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

Percentage Accurate: 99.8% → 99.8%

Time: 13.4s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(t + \left(x \cdot \log y + z\right)\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ t (+ (* x (log y)) z)) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((t + ((x * log(y)) + z)) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((t + ((x * log(y)) + z)) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((t + ((x * Math.log(y)) + z)) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((t + ((x * math.log(y)) + z)) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(t + Float64(Float64(x * log(y)) + z)) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((t + ((x * log(y)) + z)) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \left(\left(\left(t + \left(x \cdot \log y + z\right)\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
4. Add Preprocessing

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -9 \cdot 10^{+162} \lor \neg \left(x \leq 1.18 \cdot 10^{+185}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (or (<= x -9e+162) (not (<= x 1.18e+185)))
     (+ (* y i) (+ z (+ (* x (log y)) t_1)))
     (+ (* y i) (+ t_1 (+ a (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if ((x <= -9e+162) || !(x <= 1.18e+185)) {
		tmp = (y * i) + (z + ((x * log(y)) + t_1));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if ((x <= (-9d+162)) .or. (.not. (x <= 1.18d+185))) then
        tmp = (y * i) + (z + ((x * log(y)) + t_1))
    else
        tmp = (y * i) + (t_1 + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if ((x <= -9e+162) || !(x <= 1.18e+185)) {
		tmp = (y * i) + (z + ((x * Math.log(y)) + t_1));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if (x <= -9e+162) or not (x <= 1.18e+185):
		tmp = (y * i) + (z + ((x * math.log(y)) + t_1))
	else:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if ((x <= -9e+162) || !(x <= 1.18e+185))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(x * log(y)) + t_1)));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if ((x <= -9e+162) || ~((x <= 1.18e+185)))
		tmp = (y * i) + (z + ((x * log(y)) + t_1));
	else
		tmp = (y * i) + (t_1 + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9e+162], N[Not[LessEqual[x, 1.18e+185]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999944e162 or 1.18e185 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 96.3%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in a around 0 89.2%

      \[\leadsto \color{blue}{\left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)} + y \cdot i \]

   if -8.99999999999999944e162 < x < 1.18e185

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.9%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+162} \lor \neg \left(x \leq 1.18 \cdot 10^{+185}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(x \cdot \log y + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= z -1.95e+124)
     (+ (* y i) (+ t_1 (+ a (+ z t))))
     (+ (* y i) (+ t_1 (+ (* x (log y)) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if (z <= -1.95e+124) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + ((x * log(y)) + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (z <= (-1.95d+124)) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else
        tmp = (y * i) + (t_1 + ((x * log(y)) + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (z <= -1.95e+124) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + ((x * Math.log(y)) + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if z <= -1.95e+124:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	else:
		tmp = (y * i) + (t_1 + ((x * math.log(y)) + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (z <= -1.95e+124)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(Float64(x * log(y)) + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (z <= -1.95e+124)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	else
		tmp = (y * i) + (t_1 + ((x * log(y)) + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+124], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e124

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.2%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   if -1.95e124 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.9%

      \[\leadsto \left(\left(\color{blue}{x \cdot \log y} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(x \cdot \log y + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(x \cdot \log y + z\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ (* x (log y)) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (((b - 0.5) * log(c)) + (a + ((x * log(y)) + z)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + (((b - 0.5d0) * log(c)) + (a + ((x * log(y)) + z)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (((b - 0.5) * Math.log(c)) + (a + ((x * Math.log(y)) + z)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + (((b - 0.5) * math.log(c)) + (a + ((x * math.log(y)) + z)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(Float64(x * log(y)) + z))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (((b - 0.5) * log(c)) + (a + ((x * log(y)) + z)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in t around 0 87.9%

   \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

4. Final simplification 87.9%

   \[\leadsto y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(x \cdot \log y + z\right)\right)\right) \]
5. Add Preprocessing

