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

Percentage Accurate: 99.8% → 99.8%

Time: 16.7s

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, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (+ b -0.5) (log c) (+ z (fma x (log y) (+ t a))))))

C

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

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return fma(y, i, fma(Float64(b + -0.5), log(c), Float64(z + fma(x, log(y), Float64(t + a)))))
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Step-by-step derivation

   1. associate-+l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. associate-+r+ 99.5%

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

   5. +-commutative 99.5%

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

   6. +-commutative 99.5%

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

   7. associate-+l+ 99.5%

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

   8. associate-+l+ 99.5%

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

   9. +-commutative 99.5%

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

   10. fma-define 99.5%

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

   11. +-commutative 99.5%

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

   12. fma-define 99.5%

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

   13. sub-neg 99.5%

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

   14. metadata-eval 99.5%

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

   15. +-commutative 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.5%

   \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right) \]
6. Add Preprocessing

Alternative 2: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;y \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= y 2.7e+51)
     (+ a (+ t (+ z (+ (* x (log y)) t_1))))
     (+ (* y i) (+ a (+ z t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (y <= 2.7e+51) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (z + t_1));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = log(c) * (b - 0.5d0)
    if (y <= 2.7d+51) then
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    else
        tmp = (y * i) + (a + (z + t_1))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (y <= 2.7e+51) {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (z + t_1));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if y <= 2.7e+51:
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	else:
		tmp = (y * i) + (a + (z + t_1))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (y <= 2.7e+51)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t_1)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (y <= 2.7e+51)
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	else
		tmp = (y * i) + (a + (z + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.7e+51], 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[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 2.69999999999999992e51

   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 y around 0 96.1%

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

   if 2.69999999999999992e51 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 91.3%

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

   4. Taylor expanded in t around 0 79.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (* (log c) (- b 0.5)) (+ a (+ t (+ z (* x (log y)))))) (* y i)))

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = ((log(c) * (b - 0.5d0)) + (a + (t + (z + (x * log(y)))))) + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((log(c) * (b - 0.5)) + (a + (t + (z + (x * log(y)))))) + (y * i);
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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%

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

Alternative 4: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+51}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 8e+51)
   (+ a (+ t (+ z (+ (* x (log y)) (* b (log c))))))
   (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8e+51) {
		tmp = a + (t + (z + ((x * log(y)) + (b * log(c)))));
	} else {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= 8d+51) then
        tmp = a + (t + (z + ((x * log(y)) + (b * log(c)))))
    else
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8e+51) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (b * Math.log(c)))));
	} else {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 8e+51:
		tmp = a + (t + (z + ((x * math.log(y)) + (b * math.log(c)))))
	else:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 8e+51)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(b * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 8e+51)
		tmp = a + (t + (z + ((x * log(y)) + (b * log(c)))));
	else
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 8e+51], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8e51

   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 y around 0 96.1%

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

   4. Taylor expanded in b around inf 92.9%

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

   if 8e51 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 91.3%

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

   4. Taylor expanded in t around 0 79.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+51}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+180}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+247}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y - \frac{a \cdot \left(-1 - \frac{t}{a}\right)}{x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.5e+180)
   (+ a (+ t (+ z (* x (log y)))))
   (if (<= x 9.6e+247)
     (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
     (+ (* y i) (* x (- (log y) (/ (* a (- -1.0 (/ t a))) x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+180) {
		tmp = a + (t + (z + (x * log(y))));
	} else if (x <= 9.6e+247) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (log(y) - ((a * (-1.0 - (t / a))) / x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= (-7.5d+180)) then
        tmp = a + (t + (z + (x * log(y))))
    else if (x <= 9.6d+247) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + (x * (log(y) - ((a * ((-1.0d0) - (t / a))) / x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.5e+180) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else if (x <= 9.6e+247) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (Math.log(y) - ((a * (-1.0 - (t / a))) / x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -7.5e+180:
		tmp = a + (t + (z + (x * math.log(y))))
	elif x <= 9.6e+247:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + (x * (math.log(y) - ((a * (-1.0 - (t / a))) / x)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.5e+180)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	elseif (x <= 9.6e+247)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) - Float64(Float64(a * Float64(-1.0 - Float64(t / a))) / x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -7.5e+180)
		tmp = a + (t + (z + (x * log(y))));
	elseif (x <= 9.6e+247)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + (x * (log(y) - ((a * (-1.0 - (t / a))) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.5e+180], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e+247], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] - N[(N[(a * N[(-1.0 - N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000003e180

