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

Percentage Accurate: 99.8% → 99.8%

Time: 19.0s

Alternatives: 17

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

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

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]

Derivation

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. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y + \frac{\left(z + t\right) + \left(\log c \cdot b + a\right)}{x}\right) + y \cdot i\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{+14}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+ (* x (+ (log y) (/ (+ (+ z t) (+ (* (log c) b) a)) x))) (* y i))))
   (if (<= x -20000.0)
     t_1
     (if (<= x 1e+14)
       (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * (log(y) + (((z + t) + ((log(c) * b) + a)) / x))) + (y * i);
	double tmp;
	if (x <= -20000.0) {
		tmp = t_1;
	} else if (x <= 1e+14) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	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 = (x * (log(y) + (((z + t) + ((log(c) * b) + a)) / x))) + (y * i)
    if (x <= (-20000.0d0)) then
        tmp = t_1
    else if (x <= 1d+14) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    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 c, double i) {
	double t_1 = (x * (Math.log(y) + (((z + t) + ((Math.log(c) * b) + a)) / x))) + (y * i);
	double tmp;
	if (x <= -20000.0) {
		tmp = t_1;
	} else if (x <= 1e+14) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * (math.log(y) + (((z + t) + ((math.log(c) * b) + a)) / x))) + (y * i)
	tmp = 0
	if x <= -20000.0:
		tmp = t_1
	elif x <= 1e+14:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * Float64(log(y) + Float64(Float64(Float64(z + t) + Float64(Float64(log(c) * b) + a)) / x))) + Float64(y * i))
	tmp = 0.0
	if (x <= -20000.0)
		tmp = t_1;
	elseif (x <= 1e+14)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * (log(y) + (((z + t) + ((log(c) * b) + a)) / x))) + (y * i);
	tmp = 0.0;
	if (x <= -20000.0)
		tmp = t_1;
	elseif (x <= 1e+14)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(N[(z + t), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -20000.0], t$95$1, If[LessEqual[x, 1e+14], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2e4 or 1e14 < 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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around -inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -2e4 < x < 1e14

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(\left(\log c \cdot \left(-0.5 + b\right) + \left(t + z\right)\right) + x \cdot \log y\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+104}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ (+ (* (log c) (+ -0.5 b)) (+ t z)) (* x (log y))))))
   (if (<= x -1.5e+127)
     t_1
     (if (<= x 4.2e+104)
       (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (((log(c) * (-0.5 + b)) + (t + z)) + (x * log(y)));
	double tmp;
	if (x <= -1.5e+127) {
		tmp = t_1;
	} else if (x <= 4.2e+104) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	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 = a + (((log(c) * ((-0.5d0) + b)) + (t + z)) + (x * log(y)))
    if (x <= (-1.5d+127)) then
        tmp = t_1
    else if (x <= 4.2d+104) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    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 c, double i) {
	double t_1 = a + (((Math.log(c) * (-0.5 + b)) + (t + z)) + (x * Math.log(y)));
	double tmp;
	if (x <= -1.5e+127) {
		tmp = t_1;
	} else if (x <= 4.2e+104) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (((math.log(c) * (-0.5 + b)) + (t + z)) + (x * math.log(y)))
	tmp = 0
	if x <= -1.5e+127:
		tmp = t_1
	elif x <= 4.2e+104:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(Float64(Float64(log(c) * Float64(-0.5 + b)) + Float64(t + z)) + Float64(x * log(y))))
	tmp = 0.0
	if (x <= -1.5e+127)
		tmp = t_1;
	elseif (x <= 4.2e+104)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (((log(c) * (-0.5 + b)) + (t + z)) + (x * log(y)));
	tmp = 0.0;
	if (x <= -1.5e+127)
		tmp = t_1;
	elseif (x <= 4.2e+104)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(N[(N[(N[Log[c], $MachinePrecision] * N[(-0.5 + b), $MachinePrecision]), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+127], t$95$1, If[LessEqual[x, 4.2e+104], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5000000000000001e127 or 4.1999999999999997e104 < 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 y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.5000000000000001e127 < x < 4.1999999999999997e104

