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

Percentage Accurate: 99.8% → 99.8%

Time: 24.9s

Alternatives: 19

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 99.5%

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

3. Final simplification 99.5%

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

Alternative 2: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+76} \lor \neg \left(x \leq 2.5 \cdot 10^{+94}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (or (<= x -6.5e+76) (not (<= x 2.5e+94)))
     (+ a (+ t (+ z (+ (* x (log y)) t_1))))
     (+ (* y i) (+ a (+ t (+ z t_1)))))))

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 <= -6.5e+76) || !(x <= 2.5e+94)) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + 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 = (b - 0.5d0) * log(c)
    if ((x <= (-6.5d+76)) .or. (.not. (x <= 2.5d+94))) then
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    else
        tmp = (y * i) + (a + (t + (z + 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 = (b - 0.5) * Math.log(c);
	double tmp;
	if ((x <= -6.5e+76) || !(x <= 2.5e+94)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	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 <= -6.5e+76) or not (x <= 2.5e+94):
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	else:
		tmp = (y * i) + (a + (t + (z + t_1)))
	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 <= -6.5e+76) || !(x <= 2.5e+94))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	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 <= -6.5e+76) || ~((x <= 2.5e+94)))
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	else
		tmp = (y * i) + (a + (t + (z + t_1)));
	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, -6.5e+76], N[Not[LessEqual[x, 2.5e+94]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000005e76 or 2.50000000000000005e94 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 88.2%

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

   if -6.5000000000000005e76 < x < 2.50000000000000005e94

   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 97.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+76} \lor \neg \left(x \leq 2.5 \cdot 10^{+94}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+133}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_1 + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(\left(\left(t\_1 + z\right) + t\right) + a\right) + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= (- b 0.5) -2e+133)
     (+ a (+ t (+ z (+ t_1 (* (- b 0.5) (log c))))))
     (+ (* y i) (+ (+ (+ (+ t_1 z) t) a) (* (log c) -0.5))))))

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);
	double tmp;
	if ((b - 0.5) <= -2e+133) {
		tmp = a + (t + (z + (t_1 + ((b - 0.5) * log(c)))));
	} else {
		tmp = (y * i) + ((((t_1 + z) + t) + a) + (log(c) * -0.5));
	}
	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)
    if ((b - 0.5d0) <= (-2d+133)) then
        tmp = a + (t + (z + (t_1 + ((b - 0.5d0) * log(c)))))
    else
        tmp = (y * i) + ((((t_1 + z) + t) + a) + (log(c) * (-0.5d0)))
    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);
	double tmp;
	if ((b - 0.5) <= -2e+133) {
		tmp = a + (t + (z + (t_1 + ((b - 0.5) * Math.log(c)))));
	} else {
		tmp = (y * i) + ((((t_1 + z) + t) + a) + (Math.log(c) * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if (b - 0.5) <= -2e+133:
		tmp = a + (t + (z + (t_1 + ((b - 0.5) * math.log(c)))))
	else:
		tmp = (y * i) + ((((t_1 + z) + t) + a) + (math.log(c) * -0.5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (Float64(b - 0.5) <= -2e+133)
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + Float64(Float64(b - 0.5) * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(Float64(t_1 + z) + t) + a) + Float64(log(c) * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if ((b - 0.5) <= -2e+133)
		tmp = a + (t + (z + (t_1 + ((b - 0.5) * log(c)))));
	else
		tmp = (y * i) + ((((t_1 + z) + t) + a) + (log(c) * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+133], N[(a + N[(t + N[(z + N[(t$95$1 + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(N[(t$95$1 + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -2e133

   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 84.7%

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

   if -2e133 < (-.f64 b 1/2)