   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 91.4%

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

   4. Taylor expanded in x around inf 87.2%

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

   if -7.5000000000000003e180 < x < 9.6e247

   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 93.4%

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

   if 9.6e247 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 58.6%

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

      1. associate-/l* 58.6%

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

      2. sub-neg 58.6%

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

      3. metadata-eval 58.6%

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

      4. associate-/l* 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in x around inf 52.5%

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

      1. associate-*r/ 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in x around inf 75.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+180}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+247}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y - \frac{a \cdot \left(-1 - \frac{t}{a}\right)}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+176}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.12e+176)
     (+ a (+ t (+ z t_1)))
     (if (<= x 3.35e+258)
       (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
       (+ t_1 (* y i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (x <= -1.12e+176) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.35e+258) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 (x <= (-1.12d+176)) then
        tmp = a + (t + (z + t_1))
    else if (x <= 3.35d+258) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = t_1 + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (x <= -1.12e+176) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.35e+258) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.12e+176:
		tmp = a + (t + (z + t_1))
	elif x <= 3.35e+258:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = t_1 + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.12e+176)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 3.35e+258)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.12e+176)
		tmp = a + (t + (z + t_1));
	elseif (x <= 3.35e+258)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = t_1 + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e+176], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.35e+258], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12e176

   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 91.4%

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

   4. Taylor expanded in x around inf 87.2%

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

   if -1.12e176 < x < 3.34999999999999988e258

   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 93.4%

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

   if 3.34999999999999988e258 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in a around -inf 62.7%

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

   4. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. *-commutative 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+176}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+249} \lor \neg \left(b \leq -7.2 \cdot 10^{+206} \lor \neg \left(b \leq -9.4 \cdot 10^{+188}\right) \land b \leq 1.08 \cdot 10^{+250}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.65e+249)
         (not
          (or (<= b -7.2e+206) (and (not (<= b -9.4e+188)) (<= b 1.08e+250)))))
   (* b (log c))
   (+ (* y i) (+ t (+ z a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.65e+249) || !((b <= -7.2e+206) || (!(b <= -9.4e+188) && (b <= 1.08e+250)))) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 ((b <= (-1.65d+249)) .or. (.not. (b <= (-7.2d+206)) .or. (.not. (b <= (-9.4d+188))) .and. (b <= 1.08d+250))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.65e+249) || !((b <= -7.2e+206) || (!(b <= -9.4e+188) && (b <= 1.08e+250)))) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.65e+249) or not ((b <= -7.2e+206) or (not (b <= -9.4e+188) and (b <= 1.08e+250))):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.65e+249) || !((b <= -7.2e+206) || (!(b <= -9.4e+188) && (b <= 1.08e+250))))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.65e+249) || ~(((b <= -7.2e+206) || (~((b <= -9.4e+188)) && (b <= 1.08e+250)))))
		tmp = b * log(c);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.65e+249], N[Not[Or[LessEqual[b, -7.2e+206], And[N[Not[LessEqual[b, -9.4e+188]], $MachinePrecision], LessEqual[b, 1.08e+250]]]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.65000000000000007e249 or -7.20000000000000057e206 < b < -9.3999999999999995e188 or 1.08000000000000007e250 < b

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 76.4%

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -1.65000000000000007e249 < b < -7.20000000000000057e206 or -9.3999999999999995e188 < b < 1.08000000000000007e250

