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

Percentage Accurate: 96.6% → 99.1%

Time: 16.7s

Alternatives: 18

Speedup: 1.5×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% 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: 78.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ \mathbf{if}\;a \leq -0.00026:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 13:\\ \;\;\;\;\frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))))
   (if (<= a -0.00026)
     t_1
     (if (<= a 13.0) (/ x (exp (* y (- t (log z))))) 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 (a <= -0.00026) {
		tmp = t_1;
	} else if (a <= 13.0) {
		tmp = x / exp((y * (t - log(z))));
	} 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 (a <= (-0.00026d0)) then
        tmp = t_1
    else if (a <= 13.0d0) then
        tmp = x / exp((y * (t - log(z))))
    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 (a <= -0.00026) {
		tmp = t_1;
	} else if (a <= 13.0) {
		tmp = x / Math.exp((y * (t - Math.log(z))));
	} 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 a <= -0.00026:
		tmp = t_1
	elif a <= 13.0:
		tmp = x / math.exp((y * (t - math.log(z))))
	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 (a <= -0.00026)
		tmp = t_1;
	elseif (a <= 13.0)
		tmp = Float64(x / exp(Float64(y * Float64(t - log(z)))));
	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 (a <= -0.00026)
		tmp = t_1;
	elseif (a <= 13.0)
		tmp = x / exp((y * (t - log(z))));
	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[a, -0.00026], t$95$1, If[LessEqual[a, 13.0], N[(x / N[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.59999999999999977e-4 or 13 < a

   1. Initial program 91.3%

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

   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 -2.59999999999999977e-4 < a < 13

   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

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   9. Simplified 0

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

Alternative 3: 84.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.47:\\ \;\;\;\;x \cdot e^{-a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow (/ z (exp t)) y))))
   (if (<= y -1.85e-42) t_1 (if (<= y 0.47) (* 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 / exp(t)), y);
	double tmp;
	if (y <= -1.85e-42) {
		tmp = t_1;
	} else if (y <= 0.47) {
		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 / exp(t)) ** y)
    if (y <= (-1.85d-42)) then
        tmp = t_1
    else if (y <= 0.47d0) 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 / Math.exp(t)), y);
	double tmp;
	if (y <= -1.85e-42) {
		tmp = t_1;
	} else if (y <= 0.47) {
		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 / math.exp(t)), y)
	tmp = 0
	if y <= -1.85e-42:
		tmp = t_1
	elif y <= 0.47:
		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 * (Float64(z / exp(t)) ^ y))
	tmp = 0.0
	if (y <= -1.85e-42)
		tmp = t_1;
	elseif (y <= 0.47)
		tmp = Float64(x * exp(Float64(-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 <= -1.85e-42)
		tmp = t_1;
	elseif (y <= 0.47)
		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[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-42], t$95$1, If[LessEqual[y, 0.47], N[(x * N[Exp[(-N[(a * b), $MachinePrecision])], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e-42 or 0.46999999999999997 < y

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.8500000000000001e-42 < y < 0.46999999999999997

