a\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e-21)
   (/ (/ (* x 2.0) (* a a)) (* b b))
   (if (<= y 1.32e-86)
     (* x (+ 1.0 (* b (- (* 0.5 (* b (* a a))) a))))
     (if (<= y 1.22e+157)
       (* a (* a (* x (* (* b b) 0.5))))
       (* y (* y (/ x (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-21) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.32e-86) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} else if (y <= 1.22e+157) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.8d-21)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= 1.32d-86) then
        tmp = x * (1.0d0 + (b * ((0.5d0 * (b * (a * a))) - a)))
    else if (y <= 1.22d+157) then
        tmp = a * (a * (x * ((b * b) * 0.5d0)))
    else
        tmp = y * (y * (x / (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-21) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.32e-86) {
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	} else if (y <= 1.22e+157) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e-21:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= 1.32e-86:
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)))
	elif y <= 1.22e+157:
		tmp = a * (a * (x * ((b * b) * 0.5)))
	else:
		tmp = y * (y * (x / (y * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e-21)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= 1.32e-86)
		tmp = Float64(x * Float64(1.0 + Float64(b * Float64(Float64(0.5 * Float64(b * Float64(a * a))) - a))));
	elseif (y <= 1.22e+157)
		tmp = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))));
	else
		tmp = Float64(y * Float64(y * Float64(x / Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e-21)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= 1.32e-86)
		tmp = x * (1.0 + (b * ((0.5 * (b * (a * a))) - a)));
	elseif (y <= 1.22e+157)
		tmp = a * (a * (x * ((b * b) * 0.5)));
	else
		tmp = y * (y * (x / (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e-21], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-86], N[(x * N[(1.0 + N[(b * N[(N[(0.5 * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+157], N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999995e-21

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -1.79999999999999995e-21 < y < 1.32e-86

   1. Initial program 93.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.32e-86 < y < 1.22e157

   1. Initial program 96.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 1.22e157 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 50.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(1 + a \cdot \left(0.5 \cdot \left(a \cdot \left(b \cdot b\right)\right) - b\right)\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(a \cdot \left(x \cdot \left(\left(b \cdot b\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \frac{x}{y \cdot y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.9e+16)
   (/ (/ (* x 2.0) (* a a)) (* b b))
   (if (<= y 1.4e-86)
     (* x (+ 1.0 (* a (- (* 0.5 (* a (* b b))) b))))
     (if (<= y 2.55e+157)
       (* a (* a (* x (* (* b b) 0.5))))
       (* y (* y (/ x (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+16) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.4e-86) {
		tmp = x * (1.0 + (a * ((0.5 * (a * (b * b))) - b)));
	} else if (y <= 2.55e+157) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.9d+16)) then
        tmp = ((x * 2.0d0) / (a * a)) / (b * b)
    else if (y <= 1.4d-86) then
        tmp = x * (1.0d0 + (a * ((0.5d0 * (a * (b * b))) - b)))
    else if (y <= 2.55d+157) then
        tmp = a * (a * (x * ((b * b) * 0.5d0)))
    else
        tmp = y * (y * (x / (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+16) {
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	} else if (y <= 1.4e-86) {
		tmp = x * (1.0 + (a * ((0.5 * (a * (b * b))) - b)));
	} else if (y <= 2.55e+157) {
		tmp = a * (a * (x * ((b * b) * 0.5)));
	} else {
		tmp = y * (y * (x / (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.9e+16:
		tmp = ((x * 2.0) / (a * a)) / (b * b)
	elif y <= 1.4e-86:
		tmp = x * (1.0 + (a * ((0.5 * (a * (b * b))) - b)))
	elif y <= 2.55e+157:
		tmp = a * (a * (x * ((b * b) * 0.5)))
	else:
		tmp = y * (y * (x / (y * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.9e+16)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(a * a)) / Float64(b * b));
	elseif (y <= 1.4e-86)
		tmp = Float64(x * Float64(1.0 + Float64(a * Float64(Float64(0.5 * Float64(a * Float64(b * b))) - b))));
	elseif (y <= 2.55e+157)
		tmp = Float64(a * Float64(a * Float64(x * Float64(Float64(b * b) * 0.5))));
	else
		tmp = Float64(y * Float64(y * Float64(x / Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.9e+16)
		tmp = ((x * 2.0) / (a * a)) / (b * b);
	elseif (y <= 1.4e-86)
		tmp = x * (1.0 + (a * ((0.5 * (a * (b * b))) - b)));
	elseif (y <= 2.55e+157)
		tmp = a * (a * (x * ((b * b) * 0.5)));
	else
		tmp = y * (y * (x / (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.9e+16], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-86], N[(x * N[(1.0 + N[(a * N[(N[(0.5 * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+157], N[(a * N[(a * N[(x * N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9e16