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+133}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* x (+ (log y) (/ a x))))))
   (if (<= z -2.2e+117)
     (+ (* y i) (* z (+ 1.0 (/ a z))))
     (if (<= z -2.2e+17)
       t_1
       (if (<= z -5.4e-8)
         (+ a (+ z (* (- b 0.5) (log c))))
         (if (<= z -9e-300)
           t_1
           (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (log(y) + (a / x)));
	double tmp;
	if (z <= -2.2e+117) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.2e+17) {
		tmp = t_1;
	} else if (z <= -5.4e-8) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else if (z <= -9e-300) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (x * (log(y) + (a / x)))
    if (z <= (-2.2d+117)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else if (z <= (-2.2d+17)) then
        tmp = t_1
    else if (z <= (-5.4d-8)) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else if (z <= (-9d-300)) then
        tmp = t_1
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 t_1 = (y * i) + (x * (Math.log(y) + (a / x)));
	double tmp;
	if (z <= -2.2e+117) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.2e+17) {
		tmp = t_1;
	} else if (z <= -5.4e-8) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else if (z <= -9e-300) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (x * (math.log(y) + (a / x)))
	tmp = 0
	if z <= -2.2e+117:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	elif z <= -2.2e+17:
		tmp = t_1
	elif z <= -5.4e-8:
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	elif z <= -9e-300:
		tmp = t_1
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))))
	tmp = 0.0
	if (z <= -2.2e+117)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	elseif (z <= -2.2e+17)
		tmp = t_1;
	elseif (z <= -5.4e-8)
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (z <= -9e-300)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (x * (log(y) + (a / x)));
	tmp = 0.0;
	if (z <= -2.2e+117)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	elseif (z <= -2.2e+17)
		tmp = t_1;
	elseif (z <= -5.4e-8)
		tmp = a + (z + ((b - 0.5) * log(c)));
	elseif (z <= -9e-300)
		tmp = t_1;
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+117], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e+17], t$95$1, If[LessEqual[z, -5.4e-8], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-300], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.20000000000000014e117

   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 99.8%

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

   4. Taylor expanded in a around inf 80.2%

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

   if -2.20000000000000014e117 < z < -2.2e17 or -5.40000000000000005e-8 < z < -9.0000000000000001e-300

   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 80.8%

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

      1. associate-+r+ 80.8%

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

      2. sub-neg 80.8%

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

      3. metadata-eval 80.8%

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

      4. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in a around inf 62.3%

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

   if -2.2e17 < z < -5.40000000000000005e-8

   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 x around 0 81.0%

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

   4. Taylor expanded in y around 0 42.6%

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

   5. Taylor expanded in t around 0 40.9%

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

   if -9.0000000000000001e-300 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 75.1%