   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 76.7%

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

      1. associate-/l* 76.7%

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

      2. sub-neg 76.7%

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

      3. metadata-eval 76.7%

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

      4. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around inf 62.9%

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

   7. Taylor expanded in a around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-+l+ 75.4%

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

   9. Simplified 75.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+249} \lor \neg \left(b \leq -7.2 \cdot 10^{+206} \lor \neg \left(b \leq -9.4 \cdot 10^{+188}\right) \land b \leq 1.08 \cdot 10^{+250}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+109}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (- b 0.5) -5e+145)
   (+ (* y i) (* b (log c)))
   (if (<= (- b 0.5) 5e+109)
     (+ (* y i) (+ t (+ z a)))
     (+ a (+ z (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b - 0.5) <= -5e+145) {
		tmp = (y * i) + (b * log(c));
	} else if ((b - 0.5) <= 5e+109) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = a + (z + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 ((b - 0.5d0) <= (-5d+145)) then
        tmp = (y * i) + (b * log(c))
    else if ((b - 0.5d0) <= 5d+109) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b - 0.5) <= -5e+145) {
		tmp = (y * i) + (b * Math.log(c));
	} else if ((b - 0.5) <= 5e+109) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b - 0.5) <= -5e+145:
		tmp = (y * i) + (b * math.log(c))
	elif (b - 0.5) <= 5e+109:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b - 0.5) <= -5e+145)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (Float64(b - 0.5) <= 5e+109)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b - 0.5) <= -5e+145)
		tmp = (y * i) + (b * log(c));
	elseif ((b - 0.5) <= 5e+109)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = a + (z + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+145], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+109], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -4.99999999999999967e145

   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 87.7%

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

   4. Taylor expanded in t around 0 81.5%

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

   5. Taylor expanded in b around inf 74.7%

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

      1. *-commutative 74.7%

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

   7. Simplified 74.7%

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

   if -4.99999999999999967e145 < (-.f64 b #s(literal 1/2 binary64)) < 5.0000000000000001e109

   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 80.0%

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

      1. associate-/l* 80.0%

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

      2. sub-neg 80.0%

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

      3. metadata-eval 80.0%

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

      4. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in z around inf 68.2%

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

   7. Taylor expanded in a around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+l+ 80.2%

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

   9. Simplified 80.2%

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

   if 5.0000000000000001e109 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 87.3%

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

   4. Taylor expanded in t around 0 71.7%

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

   5. Taylor expanded in y around 0 54.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+109}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{+182}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.28e+182)
     (+ a (+ t (+ z t_1)))
     (if (<= x 3.9e+258)
       (+ (* y i) (+ a (+ t (+ z (* b (log c))))))
       (+ t_1 (* y i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (x <= -1.28e+182) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.9e+258) {
		tmp = (y * i) + (a + (t + (z + (b * log(c)))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 (x <= (-1.28d+182)) then
        tmp = a + (t + (z + t_1))
    else if (x <= 3.9d+258) then
        tmp = (y * i) + (a + (t + (z + (b * log(c)))))
    else
        tmp = t_1 + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (x <= -1.28e+182) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.9e+258) {
		tmp = (y * i) + (a + (t + (z + (b * Math.log(c)))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.28e+182:
		tmp = a + (t + (z + t_1))
	elif x <= 3.9e+258:
		tmp = (y * i) + (a + (t + (z + (b * math.log(c)))))
	else:
		tmp = t_1 + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.28e+182)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 3.9e+258)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(b * log(c))))));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.28e+182)
		tmp = a + (t + (z + t_1));
	elseif (x <= 3.9e+258)
		tmp = (y * i) + (a + (t + (z + (b * log(c)))));
	else
		tmp = t_1 + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e+182], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+258], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.28e182

   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 91.4%

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

   4. Taylor expanded in x around inf 87.2%

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

   if -1.28e182 < x < 3.90000000000000037e258

   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 93.4%

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

   4. Taylor expanded in b around inf 91.2%

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

   if 3.90000000000000037e258 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in a around -inf 62.7%