   1. Initial program 91.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 4: 59.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -0.00022:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.52:\\ \;\;\;\;\frac{x}{1 + b \cdot \left(a + b \cdot \left(b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + a \cdot \left(a \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -0.00022)
     t_1
     (if (<= y 0.52)
       (/
        x
        (+
         1.0
         (*
          b
          (+
           a
           (*
            b
            (+
             (* b (* 0.16666666666666666 (* a (* a a))))
             (* a (* a 0.5))))))))
       (if (<= y 1.4e+124) (* x (* 0.5 (* a (* a (* b 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 <= -0.00022) {
		tmp = t_1;
	} else if (y <= 0.52) {
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	} else if (y <= 1.4e+124) {
		tmp = x * (0.5 * (a * (a * (b * 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 <= (-0.00022d0)) then
        tmp = t_1
    else if (y <= 0.52d0) then
        tmp = x / (1.0d0 + (b * (a + (b * ((b * (0.16666666666666666d0 * (a * (a * a)))) + (a * (a * 0.5d0)))))))
    else if (y <= 1.4d+124) then
        tmp = x * (0.5d0 * (a * (a * (b * 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 <= -0.00022) {
		tmp = t_1;
	} else if (y <= 0.52) {
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	} else if (y <= 1.4e+124) {
		tmp = x * (0.5 * (a * (a * (b * 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 <= -0.00022:
		tmp = t_1
	elif y <= 0.52:
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))))
	elif y <= 1.4e+124:
		tmp = x * (0.5 * (a * (a * (b * 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 <= -0.00022)
		tmp = t_1;
	elseif (y <= 0.52)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(a + Float64(b * Float64(Float64(b * Float64(0.16666666666666666 * Float64(a * Float64(a * a)))) + Float64(a * Float64(a * 0.5))))))));
	elseif (y <= 1.4e+124)
		tmp = Float64(x * Float64(0.5 * Float64(a * Float64(a * Float64(b * 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 <= -0.00022)
		tmp = t_1;
	elseif (y <= 0.52)
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	elseif (y <= 1.4e+124)
		tmp = x * (0.5 * (a * (a * (b * 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, -0.00022], t$95$1, If[LessEqual[y, 0.52], N[(x / N[(1.0 + N[(b * N[(a + N[(b * N[(N[(b * N[(0.16666666666666666 * N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+124], N[(x * N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000008e-4 or 1.4e124 < y

   1. Initial program 99.0%

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

   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 -2.20000000000000008e-4 < y < 0.52000000000000002

   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

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in b around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 0.52000000000000002 < y < 1.4e124

   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

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

Alternative 5: 69.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.000175:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))))
   (if (<= a -1.1e-88) t_1 (if (<= a 0.000175) (/ x (exp (* y t))) 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 (a <= -1.1e-88) {
		tmp = t_1;
	} else if (a <= 0.000175) {
		tmp = x / exp((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 / exp((a * b))
    if (a <= (-1.1d-88)) then
        tmp = t_1
    else if (a <= 0.000175d0) then
        tmp = x / exp((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 / Math.exp((a * b));
	double tmp;
	if (a <= -1.1e-88) {
		tmp = t_1;
	} else if (a <= 0.000175) {
		tmp = x / Math.exp((y * t));
	} 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 a <= -1.1e-88:
		tmp = t_1
	elif a <= 0.000175:
		tmp = x / math.exp((y * t))
	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 (a <= -1.1e-88)
		tmp = t_1;
	elseif (a <= 0.000175)
		tmp = Float64(x / exp(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 / exp((a * b));
	tmp = 0.0;
	if (a <= -1.1e-88)
		tmp = t_1;
	elseif (a <= 0.000175)
		tmp = x / exp((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[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e-88], t$95$1, If[LessEqual[a, 0.000175], N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000002e-88 or 1.74999999999999998e-4 < a

   1. Initial program 92.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.10000000000000002e-88 < a < 1.74999999999999998e-4

   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

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 6: 72.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -0.016:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -0.016) t_1 (if (<= y 4.5e+123) (/ 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 <= -0.016) {
		tmp = t_1;
	} else if (y <= 4.5e+123) {
		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 <= (-0.016d0)) then
        tmp = t_1
    else if (y <= 4.5d+123) 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 <= -0.016) {
		tmp = t_1;
	} else if (y <= 4.5e+123) {
		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 <= -0.016:
		tmp = t_1
	elif y <= 4.5e+123:
		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 <= -0.016)
		tmp = t_1;
	elseif (y <= 4.5e+123)
		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 <= -0.016)
		tmp = t_1;
	elseif (y <= 4.5e+123)
		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, -0.016], t$95$1, If[LessEqual[y, 4.5e+123], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.016 or 4.49999999999999983e123 < y

   1. Initial program 99.0%

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

   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 -0.016 < y < 4.49999999999999983e123