Alternative 5: 90.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+196} \lor \neg \left(x \leq 3.25 \cdot 10^{+185}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.35e+196) (not (<= x 3.25e+185)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.35e+196) || !(x <= 3.25e+185)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.35d+196)) .or. (.not. (x <= 3.25d+185))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.35e+196) || !(x <= 3.25e+185)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.35e+196) or not (x <= 3.25e+185):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.35e+196) || !(x <= 3.25e+185))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.35e+196) || ~((x <= 3.25e+185)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.35e+196], N[Not[LessEqual[x, 3.25e+185]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e196 or 3.2500000000000001e185 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in x around inf 80.0%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   if -2.3500000000000001e196 < x < 3.2500000000000001e185

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.7%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+196} \lor \neg \left(x \leq 3.25 \cdot 10^{+185}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+196} \lor \neg \left(x \leq 4 \cdot 10^{+185}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.1e+196) (not (<= x 4e+185)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+196) || !(x <= 4e+185)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.1d+196)) .or. (.not. (x <= 4d+185))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+196) || !(x <= 4e+185)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.1e+196) or not (x <= 4e+185):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.1e+196) || !(x <= 4e+185))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.1e+196) || ~((x <= 4e+185)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.1e+196], N[Not[LessEqual[x, 4e+185]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000015e196 or 3.9999999999999999e185 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in x around inf 80.0%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   if -2.10000000000000015e196 < x < 3.9999999999999999e185

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.9%

      \[\leadsto \left(\left(\color{blue}{z} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+196} \lor \neg \left(x \leq 4 \cdot 10^{+185}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+198} \lor \neg \left(x \leq 6.6 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+198) (not (<= x 6.6e+184)))
   (+ (* x (log y)) (* y i))
   (+ a (+ t (+ z (* (- b 0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+198) || !(x <= 6.6e+184)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = a + (t + (z + ((b - 0.5) * log(c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.3d+198)) .or. (.not. (x <= 6.6d+184))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = a + (t + (z + ((b - 0.5d0) * log(c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+198) || !(x <= 6.6e+184)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = a + (t + (z + ((b - 0.5) * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+198) or not (x <= 6.6e+184):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = a + (t + (z + ((b - 0.5) * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+198) || !(x <= 6.6e+184))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.3e+198) || ~((x <= 6.6e+184)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = a + (t + (z + ((b - 0.5) * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+198], N[Not[LessEqual[x, 6.6e+184]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e198 or 6.5999999999999996e184 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in x around inf 80.0%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   if -2.3000000000000001e198 < x < 6.5999999999999996e184

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.7%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 65.8%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 65.8%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 65.8%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+198} \lor \neg \left(x \leq 6.6 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + b \cdot \frac{\log c}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.1e+99)
   (+ (* y i) (* z (+ 1.0 (* b (/ (log c) z)))))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.1e+99) {
		tmp = (y * i) + (z * (1.0 + (b * (log(c) / z))));
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.1d+99)) then
        tmp = (y * i) + (z * (1.0d0 + (b * (log(c) / z))))
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.1e+99) {
		tmp = (y * i) + (z * (1.0 + (b * (Math.log(c) / z))));
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.1e+99:
		tmp = (y * i) + (z * (1.0 + (b * (math.log(c) / z))))
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.1e+99)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(b * Float64(log(c) / z)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.1e+99)
		tmp = (y * i) + (z * (1.0 + (b * (log(c) / z))));
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.1e+99], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(b * N[(N[Log[c], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000001e99

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 85.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. +-commutative 85.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{z} + \frac{t}{z}\right)}\right)\right) + y \cdot i \]

      2. sub-neg 85.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      3. metadata-eval 85.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      4. associate-/l* 85.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\color{blue}{\log c \cdot \frac{b + -0.5}{z}} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

   6. Simplified 85.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\log c \cdot \frac{b + -0.5}{z} + \frac{t}{z}\right)\right)\right)} + y \cdot i \]

   7. Taylor expanded in b around inf 67.2%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{b \cdot \log c}{z}}\right) + y \cdot i \]
   8. Step-by-step derivation

      1. associate-/l* 67.2%

         \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]