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

   4. Taylor expanded in z around inf 60.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-300}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{if}\;a \leq 3.4 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-133}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.05:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ t (+ z (* (- b 0.5) (log c)))))))
   (if (<= a 3.4e-244)
     t_1
     (if (<= a 2.4e-133)
       (+ (* y i) (* z (+ 1.0 (/ (* x (log y)) z))))
       (if (<= a 7.5e-86)
         t_1
         (if (<= a 0.05)
           (+ (* y i) (* x (+ (log y) (/ z x))))
           (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (t + (z + ((b - 0.5) * log(c))));
	double tmp;
	if (a <= 3.4e-244) {
		tmp = t_1;
	} else if (a <= 2.4e-133) {
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	} else if (a <= 7.5e-86) {
		tmp = t_1;
	} else if (a <= 0.05) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (t + (z + ((b - 0.5d0) * log(c))))
    if (a <= 3.4d-244) then
        tmp = t_1
    else if (a <= 2.4d-133) then
        tmp = (y * i) + (z * (1.0d0 + ((x * log(y)) / z)))
    else if (a <= 7.5d-86) then
        tmp = t_1
    else if (a <= 0.05d0) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 t_1 = (y * i) + (t + (z + ((b - 0.5) * Math.log(c))));
	double tmp;
	if (a <= 3.4e-244) {
		tmp = t_1;
	} else if (a <= 2.4e-133) {
		tmp = (y * i) + (z * (1.0 + ((x * Math.log(y)) / z)));
	} else if (a <= 7.5e-86) {
		tmp = t_1;
	} else if (a <= 0.05) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (t + (z + ((b - 0.5) * math.log(c))))
	tmp = 0
	if a <= 3.4e-244:
		tmp = t_1
	elif a <= 2.4e-133:
		tmp = (y * i) + (z * (1.0 + ((x * math.log(y)) / z)))
	elif a <= 7.5e-86:
		tmp = t_1
	elif a <= 0.05:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c)))))
	tmp = 0.0
	if (a <= 3.4e-244)
		tmp = t_1;
	elseif (a <= 2.4e-133)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(Float64(x * log(y)) / z))));
	elseif (a <= 7.5e-86)
		tmp = t_1;
	elseif (a <= 0.05)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (t + (z + ((b - 0.5) * log(c))));
	tmp = 0.0;
	if (a <= 3.4e-244)
		tmp = t_1;
	elseif (a <= 2.4e-133)
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	elseif (a <= 7.5e-86)
		tmp = t_1;
	elseif (a <= 0.05)
		tmp = (y * i) + (x * (log(y) + (z / x)));
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3.4e-244], t$95$1, If[LessEqual[a, 2.4e-133], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-86], t$95$1, If[LessEqual[a, 0.05], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 3.40000000000000009e-244 or 2.4e-133 < a < 7.50000000000000055e-86

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 78.2%

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

   4. Taylor expanded in a around 0 66.5%

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

   if 3.40000000000000009e-244 < a < 2.4e-133

   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 81.7%

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

   4. Taylor expanded in x around inf 58.6%

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

   if 7.50000000000000055e-86 < a < 0.050000000000000003

   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 80.2%

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

      1. associate-+r+ 80.2%

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

      2. sub-neg 80.2%

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

      3. metadata-eval 80.2%

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

      4. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in z around inf 60.1%

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

   if 0.050000000000000003 < 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 99.8%

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

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-244}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-133}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;a \leq 0.05:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + z \cdot \left(1 + x \cdot \frac{\log y}{z}\right)\\ \mathbf{if}\;a \leq 1.32 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-245}:\\ \;\;\;\;t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* z (+ 1.0 (* x (/ (log y) z)))))))
   (if (<= a 1.32e-267)
     t_1
     (if (<= a 2.7e-245)
       (+ t (+ z (* (- b 0.5) (log c))))
       (if (<= a 3.2e+39)
         t_1
         (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ z a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z * (1.0 + (x * (log(y) / z))));
	double tmp;
	if (a <= 1.32e-267) {
		tmp = t_1;
	} else if (a <= 2.7e-245) {
		tmp = t + (z + ((b - 0.5) * log(c)));
	} else if (a <= 3.2e+39) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (z * (1.0d0 + (x * (log(y) / z))))
    if (a <= 1.32d-267) then
        tmp = t_1
    else if (a <= 2.7d-245) then
        tmp = t + (z + ((b - 0.5d0) * log(c)))
    else if (a <= 3.2d+39) then
        tmp = t_1
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 t_1 = (y * i) + (z * (1.0 + (x * (Math.log(y) / z))));
	double tmp;
	if (a <= 1.32e-267) {
		tmp = t_1;
	} else if (a <= 2.7e-245) {
		tmp = t + (z + ((b - 0.5) * Math.log(c)));
	} else if (a <= 3.2e+39) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z * (1.0 + (x * (math.log(y) / z))))
	tmp = 0
	if a <= 1.32e-267:
		tmp = t_1
	elif a <= 2.7e-245:
		tmp = t + (z + ((b - 0.5) * math.log(c)))
	elif a <= 3.2e+39:
		tmp = t_1
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(x * Float64(log(y) / z)))))
	tmp = 0.0
	if (a <= 1.32e-267)
		tmp = t_1;
	elseif (a <= 2.7e-245)
		tmp = Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (a <= 3.2e+39)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z * (1.0 + (x * (log(y) / z))));
	tmp = 0.0;
	if (a <= 1.32e-267)
		tmp = t_1;
	elseif (a <= 2.7e-245)
		tmp = t + (z + ((b - 0.5) * log(c)));
	elseif (a <= 3.2e+39)
		tmp = t_1;
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(x * N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.32e-267], t$95$1, If[LessEqual[a, 2.7e-245], N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+39], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.31999999999999997e-267 or 2.69999999999999989e-245 < a < 3.19999999999999993e39