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 4: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot \log y + a\right) + \log c \cdot b\right) + y \cdot i\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+71}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (+ (* x (log y)) a) (* (log c) b)) (* y i))))
   (if (<= x -5.2e+88)
     t_1
     (if (<= x 8.2e+71)
       (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((x * log(y)) + a) + (log(c) * b)) + (y * i);
	double tmp;
	if (x <= -5.2e+88) {
		tmp = t_1;
	} else if (x <= 8.2e+71) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	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 = (((x * log(y)) + a) + (log(c) * b)) + (y * i)
    if (x <= (-5.2d+88)) then
        tmp = t_1
    else if (x <= 8.2d+71) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    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 c, double i) {
	double t_1 = (((x * Math.log(y)) + a) + (Math.log(c) * b)) + (y * i);
	double tmp;
	if (x <= -5.2e+88) {
		tmp = t_1;
	} else if (x <= 8.2e+71) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((x * math.log(y)) + a) + (math.log(c) * b)) + (y * i)
	tmp = 0
	if x <= -5.2e+88:
		tmp = t_1
	elif x <= 8.2e+71:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(x * log(y)) + a) + Float64(log(c) * b)) + Float64(y * i))
	tmp = 0.0
	if (x <= -5.2e+88)
		tmp = t_1;
	elseif (x <= 8.2e+71)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((x * log(y)) + a) + (log(c) * b)) + (y * i);
	tmp = 0.0;
	if (x <= -5.2e+88)
		tmp = t_1;
	elseif (x <= 8.2e+71)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+88], t$95$1, If[LessEqual[x, 8.2e+71], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000001e88 or 8.2000000000000004e71 < 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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -5.2000000000000001e88 < x < 8.2000000000000004e71

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 5: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(\log y + \left(\frac{z}{x} + \frac{y \cdot i}{x}\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+176}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log c \cdot b\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6.2e+151)
   (* x (+ (log y) (+ (/ z x) (/ (* y i) x))))
   (if (<= x 2.7e+176)
     (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
     (+ (+ (* x (log y)) (* (log c) b)) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6.2e+151) {
		tmp = x * (log(y) + ((z / x) + ((y * i) / x)));
	} else if (x <= 2.7e+176) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = ((x * log(y)) + (log(c) * b)) + (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 (x <= (-6.2d+151)) then
        tmp = x * (log(y) + ((z / x) + ((y * i) / x)))
    else if (x <= 2.7d+176) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    else
        tmp = ((x * log(y)) + (log(c) * b)) + (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 (x <= -6.2e+151) {
		tmp = x * (Math.log(y) + ((z / x) + ((y * i) / x)));
	} else if (x <= 2.7e+176) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = ((x * Math.log(y)) + (Math.log(c) * b)) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -6.2e+151:
		tmp = x * (math.log(y) + ((z / x) + ((y * i) / x)))
	elif x <= 2.7e+176:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = ((x * math.log(y)) + (math.log(c) * b)) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6.2e+151)
		tmp = Float64(x * Float64(log(y) + Float64(Float64(z / x) + Float64(Float64(y * i) / x))));
	elseif (x <= 2.7e+176)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = Float64(Float64(Float64(x * log(y)) + Float64(log(c) * b)) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -6.2e+151)
		tmp = x * (log(y) + ((z / x) + ((y * i) / x)));
	elseif (x <= 2.7e+176)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = ((x * log(y)) + (log(c) * b)) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6.2e+151], N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z / x), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+176], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2000000000000004e151

   1. Initial program 99.5%

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

   3. Taylor expanded in z around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -6.2000000000000004e151 < x < 2.6999999999999998e176