   9. Simplified 67.2%

      \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]

   if -3.1000000000000001e99 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 75.3%

      \[\leadsto \left(\left(\color{blue}{t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + b \cdot \frac{\log c}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-93}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4e-17)
   (+ (* y i) (* z (+ 1.0 (/ a z))))
   (if (<= z -2e-93) (+ (* y i) (* b (log c))) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4e-17) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2e-93) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-4d-17)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else if (z <= (-2d-93)) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4e-17) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2e-93) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4e-17:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	elif z <= -2e-93:
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4e-17)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	elseif (z <= -2e-93)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4e-17)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	elseif (z <= -2e-93)
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4e-17], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-93], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000029e-17

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.3%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 83.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. +-commutative 83.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{z} + \frac{t}{z}\right)}\right)\right) + y \cdot i \]

      2. sub-neg 83.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      3. metadata-eval 83.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      4. associate-/l* 83.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\color{blue}{\log c \cdot \frac{b + -0.5}{z}} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

   6. Simplified 83.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\log c \cdot \frac{b + -0.5}{z} + \frac{t}{z}\right)\right)\right)} + y \cdot i \]

   7. Taylor expanded in a around inf 60.4%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -4.00000000000000029e-17 < z < -1.9999999999999998e-93

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in b around inf 52.0%

      \[\leadsto \color{blue}{b \cdot \log c} + y \cdot i \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto \color{blue}{\log c \cdot b} + y \cdot i \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{\log c \cdot b} + y \cdot i \]

   if -1.9999999999999998e-93 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.5%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-93}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.45e-16)
   (+ (* y i) (* z (+ 1.0 (/ a z))))
   (if (<= z -2.3e-61) (+ (* x (log y)) (* y i)) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.45e-16) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.3e-61) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.45d-16)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else if (z <= (-2.3d-61)) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.45e-16) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.3e-61) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.45e-16:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	elif z <= -2.3e-61:
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.45e-16)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	elseif (z <= -2.3e-61)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.45e-16)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	elseif (z <= -2.3e-61)
		tmp = (x * log(y)) + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.45e-16], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-61], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e-16

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 84.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{z} + \frac{t}{z}\right)}\right)\right) + y \cdot i \]

      2. sub-neg 84.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      3. metadata-eval 84.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      4. associate-/l* 84.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\color{blue}{\log c \cdot \frac{b + -0.5}{z}} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

   6. Simplified 84.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\log c \cdot \frac{b + -0.5}{z} + \frac{t}{z}\right)\right)\right)} + y \cdot i \]

   7. Taylor expanded in a around inf 62.0%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -1.4499999999999999e-16 < z < -2.29999999999999992e-61

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in x around inf 42.6%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   if -2.29999999999999992e-61 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.5%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 21.3% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.5 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+164}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.5e-110)
   z
   (if (<= a 2.6e+18)
     (* y i)
     (if (<= a 6.4e+164) z (if (<= a 6.8e+187) (* y i) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.5e-110) {
		tmp = z;
	} else if (a <= 2.6e+18) {
		tmp = y * i;
	} else if (a <= 6.4e+164) {
		tmp = z;
	} else if (a <= 6.8e+187) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.5d-110) then
        tmp = z
    else if (a <= 2.6d+18) then
        tmp = y * i
    else if (a <= 6.4d+164) then
        tmp = z
    else if (a <= 6.8d+187) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.5e-110) {
		tmp = z;
	} else if (a <= 2.6e+18) {
		tmp = y * i;
	} else if (a <= 6.4e+164) {
		tmp = z;
	} else if (a <= 6.8e+187) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.5e-110:
		tmp = z
	elif a <= 2.6e+18:
		tmp = y * i
	elif a <= 6.4e+164:
		tmp = z
	elif a <= 6.8e+187:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.5e-110)
		tmp = z;
	elseif (a <= 2.6e+18)
		tmp = Float64(y * i);
	elseif (a <= 6.4e+164)
		tmp = z;
	elseif (a <= 6.8e+187)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.5e-110)
		tmp = z;
	elseif (a <= 2.6e+18)
		tmp = y * i;
	elseif (a <= 6.4e+164)
		tmp = z;
	elseif (a <= 6.8e+187)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.5e-110], z, If[LessEqual[a, 2.6e+18], N[(y * i), $MachinePrecision], If[LessEqual[a, 6.4e+164], z, If[LessEqual[a, 6.8e+187], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.49999999999999993e-110 or 2.6e18 < a < 6.3999999999999996e164