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 76.2%

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

   4. Taylor expanded in x around inf 53.3%

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

      1. associate-/l* 53.3%

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

   6. Simplified 53.3%

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

   if 1.31999999999999997e-267 < a < 2.69999999999999989e-245

   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 x around 0 99.5%

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

   4. Taylor expanded in y around 0 99.5%

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

   5. Taylor expanded in a around 0 99.5%

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

   if 3.19999999999999993e39 < 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 99.8%

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

   4. Taylor expanded in z around inf 78.1%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.32 \cdot 10^{-267}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + x \cdot \frac{\log y}{z}\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-245}:\\ \;\;\;\;t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + x \cdot \frac{\log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + x \cdot \frac{\log y}{z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-245}:\\ \;\;\;\;t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+39}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.8e-278)
   (+ (* y i) (* z (+ 1.0 (* x (/ (log y) z)))))
   (if (<= a 6.8e-245)
     (+ t (+ z (* (- b 0.5) (log c))))
     (if (<= a 3e+39)
       (+ (* y i) (* z (+ 1.0 (/ (* x (log y)) z))))
       (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ 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 <= 7.8e-278) {
		tmp = (y * i) + (z * (1.0 + (x * (log(y) / z))));
	} else if (a <= 6.8e-245) {
		tmp = t + (z + ((b - 0.5) * log(c)));
	} else if (a <= 3e+39) {
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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 (a <= 7.8d-278) then
        tmp = (y * i) + (z * (1.0d0 + (x * (log(y) / z))))
    else if (a <= 6.8d-245) then
        tmp = t + (z + ((b - 0.5d0) * log(c)))
    else if (a <= 3d+39) then
        tmp = (y * i) + (z * (1.0d0 + ((x * log(y)) / z)))
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 (a <= 7.8e-278) {
		tmp = (y * i) + (z * (1.0 + (x * (Math.log(y) / z))));
	} else if (a <= 6.8e-245) {
		tmp = t + (z + ((b - 0.5) * Math.log(c)));
	} else if (a <= 3e+39) {
		tmp = (y * i) + (z * (1.0 + ((x * Math.log(y)) / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7.8e-278:
		tmp = (y * i) + (z * (1.0 + (x * (math.log(y) / z))))
	elif a <= 6.8e-245:
		tmp = t + (z + ((b - 0.5) * math.log(c)))
	elif a <= 3e+39:
		tmp = (y * i) + (z * (1.0 + ((x * math.log(y)) / z)))
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.8e-278)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(x * Float64(log(y) / z)))));
	elseif (a <= 6.8e-245)
		tmp = Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (a <= 3e+39)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(Float64(x * log(y)) / z))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7.8e-278)
		tmp = (y * i) + (z * (1.0 + (x * (log(y) / z))));
	elseif (a <= 6.8e-245)
		tmp = t + (z + ((b - 0.5) * log(c)));
	elseif (a <= 3e+39)
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.8e-278], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(x * N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-245], N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+39], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 7.8000000000000002e-278