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

   4. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. *-commutative 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+182}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -4.15 \cdot 10^{+180}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -4.15e+180)
     (+ a (+ t (+ z t_1)))
     (if (<= x 3.6e+258)
       (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))
       (+ t_1 (* y i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 (x <= -4.15e+180) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.6e+258) {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 (x <= (-4.15d+180)) then
        tmp = a + (t + (z + t_1))
    else if (x <= 3.6d+258) then
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = t_1 + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 (x <= -4.15e+180) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 3.6e+258) {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -4.15e+180:
		tmp = a + (t + (z + t_1))
	elif x <= 3.6e+258:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = t_1 + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -4.15e+180)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 3.6e+258)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -4.15e+180)
		tmp = a + (t + (z + t_1));
	elseif (x <= 3.6e+258)
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	else
		tmp = t_1 + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.15e+180], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+258], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1500000000000004e180

   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 91.4%

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

   4. Taylor expanded in x around inf 87.2%

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

   if -4.1500000000000004e180 < x < 3.5999999999999999e258

   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 93.4%

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

   4. Taylor expanded in t around 0 74.3%

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

   if 3.5999999999999999e258 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in a around -inf 62.7%

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

   4. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. *-commutative 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.15 \cdot 10^{+180}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+258}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+145} \lor \neg \left(b \leq 3.8 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -5.2e+145) (not (<= b 3.8e+109)))
   (+ (* y i) (* b (log c)))
   (+ (* y i) (+ t (+ z a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -5.2e+145) || !(b <= 3.8e+109)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 ((b <= (-5.2d+145)) .or. (.not. (b <= 3.8d+109))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -5.2e+145) || !(b <= 3.8e+109)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -5.2e+145) or not (b <= 3.8e+109):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -5.2e+145) || !(b <= 3.8e+109))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -5.2e+145) || ~((b <= 3.8e+109)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -5.2e+145], N[Not[LessEqual[b, 3.8e+109]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.20000000000000005e145 or 3.80000000000000039e109 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 87.7%

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

   4. Taylor expanded in t around 0 77.1%

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

   5. Taylor expanded in b around inf 70.0%

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

      1. *-commutative 70.0%

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

   7. Simplified 70.0%

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

   if -5.20000000000000005e145 < b < 3.80000000000000039e109

   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 79.9%

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

      1. associate-/l* 79.9%

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

      2. sub-neg 79.9%

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

      3. metadata-eval 79.9%

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

      4. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in z around inf 68.0%

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

   7. Taylor expanded in a around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-+l+ 80.1%

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

   9. Simplified 80.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+145} \lor \neg \left(b \leq 3.8 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.06e+192) (* x (log y)) (+ (* y i) (+ t (+ z a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.06e+192) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= (-1.06d+192)) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.06e+192) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.06e+192:
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.06e+192)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.06e+192)
		tmp = x * log(y);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.06e+192], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06000000000000006e192

   1. Initial program 99.6%

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

   3. Taylor expanded in a around -inf 70.7%

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

   4. Taylor expanded in x around inf 74.0%

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

   if -1.06000000000000006e192 < x

   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 74.0%

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

      1. associate-/l* 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. associate-/l* 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around inf 58.0%

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

   7. Taylor expanded in a around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-+l+ 69.5%

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

   9. Simplified 69.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.1% accurate, 10.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+204} \lor \neg \left(z \leq -8.8 \cdot 10^{+161}\right) \land z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -3.2e+204) (and (not (<= z -8.8e+161)) (<= z -5e+113)))
   z
   (+ a (* y i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.2e+204) || (!(z <= -8.8e+161) && (z <= -5e+113))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-3.2d+204)) .or. (.not. (z <= (-8.8d+161))) .and. (z <= (-5d+113))) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.2e+204) || (!(z <= -8.8e+161) && (z <= -5e+113))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -3.2e+204) or (not (z <= -8.8e+161) and (z <= -5e+113)):
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -3.2e+204) || (!(z <= -8.8e+161) && (z <= -5e+113)))
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -3.2e+204) || (~((z <= -8.8e+161)) && (z <= -5e+113)))
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -3.2e+204], And[N[Not[LessEqual[z, -8.8e+161]], $MachinePrecision], LessEqual[z, -5e+113]]], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e204 or -8.7999999999999999e161 < z < -5e113