   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

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 7: 49.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+158}:\\ \;\;\;\;x + t \cdot \left(\left(t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right) \cdot x\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.65:\\ \;\;\;\;\frac{x}{1 + b \cdot \left(a + b \cdot \left(b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + a \cdot \left(a \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a \cdot \left(b + a \cdot \left(a \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right) + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -1.6e+158)
     (+ x (* t (* (* t (* 0.5 (* y y))) x)))
     (if (<= y -3e+33)
       t_1
       (if (<= y 0.65)
         (/
          x
          (+
           1.0
           (*
            b
            (+
             a
             (*
              b
              (+
               (* b (* 0.16666666666666666 (* a (* a a))))
               (* a (* a 0.5))))))))
         (if (<= y 2.7e+243)
           t_1
           (/
            x
            (+
             1.0
             (*
              a
              (+
               b
               (*
                a
                (+
                 (* a (* 0.16666666666666666 (* b (* b b))))
                 (* 0.5 (* b b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -1.6e+158) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -3e+33) {
		tmp = t_1;
	} else if (y <= 0.65) {
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	} else if (y <= 2.7e+243) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 + (a * (b + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-1.6d+158)) then
        tmp = x + (t * ((t * (0.5d0 * (y * y))) * x))
    else if (y <= (-3d+33)) then
        tmp = t_1
    else if (y <= 0.65d0) then
        tmp = x / (1.0d0 + (b * (a + (b * ((b * (0.16666666666666666d0 * (a * (a * a)))) + (a * (a * 0.5d0)))))))
    else if (y <= 2.7d+243) then
        tmp = t_1
    else
        tmp = x / (1.0d0 + (a * (b + (a * ((a * (0.16666666666666666d0 * (b * (b * b)))) + (0.5d0 * (b * b)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -1.6e+158) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -3e+33) {
		tmp = t_1;
	} else if (y <= 0.65) {
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	} else if (y <= 2.7e+243) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 + (a * (b + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -1.6e+158:
		tmp = x + (t * ((t * (0.5 * (y * y))) * x))
	elif y <= -3e+33:
		tmp = t_1
	elif y <= 0.65:
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))))
	elif y <= 2.7e+243:
		tmp = t_1
	else:
		tmp = x / (1.0 + (a * (b + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -1.6e+158)
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(0.5 * Float64(y * y))) * x)));
	elseif (y <= -3e+33)
		tmp = t_1;
	elseif (y <= 0.65)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(a + Float64(b * Float64(Float64(b * Float64(0.16666666666666666 * Float64(a * Float64(a * a)))) + Float64(a * Float64(a * 0.5))))))));
	elseif (y <= 2.7e+243)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 + Float64(a * Float64(b + Float64(a * Float64(Float64(a * Float64(0.16666666666666666 * Float64(b * Float64(b * b)))) + Float64(0.5 * Float64(b * b))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -1.6e+158)
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	elseif (y <= -3e+33)
		tmp = t_1;
	elseif (y <= 0.65)
		tmp = x / (1.0 + (b * (a + (b * ((b * (0.16666666666666666 * (a * (a * a)))) + (a * (a * 0.5)))))));
	elseif (y <= 2.7e+243)
		tmp = t_1;
	else
		tmp = x / (1.0 + (a * (b + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+158], N[(x + N[(t * N[(N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+33], t$95$1, If[LessEqual[y, 0.65], N[(x / N[(1.0 + N[(b * N[(a + N[(b * N[(N[(b * N[(0.16666666666666666 * N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+243], t$95$1, N[(x / N[(1.0 + N[(a * N[(b + N[(a * N[(N[(a * N[(0.16666666666666666 * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999997e158

   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 t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -1.59999999999999997e158 < y < -2.99999999999999984e33 or 0.650000000000000022 < y < 2.7000000000000001e243

   1. Initial program 98.7%

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

   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 -2.99999999999999984e33 < y < 0.650000000000000022

   1. Initial program 92.6%

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

   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 b around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 2.7000000000000001e243 < 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 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