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 77.1%

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

   4. Taylor expanded in x around inf 53.2%

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

      1. associate-/l* 53.3%

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

   6. Simplified 53.3%

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

   if 7.8000000000000002e-278 < a < 6.7999999999999999e-245

   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 x around 0 99.5%

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

   4. Taylor expanded in y around 0 99.5%

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

   5. Taylor expanded in a around 0 99.5%

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

   if 6.7999999999999999e-245 < a < 3e39

   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 74.3%

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

   4. Taylor expanded in x around inf 53.6%

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

   if 3e39 < 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 99.8%

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

   4. Taylor expanded in z around inf 78.1%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + x \cdot \frac{\log y}{z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-245}:\\ \;\;\;\;t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+39}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -8.5e+193)
   (+ (* y i) (* x (+ (log y) (/ a x))))
   (if (<= x 5.8e+243)
     (+ (* y i) (+ a (+ t (+ z (* (- b 0.5) (log c))))))
     (+ (* y i) (* x (+ (log y) (/ z x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8.5e+193) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else if (x <= 5.8e+243) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	} else {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	}
	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 <= (-8.5d+193)) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else if (x <= 5.8d+243) then
        tmp = (y * i) + (a + (t + (z + ((b - 0.5d0) * log(c)))))
    else
        tmp = (y * i) + (x * (log(y) + (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -8.5e+193) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else if (x <= 5.8e+243) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	} else {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -8.5e+193:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	elif x <= 5.8e+243:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	else:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -8.5e+193)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	elseif (x <= 5.8e+243)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -8.5e+193)
		tmp = (y * i) + (x * (log(y) + (a / x)));
	elseif (x <= 5.8e+243)
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	else
		tmp = (y * i) + (x * (log(y) + (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -8.5e+193], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+243], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000003e193

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 95.6%

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

      1. associate-+r+ 95.6%

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

      2. sub-neg 95.6%

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

      3. metadata-eval 95.6%

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

      4. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in a around inf 87.8%

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

   if -8.5000000000000003e193 < x < 5.80000000000000013e243

   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 91.1%

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

   if 5.80000000000000013e243 < 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 x around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 82.2%

      \[\leadsto x \cdot \left(\log y + \color{blue}{\frac{z}{x}}\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.2 \cdot 10^{-245}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{b \cdot \log c}{z}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 8.2e-245)
   (+ (* y i) (* z (+ 1.0 (/ (* b (log c)) z))))
   (if (<= a 6.5e+41)
     (+ (* y i) (* z (+ 1.0 (/ (* x (log y)) z))))
     (+ (* y i) (* a (+ 1.0 (+ (/ t a) (/ 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 <= 8.2e-245) {
		tmp = (y * i) + (z * (1.0 + ((b * log(c)) / z)));
	} else if (a <= 6.5e+41) {
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (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 (a <= 8.2d-245) then
        tmp = (y * i) + (z * (1.0d0 + ((b * log(c)) / z)))
    else if (a <= 6.5d+41) then
        tmp = (y * i) + (z * (1.0d0 + ((x * log(y)) / z)))
    else
        tmp = (y * i) + (a * (1.0d0 + ((t / a) + (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 (a <= 8.2e-245) {
		tmp = (y * i) + (z * (1.0 + ((b * Math.log(c)) / z)));
	} else if (a <= 6.5e+41) {
		tmp = (y * i) + (z * (1.0 + ((x * Math.log(y)) / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8.2e-245:
		tmp = (y * i) + (z * (1.0 + ((b * math.log(c)) / z)))
	elif a <= 6.5e+41:
		tmp = (y * i) + (z * (1.0 + ((x * math.log(y)) / z)))
	else:
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8.2e-245)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(Float64(b * log(c)) / z))));
	elseif (a <= 6.5e+41)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(Float64(x * log(y)) / z))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(Float64(t / a) + Float64(z / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 8.2e-245)
		tmp = (y * i) + (z * (1.0 + ((b * log(c)) / z)));
	elseif (a <= 6.5e+41)
		tmp = (y * i) + (z * (1.0 + ((x * log(y)) / z)));
	else
		tmp = (y * i) + (a * (1.0 + ((t / a) + (z / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8.2e-245], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+41], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 8.20000000000000073e-245