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.4%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 58.2%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 58.2%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 58.2%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 58.3%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in z around inf 20.6%

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

   if 1.49999999999999993e-110 < a < 2.6e18 or 6.3999999999999996e164 < a < 6.7999999999999999e187

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.3%

      \[\leadsto \color{blue}{a} + y \cdot i \]

   4. Taylor expanded in a around 0 40.5%

      \[\leadsto \color{blue}{i \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto \color{blue}{y \cdot i} \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{y \cdot i} \]

   if 6.7999999999999999e187 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.8%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 44.7%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 44.7%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 44.7%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 44.7%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 52.4%

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

Alternative 12: 44.1% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.6e-41) (+ (* y i) (* z (+ 1.0 (/ a z)))) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.6e-41) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.6d-41)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.6e-41) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.6e-41:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.6e-41)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.6e-41)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.6e-41], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999999e-41

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 83.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. +-commutative 83.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{z} + \frac{t}{z}\right)}\right)\right) + y \cdot i \]

      2. sub-neg 83.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      3. metadata-eval 83.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

      4. associate-/l* 83.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\color{blue}{\log c \cdot \frac{b + -0.5}{z}} + \frac{t}{z}\right)\right)\right) + y \cdot i \]

   6. Simplified 83.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\log c \cdot \frac{b + -0.5}{z} + \frac{t}{z}\right)\right)\right)} + y \cdot i \]

   7. Taylor expanded in a around inf 58.2%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -2.5999999999999999e-41 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+164}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 6.2e+164) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.2e+164) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 6.2d+164) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.2e+164) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 6.2e+164:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 6.2e+164)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 6.2e+164)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 6.2e+164], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.2000000000000003e164

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 86.8%

      \[\leadsto \left(\left(\color{blue}{\left(z + x \cdot \log y\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 37.7%

      \[\leadsto \color{blue}{z} + y \cdot i \]

   if 6.2000000000000003e164 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 67.9%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 40.3% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+216}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.1e+216) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.1e+216) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.1d+216)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.1e+216) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.1e+216:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.1e+216)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.1e+216)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.1e+216], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000001e216

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.4%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 37.9%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 37.9%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 37.9%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 37.9%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 37.9%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in z around inf 71.2%

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

   if -2.10000000000000001e216 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 20.4% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.35 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.35e+165) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.35e+165) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.35d+165) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.35e+165) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.35e+165:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.35e+165)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.35e+165)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.35e+165], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 2.35000000000000008e165

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 58.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 58.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 58.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 58.4%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in z around inf 20.9%

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

   if 2.35000000000000008e165 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.3%

      \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in y around inf 51.4%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 51.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

      2. metadata-eval 51.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

      3. associate-/l* 51.4%

         \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

   6. Simplified 51.4%

      \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 48.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 16.0% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in x around 0 84.1%

   \[\leadsto \left(\left(\color{blue}{\left(t + z\right)} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

4. Taylor expanded in y around inf 57.3%

   \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b - 0.5\right)}{y}\right)\right)\right)\right)} \]
5. Step-by-step derivation

   1. sub-neg 57.3%

      \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{y}\right)\right)\right)\right) \]

   2. metadata-eval 57.3%

      \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{y}\right)\right)\right)\right) \]

   3. associate-/l* 57.3%

      \[\leadsto y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \color{blue}{\log c \cdot \frac{b + -0.5}{y}}\right)\right)\right)\right) \]

6. Simplified 57.3%

   \[\leadsto \color{blue}{y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \left(\frac{z}{y} + \log c \cdot \frac{b + -0.5}{y}\right)\right)\right)\right)} \]

7. Taylor expanded in a around inf 18.2%

   \[\leadsto \color{blue}{a} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024106 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))