   1. Initial program 98.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   13. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   15. Simplified 0

       \[\leadsto expr\]

   if -1.9e16 < y < 1.40000000000000005e-86

   1. Initial program 93.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.40000000000000005e-86 < y < 2.55e157

   1. Initial program 96.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 2.55e157 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 27.4% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.3 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(0 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(x \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 5.3e-220)
   (* y (/ x y))
   (if (<= x 1.6e-120)
     (* x (- 1.0 (* y t)))
     (if (<= x 2.1e-61) (* x (- 0.0 (* a b))) (- x (* (* x a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 5.3e-220) {
		tmp = y * (x / y);
	} else if (x <= 1.6e-120) {
		tmp = x * (1.0 - (y * t));
	} else if (x <= 2.1e-61) {
		tmp = x * (0.0 - (a * b));
	} else {
		tmp = x - ((x * 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 (x <= 5.3d-220) then
        tmp = y * (x / y)
    else if (x <= 1.6d-120) then
        tmp = x * (1.0d0 - (y * t))
    else if (x <= 2.1d-61) then
        tmp = x * (0.0d0 - (a * b))
    else
        tmp = x - ((x * 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 (x <= 5.3e-220) {
		tmp = y * (x / y);
	} else if (x <= 1.6e-120) {
		tmp = x * (1.0 - (y * t));
	} else if (x <= 2.1e-61) {
		tmp = x * (0.0 - (a * b));
	} else {
		tmp = x - ((x * a) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 5.3e-220:
		tmp = y * (x / y)
	elif x <= 1.6e-120:
		tmp = x * (1.0 - (y * t))
	elif x <= 2.1e-61:
		tmp = x * (0.0 - (a * b))
	else:
		tmp = x - ((x * a) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 5.3e-220)
		tmp = Float64(y * Float64(x / y));
	elseif (x <= 1.6e-120)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif (x <= 2.1e-61)
		tmp = Float64(x * Float64(0.0 - Float64(a * b)));
	else
		tmp = Float64(x - Float64(Float64(x * a) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 5.3e-220)
		tmp = y * (x / y);
	elseif (x <= 1.6e-120)
		tmp = x * (1.0 - (y * t));
	elseif (x <= 2.1e-61)
		tmp = x * (0.0 - (a * b));
	else
		tmp = x - ((x * a) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 5.3e-220], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-120], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-61], N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 5.3e-220

   1. Initial program 96.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 5.3e-220 < x < 1.6e-120

   1. Initial program 95.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.6e-120 < x < 2.0999999999999999e-61

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 2.0999999999999999e-61 < x

   1. Initial program 93.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 24.8% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0 - a \cdot b\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 0.0 (* a b)))))
   (if (<= b -4.2e+154)
     t_1
     (if (<= b 1.32e-261) (* y (/ x y)) (if (<= b 1.15e+86) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (b <= -4.2e+154) {
		tmp = t_1;
	} else if (b <= 1.32e-261) {
		tmp = y * (x / y);
	} else if (b <= 1.15e+86) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (0.0d0 - (a * b))
    if (b <= (-4.2d+154)) then
        tmp = t_1
    else if (b <= 1.32d-261) then
        tmp = y * (x / y)
    else if (b <= 1.15d+86) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (b <= -4.2e+154) {
		tmp = t_1;
	} else if (b <= 1.32e-261) {
		tmp = y * (x / y);
	} else if (b <= 1.15e+86) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.0 - (a * b))
	tmp = 0
	if b <= -4.2e+154:
		tmp = t_1
	elif b <= 1.32e-261:
		tmp = y * (x / y)
	elif b <= 1.15e+86:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(0.0 - Float64(a * b)))
	tmp = 0.0
	if (b <= -4.2e+154)
		tmp = t_1;
	elseif (b <= 1.32e-261)
		tmp = Float64(y * Float64(x / y));
	elseif (b <= 1.15e+86)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (0.0 - (a * b));
	tmp = 0.0;
	if (b <= -4.2e+154)
		tmp = t_1;
	elseif (b <= 1.32e-261)
		tmp = y * (x / y);
	elseif (b <= 1.15e+86)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+154], t$95$1, If[LessEqual[b, 1.32e-261], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+86], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.19999999999999989e154 or 1.14999999999999995e86 < b