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 76.9%

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

   4. Taylor expanded in b around inf 52.3%

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

      1. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   if 8.20000000000000073e-245 < a < 6.49999999999999975e41

   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 74.7%

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

   4. Taylor expanded in x around inf 54.3%

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

   if 6.49999999999999975e41 < 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 99.8%

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

   4. Taylor expanded in z around inf 79.4%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.2 \cdot 10^{-245}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{b \cdot \log c}{z}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \left(\frac{t}{a} + \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+84}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+107}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4e+84)
   (+ a (+ z (* (- b 0.5) (log c))))
   (if (<= y 1.75e+107)
     (+ (* y i) (+ (* x (log y)) t))
     (if (<= y 1.2e+181)
       (+ (* y i) (* z (+ 1.0 (/ a z))))
       (+ (* y i) (* a (+ 1.0 (/ t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4e+84) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else if (y <= 1.75e+107) {
		tmp = (y * i) + ((x * log(y)) + t);
	} else if (y <= 1.2e+181) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (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 (y <= 4d+84) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else if (y <= 1.75d+107) then
        tmp = (y * i) + ((x * log(y)) + t)
    else if (y <= 1.2d+181) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else
        tmp = (y * i) + (a * (1.0d0 + (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 (y <= 4e+84) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else if (y <= 1.75e+107) {
		tmp = (y * i) + ((x * Math.log(y)) + t);
	} else if (y <= 1.2e+181) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (t / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4e+84:
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	elif y <= 1.75e+107:
		tmp = (y * i) + ((x * math.log(y)) + t)
	elif y <= 1.2e+181:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	else:
		tmp = (y * i) + (a * (1.0 + (t / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4e+84)
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (y <= 1.75e+107)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t));
	elseif (y <= 1.2e+181)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(t / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4e+84)
		tmp = a + (z + ((b - 0.5) * log(c)));
	elseif (y <= 1.75e+107)
		tmp = (y * i) + ((x * log(y)) + t);
	elseif (y <= 1.2e+181)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	else
		tmp = (y * i) + (a * (1.0 + (t / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4e+84], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+107], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+181], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 4.00000000000000023e84

   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 78.6%

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

   4. Taylor expanded in y around 0 71.8%

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

   5. Taylor expanded in t around 0 55.3%

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

   if 4.00000000000000023e84 < y < 1.7499999999999999e107

   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 t around inf 55.5%

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

      1. associate-/l* 55.3%

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

      2. sub-neg 55.3%

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

      3. metadata-eval 55.3%

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

      4. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. associate-*r/ 55.9%

         \[\leadsto t \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{t}}\right) + y \cdot i \]

   8. Simplified 55.9%

      \[\leadsto t \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{t}}\right) + y \cdot i \]