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

Alternative 8: 48.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a \cdot \left(b + a \cdot \left(a \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right) + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ t_2 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+157}:\\ \;\;\;\;x + t \cdot \left(\left(t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right) \cdot x\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+243}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           1.0
           (*
            a
            (+
             b
             (*
              a
              (+
               (* a (* 0.16666666666666666 (* b (* b b))))
               (* 0.5 (* b b)))))))))
        (t_2 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -9.6e+157)
     (+ x (* t (* (* t (* 0.5 (* y y))) x)))
     (if (<= y -6e+22)
       t_2
       (if (<= y 5.1e-25) t_1 (if (<= y 2.9e+243) t_2 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 + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	double t_2 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -6e+22) {
		tmp = t_2;
	} else if (y <= 5.1e-25) {
		tmp = t_1;
	} else if (y <= 2.9e+243) {
		tmp = t_2;
	} 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 = x / (1.0d0 + (a * (b + (a * ((a * (0.16666666666666666d0 * (b * (b * b)))) + (0.5d0 * (b * b)))))))
    t_2 = x * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-9.6d+157)) then
        tmp = x + (t * ((t * (0.5d0 * (y * y))) * x))
    else if (y <= (-6d+22)) then
        tmp = t_2
    else if (y <= 5.1d-25) then
        tmp = t_1
    else if (y <= 2.9d+243) then
        tmp = t_2
    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 + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	double t_2 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -6e+22) {
		tmp = t_2;
	} else if (y <= 5.1e-25) {
		tmp = t_1;
	} else if (y <= 2.9e+243) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a * (b + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))))
	t_2 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -9.6e+157:
		tmp = x + (t * ((t * (0.5 * (y * y))) * x))
	elif y <= -6e+22:
		tmp = t_2
	elif y <= 5.1e-25:
		tmp = t_1
	elif y <= 2.9e+243:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a * Float64(b + Float64(a * Float64(Float64(a * Float64(0.16666666666666666 * Float64(b * Float64(b * b)))) + Float64(0.5 * Float64(b * b))))))))
	t_2 = Float64(x * Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -9.6e+157)
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(0.5 * Float64(y * y))) * x)));
	elseif (y <= -6e+22)
		tmp = t_2;
	elseif (y <= 5.1e-25)
		tmp = t_1;
	elseif (y <= 2.9e+243)
		tmp = t_2;
	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 + (a * ((a * (0.16666666666666666 * (b * (b * b)))) + (0.5 * (b * b)))))));
	t_2 = x * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -9.6e+157)
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	elseif (y <= -6e+22)
		tmp = t_2;
	elseif (y <= 5.1e-25)
		tmp = t_1;
	elseif (y <= 2.9e+243)
		tmp = t_2;
	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 * N[(b + N[(a * N[(N[(a * N[(0.16666666666666666 * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+157], N[(x + N[(t * N[(N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e+22], t$95$2, If[LessEqual[y, 5.1e-25], t$95$1, If[LessEqual[y, 2.9e+243], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5999999999999998e157

   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 t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -9.5999999999999998e157 < y < -6e22 or 5.1000000000000003e-25 < y < 2.90000000000000006e243

   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 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 -6e22 < y < 5.1000000000000003e-25 or 2.90000000000000006e243 < y