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.6999999999999998e176 < 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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 6: 53.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ t_2 := z + \left(\log c \cdot \left(b + -0.5\right) + a\right)\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(1 + \log y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+74}:\\ \;\;\;\;a + y \cdot i\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i)))
        (t_2 (+ z (+ (* (log c) (+ b -0.5)) a))))
   (if (<= x -5.7e+141)
     (* z (+ 1.0 (* (log y) (/ x z))))
     (if (<= x -4e+74)
       (+ a (* y i))
       (if (<= x 1.9e+72)
         t_2
         (if (<= x 9.8e+104) t_1 (if (<= x 1.55e+186) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (y * i);
	double t_2 = z + ((log(c) * (b + -0.5)) + a);
	double tmp;
	if (x <= -5.7e+141) {
		tmp = z * (1.0 + (log(y) * (x / z)));
	} else if (x <= -4e+74) {
		tmp = a + (y * i);
	} else if (x <= 1.9e+72) {
		tmp = t_2;
	} else if (x <= 9.8e+104) {
		tmp = t_1;
	} else if (x <= 1.55e+186) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    t_2 = z + ((log(c) * (b + (-0.5d0))) + a)
    if (x <= (-5.7d+141)) then
        tmp = z * (1.0d0 + (log(y) * (x / z)))
    else if (x <= (-4d+74)) then
        tmp = a + (y * i)
    else if (x <= 1.9d+72) then
        tmp = t_2
    else if (x <= 9.8d+104) then
        tmp = t_1
    else if (x <= 1.55d+186) 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 c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double t_2 = z + ((Math.log(c) * (b + -0.5)) + a);
	double tmp;
	if (x <= -5.7e+141) {
		tmp = z * (1.0 + (Math.log(y) * (x / z)));
	} else if (x <= -4e+74) {
		tmp = a + (y * i);
	} else if (x <= 1.9e+72) {
		tmp = t_2;
	} else if (x <= 9.8e+104) {
		tmp = t_1;
	} else if (x <= 1.55e+186) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	t_2 = z + ((math.log(c) * (b + -0.5)) + a)
	tmp = 0
	if x <= -5.7e+141:
		tmp = z * (1.0 + (math.log(y) * (x / z)))
	elif x <= -4e+74:
		tmp = a + (y * i)
	elif x <= 1.9e+72:
		tmp = t_2
	elif x <= 9.8e+104:
		tmp = t_1
	elif x <= 1.55e+186:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	t_2 = Float64(z + Float64(Float64(log(c) * Float64(b + -0.5)) + a))
	tmp = 0.0
	if (x <= -5.7e+141)
		tmp = Float64(z * Float64(1.0 + Float64(log(y) * Float64(x / z))));
	elseif (x <= -4e+74)
		tmp = Float64(a + Float64(y * i));
	elseif (x <= 1.9e+72)
		tmp = t_2;
	elseif (x <= 9.8e+104)
		tmp = t_1;
	elseif (x <= 1.55e+186)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	t_2 = z + ((log(c) * (b + -0.5)) + a);
	tmp = 0.0;
	if (x <= -5.7e+141)
		tmp = z * (1.0 + (log(y) * (x / z)));
	elseif (x <= -4e+74)
		tmp = a + (y * i);
	elseif (x <= 1.9e+72)
		tmp = t_2;
	elseif (x <= 9.8e+104)
		tmp = t_1;
	elseif (x <= 1.55e+186)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.7e+141], N[(z * N[(1.0 + N[(N[Log[y], $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e+74], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+72], t$95$2, If[LessEqual[x, 9.8e+104], t$95$1, If[LessEqual[x, 1.55e+186], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.69999999999999998e141

   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 z around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -5.69999999999999998e141 < x < -3.99999999999999981e74

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.99999999999999981e74 < x < 1.90000000000000003e72 or 9.7999999999999997e104 < x < 1.5500000000000001e186

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.90000000000000003e72 < x < 9.7999999999999997e104 or 1.5500000000000001e186 < 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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 7: 90.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y + \left(\frac{z}{x} + \frac{y \cdot i}{x}\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (+ (log y) (+ (/ z x) (/ (* y i) x))))))
   (if (<= x -2.7e+153)
     t_1
     (if (<= x 1.65e+161)
       (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (log(y) + ((z / x) + ((y * i) / x)));
	double tmp;
	if (x <= -2.7e+153) {
		tmp = t_1;
	} else if (x <= 1.65e+161) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	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 = x * (log(y) + ((z / x) + ((y * i) / x)))
    if (x <= (-2.7d+153)) then
        tmp = t_1
    else if (x <= 1.65d+161) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    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 c, double i) {
	double t_1 = x * (Math.log(y) + ((z / x) + ((y * i) / x)));
	double tmp;
	if (x <= -2.7e+153) {
		tmp = t_1;
	} else if (x <= 1.65e+161) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (math.log(y) + ((z / x) + ((y * i) / x)))
	tmp = 0
	if x <= -2.7e+153:
		tmp = t_1
	elif x <= 1.65e+161:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(log(y) + Float64(Float64(z / x) + Float64(Float64(y * i) / x))))
	tmp = 0.0
	if (x <= -2.7e+153)
		tmp = t_1;
	elseif (x <= 1.65e+161)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (log(y) + ((z / x) + ((y * i) / x)));
	tmp = 0.0;
	if (x <= -2.7e+153)
		tmp = t_1;
	elseif (x <= 1.65e+161)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z / x), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+153], t$95$1, If[LessEqual[x, 1.65e+161], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e153 or 1.64999999999999999e161 < 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 z around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -2.7000000000000001e153 < x < 1.64999999999999999e161