   9. Taylor expanded in t around 0 76.8%

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

   if 1.7499999999999999e107 < y < 1.20000000000000001e181

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in a around inf 59.4%

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

   if 1.20000000000000001e181 < y

   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 67.9%

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

   4. Taylor expanded in t around inf 70.3%

      \[\leadsto a \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+84}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+107}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.3e+84)
   (+ a (+ t (+ z (* (- b 0.5) (log c)))))
   (if (<= y 3.6e+106)
     (+ (* y i) (+ (* x (log y)) t))
     (if (<= y 2.9e+181)
       (+ (* y i) (* z (+ 1.0 (/ a z))))
       (+ (* y i) (* a (+ 1.0 (/ t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.3e+84) {
		tmp = a + (t + (z + ((b - 0.5) * log(c))));
	} else if (y <= 3.6e+106) {
		tmp = (y * i) + ((x * log(y)) + t);
	} else if (y <= 2.9e+181) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (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 (y <= 1.3d+84) then
        tmp = a + (t + (z + ((b - 0.5d0) * log(c))))
    else if (y <= 3.6d+106) then
        tmp = (y * i) + ((x * log(y)) + t)
    else if (y <= 2.9d+181) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else
        tmp = (y * i) + (a * (1.0d0 + (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 (y <= 1.3e+84) {
		tmp = a + (t + (z + ((b - 0.5) * Math.log(c))));
	} else if (y <= 3.6e+106) {
		tmp = (y * i) + ((x * Math.log(y)) + t);
	} else if (y <= 2.9e+181) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (t / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.3e+84:
		tmp = a + (t + (z + ((b - 0.5) * math.log(c))))
	elif y <= 3.6e+106:
		tmp = (y * i) + ((x * math.log(y)) + t)
	elif y <= 2.9e+181:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	else:
		tmp = (y * i) + (a * (1.0 + (t / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.3e+84)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c)))));
	elseif (y <= 3.6e+106)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t));
	elseif (y <= 2.9e+181)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + Float64(t / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.3e+84)
		tmp = a + (t + (z + ((b - 0.5) * log(c))));
	elseif (y <= 3.6e+106)
		tmp = (y * i) + ((x * log(y)) + t);
	elseif (y <= 2.9e+181)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	else
		tmp = (y * i) + (a * (1.0 + (t / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.3e+84], N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+106], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+181], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 1.3000000000000001e84

   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 78.6%

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

   4. Taylor expanded in y around 0 71.8%

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

   if 1.3000000000000001e84 < y < 3.6000000000000001e106

   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 t around inf 55.5%

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

      1. associate-/l* 55.3%

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

      2. sub-neg 55.3%

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

      3. metadata-eval 55.3%

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

      4. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. associate-*r/ 55.9%

         \[\leadsto t \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{t}}\right) + y \cdot i \]

   8. Simplified 55.9%

      \[\leadsto t \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{t}}\right) + y \cdot i \]

   9. Taylor expanded in t around 0 76.8%

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

   if 3.6000000000000001e106 < y < 2.9e181

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in a around inf 59.4%

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

   if 2.9e181 < y

   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 67.9%

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

   4. Taylor expanded in t around inf 70.3%

      \[\leadsto a \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-7}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.16e-7)
   (+ (* y i) (* z (+ 1.0 (/ a z))))
   (if (<= z -2.7e-189)
     (+ (* x (log y)) (* y i))
     (+ (* y i) (* a (+ 1.0 (/ 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 <= -1.16e-7) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.7e-189) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + (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 <= (-1.16d-7)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else if (z <= (-2.7d-189)) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a * (1.0d0 + (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 <= -1.16e-7) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else if (z <= -2.7e-189) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + (t / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.16e-7:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	elif z <= -2.7e-189:
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a * (1.0 + (t / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.16e-7)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	elseif (z <= -2.7e-189)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + 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 <= -1.16e-7)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	elseif (z <= -2.7e-189)
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a * (1.0 + (t / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.16e-7], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-189], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1600000000000001e-7

   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 99.8%

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

   4. Taylor expanded in a around inf 65.7%

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

   if -1.1600000000000001e-7 < z < -2.6999999999999999e-189

   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 69.5%

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

   4. Taylor expanded in x around inf 52.9%

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

   if -2.6999999999999999e-189 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf 76.2%

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

   4. Taylor expanded in t around inf 50.1%

      \[\leadsto a \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-7}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+121}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.5e+121) (+ z (* y i)) (+ (* y i) (* a (+ 1.0 (/ 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 <= -9.5e+121) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + (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 <= (-9.5d+121)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a * (1.0d0 + (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 <= -9.5e+121) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * (1.0 + (t / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.5e+121:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a * (1.0 + (t / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.5e+121)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + 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 <= -9.5e+121)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a * (1.0 + (t / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.5e+121], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999949e121