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -4.19999999999999989e154 < b < 1.3200000000000001e-261

   1. Initial program 92.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if 1.3200000000000001e-261 < b < 1.14999999999999995e86

   1. Initial program 95.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 31.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - a \cdot b\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 180000000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (* a b)))))
   (if (<= a -2.1e-221)
     t_1
     (if (<= a 180000000000.0) (* x (- 1.0 (* y t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (a * b));
	double tmp;
	if (a <= -2.1e-221) {
		tmp = t_1;
	} else if (a <= 180000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (a * b))
    if (a <= (-2.1d-221)) then
        tmp = t_1
    else if (a <= 180000000000.0d0) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (1.0 - (a * b));
	double tmp;
	if (a <= -2.1e-221) {
		tmp = t_1;
	} else if (a <= 180000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (1.0 - (a * b))
	tmp = 0
	if a <= -2.1e-221:
		tmp = t_1
	elif a <= 180000000000.0:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(1.0 - Float64(a * b)))
	tmp = 0.0
	if (a <= -2.1e-221)
		tmp = t_1;
	elseif (a <= 180000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (1.0 - (a * b));
	tmp = 0.0;
	if (a <= -2.1e-221)
		tmp = t_1;
	elseif (a <= 180000000000.0)
		tmp = x * (1.0 - (y * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e-221], t$95$1, If[LessEqual[a, 180000000000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1e-221 or 1.8e11 < a

   1. Initial program 93.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -2.1e-221 < a < 1.8e11

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 32.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0 - a \cdot b\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (- 0.0 (* a b)))))
   (if (<= y -1.25e+32) t_1 (if (<= y 2.8e-14) (* x (- 1.0 (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (y <= -1.25e+32) {
		tmp = t_1;
	} else if (y <= 2.8e-14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (0.0d0 - (a * b))
    if (y <= (-1.25d+32)) then
        tmp = t_1
    else if (y <= 2.8d-14) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.0 - (a * b));
	double tmp;
	if (y <= -1.25e+32) {
		tmp = t_1;
	} else if (y <= 2.8e-14) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.0 - (a * b))
	tmp = 0
	if y <= -1.25e+32:
		tmp = t_1
	elif y <= 2.8e-14:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(0.0 - Float64(a * b)))
	tmp = 0.0
	if (y <= -1.25e+32)
		tmp = t_1;
	elseif (y <= 2.8e-14)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (0.0 - (a * b));
	tmp = 0.0;
	if (y <= -1.25e+32)
		tmp = t_1;
	elseif (y <= 2.8e-14)
		tmp = x * (1.0 - (a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+32], t$95$1, If[LessEqual[y, 2.8e-14], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e32 or 2.8000000000000001e-14 < y

   1. Initial program 98.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in a around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -1.2499999999999999e32 < y < 2.8000000000000001e-14

   1. Initial program 93.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 24.0% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{x}{y} \end{array} \]

FPCore

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

C

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

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 = y * (x / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in t around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]

11. Taylor expanded in y around inf 0

    \[\leadsto expr\]

13. Simplified 0

    \[\leadsto expr\]

14. Taylor expanded in y around 0 0

    \[\leadsto expr\]

16. Simplified 0

    \[\leadsto expr\]
17. Add Preprocessing

Alternative 22: 19.5% 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%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in t around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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))))))