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 8: 77.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\log y + \left(\frac{z}{x} + \frac{y \cdot i}{x}\right)\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+162}:\\ \;\;\;\;\left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (+ (log y) (+ (/ z x) (/ (* y i) x))))))
   (if (<= x -1.45e+146)
     t_1
     (if (<= x 2.4e+162) (+ (+ (+ z a) (* (- b 0.5) (log c))) (* y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (log(y) + ((z / x) + ((y * i) / x)));
	double tmp;
	if (x <= -1.45e+146) {
		tmp = t_1;
	} else if (x <= 2.4e+162) {
		tmp = ((z + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	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 = x * (log(y) + ((z / x) + ((y * i) / x)))
    if (x <= (-1.45d+146)) then
        tmp = t_1
    else if (x <= 2.4d+162) then
        tmp = ((z + a) + ((b - 0.5d0) * log(c))) + (y * i)
    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 c, double i) {
	double t_1 = x * (Math.log(y) + ((z / x) + ((y * i) / x)));
	double tmp;
	if (x <= -1.45e+146) {
		tmp = t_1;
	} else if (x <= 2.4e+162) {
		tmp = ((z + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (math.log(y) + ((z / x) + ((y * i) / x)))
	tmp = 0
	if x <= -1.45e+146:
		tmp = t_1
	elif x <= 2.4e+162:
		tmp = ((z + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(log(y) + Float64(Float64(z / x) + Float64(Float64(y * i) / x))))
	tmp = 0.0
	if (x <= -1.45e+146)
		tmp = t_1;
	elseif (x <= 2.4e+162)
		tmp = Float64(Float64(Float64(z + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (log(y) + ((z / x) + ((y * i) / x)));
	tmp = 0.0;
	if (x <= -1.45e+146)
		tmp = t_1;
	elseif (x <= 2.4e+162)
		tmp = ((z + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(z / x), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+146], t$95$1, If[LessEqual[x, 2.4e+162], N[(N[(N[(z + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e146 or 2.40000000000000009e162 < 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 z around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.4499999999999999e146 < x < 2.40000000000000009e162

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 9: 60.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;\left(z + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+207}:\\ \;\;\;\;z + \left(\log c \cdot \left(b + -0.5\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + a\right) + \log c \cdot b\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.12e+108)
   (+ (+ z (* (- b 0.5) (log c))) (* y i))
   (if (<= a 1.5e+207)
     (+ z (+ (* (log c) (+ b -0.5)) a))
     (+ (+ (+ t a) (* (log c) b)) (* 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 <= 1.12e+108) {
		tmp = (z + ((b - 0.5) * log(c))) + (y * i);
	} else if (a <= 1.5e+207) {
		tmp = z + ((log(c) * (b + -0.5)) + a);
	} else {
		tmp = ((t + a) + (log(c) * b)) + (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 <= 1.12d+108) then
        tmp = (z + ((b - 0.5d0) * log(c))) + (y * i)
    else if (a <= 1.5d+207) then
        tmp = z + ((log(c) * (b + (-0.5d0))) + a)
    else
        tmp = ((t + a) + (log(c) * b)) + (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 <= 1.12e+108) {
		tmp = (z + ((b - 0.5) * Math.log(c))) + (y * i);
	} else if (a <= 1.5e+207) {
		tmp = z + ((Math.log(c) * (b + -0.5)) + a);
	} else {
		tmp = ((t + a) + (Math.log(c) * b)) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.12e+108:
		tmp = (z + ((b - 0.5) * math.log(c))) + (y * i)
	elif a <= 1.5e+207:
		tmp = z + ((math.log(c) * (b + -0.5)) + a)
	else:
		tmp = ((t + a) + (math.log(c) * b)) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.12e+108)
		tmp = Float64(Float64(z + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	elseif (a <= 1.5e+207)
		tmp = Float64(z + Float64(Float64(log(c) * Float64(b + -0.5)) + a));
	else
		tmp = Float64(Float64(Float64(t + a) + Float64(log(c) * b)) + 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 <= 1.12e+108)
		tmp = (z + ((b - 0.5) * log(c))) + (y * i);
	elseif (a <= 1.5e+207)
		tmp = z + ((log(c) * (b + -0.5)) + a);
	else
		tmp = ((t + a) + (log(c) * b)) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.12e+108], N[(N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+207], N[(z + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.11999999999999994e108