   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 99.8%

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

   4. Taylor expanded in z around inf 74.8%

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

   if -9.49999999999999949e121 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 75.6%

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

   4. Taylor expanded in t around inf 49.1%

      \[\leadsto a \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+121}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.85e-7)
   (+ (* y i) (* z (+ 1.0 (/ a z))))
   (+ (* y i) (* a (+ 1.0 (/ 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 <= -1.85e-7) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (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 <= (-1.85d-7)) then
        tmp = (y * i) + (z * (1.0d0 + (a / z)))
    else
        tmp = (y * i) + (a * (1.0d0 + (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 <= -1.85e-7) {
		tmp = (y * i) + (z * (1.0 + (a / z)));
	} else {
		tmp = (y * i) + (a * (1.0 + (t / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.85e-7:
		tmp = (y * i) + (z * (1.0 + (a / z)))
	else:
		tmp = (y * i) + (a * (1.0 + (t / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.85e-7)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(a / z))));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(1.0 + 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 <= -1.85e-7)
		tmp = (y * i) + (z * (1.0 + (a / z)));
	else
		tmp = (y * i) + (a * (1.0 + (t / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.85e-7], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000002e-7

   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 99.8%

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

   4. Taylor expanded in a around inf 65.7%

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

   if -1.85000000000000002e-7 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 75.8%

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

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto a \cdot \left(1 + \color{blue}{\frac{t}{a}}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 23.1% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+116}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-186}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.45e+116) z (if (<= z -2.6e-186) (* 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 (z <= -2.45e+116) {
		tmp = z;
	} else if (z <= -2.6e-186) {
		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 (z <= (-2.45d+116)) then
        tmp = z
    else if (z <= (-2.6d-186)) 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 (z <= -2.45e+116) {
		tmp = z;
	} else if (z <= -2.6e-186) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.45e+116:
		tmp = z
	elif z <= -2.6e-186:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.45e+116)
		tmp = z;
	elseif (z <= -2.6e-186)
		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 (z <= -2.45e+116)
		tmp = z;
	elseif (z <= -2.6e-186)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.45e+116], z, If[LessEqual[z, -2.6e-186], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4499999999999999e116

   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 49.9%

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

   if -2.4499999999999999e116 < z < -2.59999999999999993e-186

   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 inf 32.0%

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

      1. *-commutative 32.0%

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

   5. Simplified 32.0%

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

   if -2.59999999999999993e-186 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf 16.2%

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

4. Final simplification 24.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+116}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-186}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.9e+182) 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 <= -1.9e+182) {
		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 <= (-1.9d+182)) 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 <= -1.9e+182) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.9e+182:
		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 <= -1.9e+182)
		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 <= -1.9e+182)
		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, -1.9e+182], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000006e182

   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 60.3%

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

   if -1.90000000000000006e182 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 70.5%

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

   4. Taylor expanded in a around inf 40.6%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.75e+120) (+ 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 <= -1.75e+120) {
		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 (z <= (-1.75d+120)) 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 (z <= -1.75e+120) {
		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 z <= -1.75e+120:
		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 (z <= -1.75e+120)
		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 (z <= -1.75e+120)
		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[z, -1.75e+120], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000004e120

   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 99.8%

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

   4. Taylor expanded in z around inf 74.8%

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

   if -1.75000000000000004e120 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 69.0%

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

   4. Taylor expanded in a around inf 40.5%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.6% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.8e+109) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+109) {
		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 (z <= (-2.8d+109)) 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 (z <= -2.8e+109) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+109:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.8e+109)
		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 (z <= -2.8e+109)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.8e+109], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e109

   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 48.6%

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

   if -2.8000000000000002e109 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 15.7%

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

4. Final simplification 20.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 16.6% 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 99.5%

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

3. Taylor expanded in a around inf 14.3%

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

4. Final simplification 14.3%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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)))