   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

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 9: 48.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a \cdot \left(b + a \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ t_2 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+157}:\\ \;\;\;\;x + t \cdot \left(\left(t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right) \cdot x\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.46:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* a (+ b (* a (* 0.5 (* b b))))))))
        (t_2 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -9.6e+157)
     (+ x (* t (* (* t (* 0.5 (* y y))) x)))
     (if (<= y -2e+33)
       t_2
       (if (<= y 0.46) t_1 (if (<= y 1.65e+239) t_2 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 + (a * (0.5 * (b * b))))));
	double t_2 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -2e+33) {
		tmp = t_2;
	} else if (y <= 0.46) {
		tmp = t_1;
	} else if (y <= 1.65e+239) {
		tmp = t_2;
	} 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 = x / (1.0d0 + (a * (b + (a * (0.5d0 * (b * b))))))
    t_2 = x * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-9.6d+157)) then
        tmp = x + (t * ((t * (0.5d0 * (y * y))) * x))
    else if (y <= (-2d+33)) then
        tmp = t_2
    else if (y <= 0.46d0) then
        tmp = t_1
    else if (y <= 1.65d+239) then
        tmp = t_2
    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 + (a * (0.5 * (b * b))))));
	double t_2 = x * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -2e+33) {
		tmp = t_2;
	} else if (y <= 0.46) {
		tmp = t_1;
	} else if (y <= 1.65e+239) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a * (b + (a * (0.5 * (b * b))))))
	t_2 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -9.6e+157:
		tmp = x + (t * ((t * (0.5 * (y * y))) * x))
	elif y <= -2e+33:
		tmp = t_2
	elif y <= 0.46:
		tmp = t_1
	elif y <= 1.65e+239:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a * Float64(b + Float64(a * Float64(0.5 * Float64(b * b)))))))
	t_2 = Float64(x * Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -9.6e+157)
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(0.5 * Float64(y * y))) * x)));
	elseif (y <= -2e+33)
		tmp = t_2;
	elseif (y <= 0.46)
		tmp = t_1;
	elseif (y <= 1.65e+239)
		tmp = t_2;
	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 + (a * (0.5 * (b * b))))));
	t_2 = x * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -9.6e+157)
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	elseif (y <= -2e+33)
		tmp = t_2;
	elseif (y <= 0.46)
		tmp = t_1;
	elseif (y <= 1.65e+239)
		tmp = t_2;
	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 * N[(b + N[(a * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+157], N[(x + N[(t * N[(N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e+33], t$95$2, If[LessEqual[y, 0.46], t$95$1, If[LessEqual[y, 1.65e+239], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5999999999999998e157

   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 t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -9.5999999999999998e157 < y < -1.9999999999999999e33 or 0.46000000000000002 < y < 1.6499999999999999e239

   1. Initial program 98.7%

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

   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 -1.9999999999999999e33 < y < 0.46000000000000002 or 1.6499999999999999e239 < y

   1. Initial program 93.3%

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

   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

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 10: 46.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+157}:\\ \;\;\;\;x + t \cdot \left(\left(t \cdot \left(0.5 \cdot \left(y \cdot y\right)\right)\right) \cdot x\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -9.6e+157)
     (+ x (* t (* (* t (* 0.5 (* y y))) x)))
     (if (<= y -6.6e-10) t_1 (if (<= y 1.95e-24) (/ 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -6.6e-10) {
		tmp = t_1;
	} else if (y <= 1.95e-24) {
		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 * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-9.6d+157)) then
        tmp = x + (t * ((t * (0.5d0 * (y * y))) * x))
    else if (y <= (-6.6d-10)) then
        tmp = t_1
    else if (y <= 1.95d-24) 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -9.6e+157) {
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	} else if (y <= -6.6e-10) {
		tmp = t_1;
	} else if (y <= 1.95e-24) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -9.6e+157:
		tmp = x + (t * ((t * (0.5 * (y * y))) * x))
	elif y <= -6.6e-10:
		tmp = t_1
	elif y <= 1.95e-24:
		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(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -9.6e+157)
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(0.5 * Float64(y * y))) * x)));
	elseif (y <= -6.6e-10)
		tmp = t_1;
	elseif (y <= 1.95e-24)
		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 * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -9.6e+157)
		tmp = x + (t * ((t * (0.5 * (y * y))) * x));
	elseif (y <= -6.6e-10)
		tmp = t_1;
	elseif (y <= 1.95e-24)
		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[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+157], N[(x + N[(t * N[(N[(t * N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-10], t$95$1, If[LessEqual[y, 1.95e-24], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5999999999999998e157

   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 t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -9.5999999999999998e157 < y < -6.6e-10 or 1.95e-24 < y