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.11999999999999994e108 < a < 1.49999999999999992e207

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 1.49999999999999992e207 < a

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 10: 60.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;a \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;\left(z + t\_1\right) + y \cdot i\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+207}:\\ \;\;\;\;z + \left(\log c \cdot \left(b + -0.5\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\_1\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= a 1.12e+108)
     (+ (+ z t_1) (* y i))
     (if (<= a 2.8e+207)
       (+ z (+ (* (log c) (+ b -0.5)) a))
       (+ (+ a t_1) (* y i))))))

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 (a <= 1.12e+108) {
		tmp = (z + t_1) + (y * i);
	} else if (a <= 2.8e+207) {
		tmp = z + ((log(c) * (b + -0.5)) + a);
	} else {
		tmp = (a + t_1) + (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) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if (a <= 1.12d+108) then
        tmp = (z + t_1) + (y * i)
    else if (a <= 2.8d+207) then
        tmp = z + ((log(c) * (b + (-0.5d0))) + a)
    else
        tmp = (a + t_1) + (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 t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if (a <= 1.12e+108) {
		tmp = (z + t_1) + (y * i);
	} else if (a <= 2.8e+207) {
		tmp = z + ((Math.log(c) * (b + -0.5)) + a);
	} else {
		tmp = (a + t_1) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if a <= 1.12e+108:
		tmp = (z + t_1) + (y * i)
	elif a <= 2.8e+207:
		tmp = z + ((math.log(c) * (b + -0.5)) + a)
	else:
		tmp = (a + t_1) + (y * i)
	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 (a <= 1.12e+108)
		tmp = Float64(Float64(z + t_1) + Float64(y * i));
	elseif (a <= 2.8e+207)
		tmp = Float64(z + Float64(Float64(log(c) * Float64(b + -0.5)) + a));
	else
		tmp = Float64(Float64(a + t_1) + Float64(y * i));
	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 (a <= 1.12e+108)
		tmp = (z + t_1) + (y * i);
	elseif (a <= 2.8e+207)
		tmp = z + ((log(c) * (b + -0.5)) + a);
	else
		tmp = (a + t_1) + (y * i);
	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[a, 1.12e+108], N[(N[(z + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+207], N[(z + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(a + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.11999999999999994e108

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.11999999999999994e108 < a < 2.80000000000000011e207

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 2.80000000000000011e207 < a

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 11: 59.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+60}:\\ \;\;\;\;\left(\frac{a}{z} + 1\right) \cdot z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1e+60)
   (+ (* (+ (/ a z) 1.0) z) (* y i))
   (+ (+ 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) {
	double tmp;
	if (z <= -1e+60) {
		tmp = (((a / z) + 1.0) * z) + (y * i);
	} else {
		tmp = (a + ((b - 0.5) * log(c))) + (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 <= (-1d+60)) then
        tmp = (((a / z) + 1.0d0) * z) + (y * i)
    else
        tmp = (a + ((b - 0.5d0) * log(c))) + (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 <= -1e+60) {
		tmp = (((a / z) + 1.0) * z) + (y * i);
	} else {
		tmp = (a + ((b - 0.5) * Math.log(c))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1e+60:
		tmp = (((a / z) + 1.0) * z) + (y * i)
	else:
		tmp = (a + ((b - 0.5) * math.log(c))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1e+60)
		tmp = Float64(Float64(Float64(Float64(a / z) + 1.0) * z) + Float64(y * i));
	else
		tmp = Float64(Float64(a + Float64(Float64(b - 0.5) * log(c))) + 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 <= -1e+60)
		tmp = (((a / z) + 1.0) * z) + (y * i);
	else
		tmp = (a + ((b - 0.5) * log(c))) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1e+60], N[(N[(N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e59