   1. Initial program 98.0%

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

   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 -6.6e-10 < y < 1.95e-24

   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

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 11: 44.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -1.1e+159)
     (* (* x (* y y)) (* 0.5 (* t t)))
     (if (<= y -4e-12) t_1 (if (<= y 6.6e-24) (/ 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -1.1e+159) {
		tmp = (x * (y * y)) * (0.5 * (t * t));
	} else if (y <= -4e-12) {
		tmp = t_1;
	} else if (y <= 6.6e-24) {
		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 * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-1.1d+159)) then
        tmp = (x * (y * y)) * (0.5d0 * (t * t))
    else if (y <= (-4d-12)) then
        tmp = t_1
    else if (y <= 6.6d-24) 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -1.1e+159) {
		tmp = (x * (y * y)) * (0.5 * (t * t));
	} else if (y <= -4e-12) {
		tmp = t_1;
	} else if (y <= 6.6e-24) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -1.1e+159:
		tmp = (x * (y * y)) * (0.5 * (t * t))
	elif y <= -4e-12:
		tmp = t_1
	elif y <= 6.6e-24:
		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(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -1.1e+159)
		tmp = Float64(Float64(x * Float64(y * y)) * Float64(0.5 * Float64(t * t)));
	elseif (y <= -4e-12)
		tmp = t_1;
	elseif (y <= 6.6e-24)
		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 * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -1.1e+159)
		tmp = (x * (y * y)) * (0.5 * (t * t));
	elseif (y <= -4e-12)
		tmp = t_1;
	elseif (y <= 6.6e-24)
		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[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+159], N[(N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-12], t$95$1, If[LessEqual[y, 6.6e-24], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e159

   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 t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   14. Taylor expanded in t around inf 0

       \[\leadsto expr\]

   16. Simplified 0

       \[\leadsto expr\]

   if -1.1e159 < y < -3.99999999999999992e-12 or 6.59999999999999968e-24 < y

   1. Initial program 98.0%

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

   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 -3.99999999999999992e-12 < y < 6.59999999999999968e-24

   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

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 12: 43.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* 0.5 (* a (* a (* b b)))))))
   (if (<= y -5.2e-12) t_1 (if (<= y 4.9e-26) (/ 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -5.2e-12) {
		tmp = t_1;
	} else if (y <= 4.9e-26) {
		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 * (0.5d0 * (a * (a * (b * b))))
    if (y <= (-5.2d-12)) then
        tmp = t_1
    else if (y <= 4.9d-26) 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 * (0.5 * (a * (a * (b * b))));
	double tmp;
	if (y <= -5.2e-12) {
		tmp = t_1;
	} else if (y <= 4.9e-26) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (0.5 * (a * (a * (b * b))))
	tmp = 0
	if y <= -5.2e-12:
		tmp = t_1
	elif y <= 4.9e-26:
		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(0.5 * Float64(a * Float64(a * Float64(b * b)))))
	tmp = 0.0
	if (y <= -5.2e-12)
		tmp = t_1;
	elseif (y <= 4.9e-26)
		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 * (0.5 * (a * (a * (b * b))));
	tmp = 0.0;
	if (y <= -5.2e-12)
		tmp = t_1;
	elseif (y <= 4.9e-26)
		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[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e-12], t$95$1, If[LessEqual[y, 4.9e-26], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999965e-12 or 4.8999999999999999e-26 < y

   1. Initial program 98.5%

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

   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 -5.19999999999999965e-12 < y < 4.8999999999999999e-26

   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

      \[\leadsto expr\]

   10. Taylor expanded in a around 0 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 13: 29.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e-37)
   (* x (- 1.0 (* a b)))
   (if (<= b 9e+20) (* x (- 1.0 (* y t))) (* t (- 0.0 (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e-37) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 9e+20) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t * (0.0 - (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d-37)) then
        tmp = x * (1.0d0 - (a * b))
    else if (b <= 9d+20) then
        tmp = x * (1.0d0 - (y * t))
    else
        tmp = t * (0.0d0 - (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e-37) {
		tmp = x * (1.0 - (a * b));
	} else if (b <= 9e+20) {
		tmp = x * (1.0 - (y * t));
	} else {
		tmp = t * (0.0 - (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e-37:
		tmp = x * (1.0 - (a * b))
	elif b <= 9e+20:
		tmp = x * (1.0 - (y * t))
	else:
		tmp = t * (0.0 - (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e-37)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (b <= 9e+20)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	else
		tmp = Float64(t * Float64(0.0 - Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e-37)
		tmp = x * (1.0 - (a * b));
	elseif (b <= 9e+20)
		tmp = x * (1.0 - (y * t));
	else
		tmp = t * (0.0 - (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e-37], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e+20], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(0.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.20000000000000002e-37