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -9.9999999999999995e59 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 12: 22.5% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-280}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-124}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+46}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.5e-280)
   z
   (if (<= a 1.56e-124)
     (* y i)
     (if (<= a 1.7e+46) z (if (<= a 2.1e+113) (* 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 <= 4.5e-280) {
		tmp = z;
	} else if (a <= 1.56e-124) {
		tmp = y * i;
	} else if (a <= 1.7e+46) {
		tmp = z;
	} else if (a <= 2.1e+113) {
		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 <= 4.5d-280) then
        tmp = z
    else if (a <= 1.56d-124) then
        tmp = y * i
    else if (a <= 1.7d+46) then
        tmp = z
    else if (a <= 2.1d+113) 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 <= 4.5e-280) {
		tmp = z;
	} else if (a <= 1.56e-124) {
		tmp = y * i;
	} else if (a <= 1.7e+46) {
		tmp = z;
	} else if (a <= 2.1e+113) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.5e-280:
		tmp = z
	elif a <= 1.56e-124:
		tmp = y * i
	elif a <= 1.7e+46:
		tmp = z
	elif a <= 2.1e+113:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.5e-280)
		tmp = z;
	elseif (a <= 1.56e-124)
		tmp = Float64(y * i);
	elseif (a <= 1.7e+46)
		tmp = z;
	elseif (a <= 2.1e+113)
		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 <= 4.5e-280)
		tmp = z;
	elseif (a <= 1.56e-124)
		tmp = y * i;
	elseif (a <= 1.7e+46)
		tmp = z;
	elseif (a <= 2.1e+113)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.5e-280], z, If[LessEqual[a, 1.56e-124], N[(y * i), $MachinePrecision], If[LessEqual[a, 1.7e+46], z, If[LessEqual[a, 2.1e+113], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < 4.4999999999999996e-280 or 1.55999999999999993e-124 < a < 1.6999999999999999e46

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4.4999999999999996e-280 < a < 1.55999999999999993e-124 or 1.6999999999999999e46 < a < 2.0999999999999999e113

   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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.0999999999999999e113 < a

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 13: 44.8% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-27}:\\ \;\;\;\;\left(\frac{a}{z} + 1\right) \cdot z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.6e-27) (+ (* (+ (/ a z) 1.0) 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 (z <= -1.6e-27) {
		tmp = (((a / z) + 1.0) * 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 (z <= (-1.6d-27)) then
        tmp = (((a / z) + 1.0d0) * 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 (z <= -1.6e-27) {
		tmp = (((a / z) + 1.0) * z) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.6e-27:
		tmp = (((a / z) + 1.0) * 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 (z <= -1.6e-27)
		tmp = Float64(Float64(Float64(Float64(a / z) + 1.0) * 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 (z <= -1.6e-27)
		tmp = (((a / z) + 1.0) * 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[z, -1.6e-27], N[(N[(N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999995e-27

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.59999999999999995e-27 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 14: 43.3% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.75 \cdot 10^{+115}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.75e+115) (+ 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 <= 1.75e+115) {
		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 <= 1.75d+115) 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 <= 1.75e+115) {
		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 <= 1.75e+115:
		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 <= 1.75e+115)
		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 <= 1.75e+115)
		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, 1.75e+115], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.75000000000000003e115

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.75000000000000003e115 < a

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 15: 40.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+189}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.2e+189) 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 <= -6.2e+189) {
		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 <= (-6.2d+189)) 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 <= -6.2e+189) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+189:
		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 <= -6.2e+189)
		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 <= -6.2e+189)
		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, -6.2e+189], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999999e189

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.1999999999999999e189 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 16: 21.3% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.05 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.05e+111) 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 <= 1.05e+111) {
		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 <= 1.05d+111) 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 <= 1.05e+111) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.05e+111:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.05e+111)
		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 <= 1.05e+111)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.05e+111], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.04999999999999997e111

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.04999999999999997e111 < a

   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 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 17: 15.6% 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 99.8%

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

3. Taylor expanded in a around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))