   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

      \[\leadsto expr\]

   8. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -2.20000000000000002e-37 < b < 9e20

   1. Initial program 91.9%

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

   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

       \[\leadsto expr\]

   if 9e20 < 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 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

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

Alternative 14: 30.4% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(t \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.5e-59) (/ x (+ 1.0 (* a b))) (- x (* y (* t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.5e-59) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (y * (t * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.5d-59) then
        tmp = x / (1.0d0 + (a * b))
    else
        tmp = x - (y * (t * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.5e-59) {
		tmp = x / (1.0 + (a * b));
	} else {
		tmp = x - (y * (t * x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.5e-59:
		tmp = x / (1.0 + (a * b))
	else:
		tmp = x - (y * (t * x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.5e-59)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	else
		tmp = Float64(x - Float64(y * Float64(t * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.5e-59)
		tmp = x / (1.0 + (a * b));
	else
		tmp = x - (y * (t * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.5e-59], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.50000000000000012e-59

   1. Initial program 95.7%

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

   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

       \[\leadsto expr\]

   if 4.50000000000000012e-59 < x

   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 t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in t around 0 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 15: 28.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(0 - x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.02e+62) (* t (- 0.0 (* x y))) (* x (- 1.0 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.02e+62) {
		tmp = t * (0.0 - (x * y));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.02d+62)) then
        tmp = t * (0.0d0 - (x * y))
    else
        tmp = x * (1.0d0 - (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.02e+62) {
		tmp = t * (0.0 - (x * y));
	} else {
		tmp = x * (1.0 - (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.02e+62:
		tmp = t * (0.0 - (x * y))
	else:
		tmp = x * (1.0 - (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.02e+62)
		tmp = Float64(t * Float64(0.0 - Float64(x * y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.02e+62)
		tmp = t * (0.0 - (x * y));
	else
		tmp = x * (1.0 - (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.02e+62], N[(t * N[(0.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02000000000000002e62

   1. Initial program 91.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in 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 -1.02000000000000002e62 < t

   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 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 16: 21.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0 - t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.1e-45) x (* x (- 0.0 (* t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-45) {
		tmp = x;
	} else {
		tmp = x * (0.0 - (t * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.1d-45) then
        tmp = x
    else
        tmp = x * (0.0d0 - (t * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-45) {
		tmp = x;
	} else {
		tmp = x * (0.0 - (t * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.1e-45:
		tmp = x
	else:
		tmp = x * (0.0 - (t * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.1e-45)
		tmp = x;
	else
		tmp = Float64(x * Float64(0.0 - Float64(t * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.1e-45)
		tmp = x;
	else
		tmp = x * (0.0 - (t * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.1e-45], x, N[(x * N[(0.0 - N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.1000000000000001e-45

   1. Initial program 94.1%

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

   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 3.1000000000000001e-45 < 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 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

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

Alternative 17: 21.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.6e-7) x (* t (- 0.0 (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.6e-7) {
		tmp = x;
	} else {
		tmp = t * (0.0 - (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.6d-7) then
        tmp = x
    else
        tmp = t * (0.0d0 - (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.6e-7) {
		tmp = x;
	} else {
		tmp = t * (0.0 - (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.6e-7:
		tmp = x
	else:
		tmp = t * (0.0 - (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.6e-7)
		tmp = x;
	else
		tmp = Float64(t * Float64(0.0 - Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.6e-7)
		tmp = x;
	else
		tmp = t * (0.0 - (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.6e-7], x, N[(t * N[(0.0 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.59999999999999994e-7

   1. Initial program 94.4%

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

   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 3.59999999999999994e-7 < 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 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

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

Alternative 18: 19.4% 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 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. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(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))))))