   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 53.0%

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

   if -3.2e204 < z < -8.7999999999999999e161 or -5e113 < z

   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 84.8%

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

   4. Taylor expanded in a around inf 40.4%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+204} \lor \neg \left(z \leq -8.8 \cdot 10^{+161}\right) \land z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-218}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 5.8e-229) z (if (<= y 3e-218) a (if (<= y 1.16e+51) z (* y i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.8e-229) {
		tmp = z;
	} else if (y <= 3e-218) {
		tmp = a;
	} else if (y <= 1.16e+51) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= 5.8d-229) then
        tmp = z
    else if (y <= 3d-218) then
        tmp = a
    else if (y <= 1.16d+51) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.8e-229) {
		tmp = z;
	} else if (y <= 3e-218) {
		tmp = a;
	} else if (y <= 1.16e+51) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 5.8e-229:
		tmp = z
	elif y <= 3e-218:
		tmp = a
	elif y <= 1.16e+51:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 5.8e-229)
		tmp = z;
	elseif (y <= 3e-218)
		tmp = a;
	elseif (y <= 1.16e+51)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 5.8e-229)
		tmp = z;
	elseif (y <= 3e-218)
		tmp = a;
	elseif (y <= 1.16e+51)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 5.8e-229], z, If[LessEqual[y, 3e-218], a, If[LessEqual[y, 1.16e+51], z, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.7999999999999999e-229 or 2.9999999999999998e-218 < y < 1.16e51

   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 15.9%

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

   if 5.7999999999999999e-229 < y < 2.9999999999999998e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 44.3%

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

   if 1.16e51 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. *-commutative 53.4%

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

   5. Simplified 53.4%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-218}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.8e+71) (+ z (* y i)) (+ a (* y i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.8e+71) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= (-1.8d+71)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.8e+71) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.8e+71:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.8e+71)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.8e+71)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.8e+71], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e71

   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 95.0%

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

   4. Taylor expanded in z around inf 57.0%

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

   if -1.8e71 < 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 x around 0 84.1%

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

   4. Taylor expanded in a around inf 40.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.9% accurate, 24.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ y \cdot i + \left(t + \left(z + a\right)\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ t (+ z a))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (t + (z + a));
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + (t + (z + a))
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (t + (z + a));
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	return (y * i) + (t + (z + a))

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(t + Float64(z + a)))
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (t + (z + a));
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $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. Taylor expanded in a around inf 73.7%

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

   1. associate-/l* 73.6%

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

   2. sub-neg 73.6%

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

   3. metadata-eval 73.6%

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

   4. associate-/l* 73.6%

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

5. Simplified 73.6%

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

6. Taylor expanded in z around inf 55.4%

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

7. Taylor expanded in a around 0 66.4%

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

   1. +-commutative 66.4%

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

   2. associate-+l+ 66.4%

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

9. Simplified 66.4%

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

10. Final simplification 66.4%

    \[\leadsto y \cdot i + \left(t + \left(z + a\right)\right) \]
11. Add Preprocessing

Alternative 17: 66.5% accurate, 31.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ y \cdot i + \left(z + a\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ z a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (z + a);
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + (z + a)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (z + a);
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	return (y * i) + (z + a)

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(z + a))
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (z + a);
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(z + a), $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. Taylor expanded in a around inf 73.7%

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

   1. associate-/l* 73.6%

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

   2. sub-neg 73.6%

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

   3. metadata-eval 73.6%

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

   4. associate-/l* 73.6%

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

5. Simplified 73.6%

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

6. Taylor expanded in z around inf 55.4%

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

7. Taylor expanded in t around 0 44.9%

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

8. Taylor expanded in a around 0 50.0%

   \[\leadsto \color{blue}{\left(a + z\right)} + y \cdot i \]
9. Step-by-step derivation

   1. +-commutative 50.0%

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

10. Simplified 50.0%

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

11. Final simplification 50.0%

    \[\leadsto y \cdot i + \left(z + a\right) \]
12. Add Preprocessing

Alternative 18: 38.2% accurate, 36.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+71}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.8e+71) z a))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+71) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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+71)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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+71) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+71:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.8e+71)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.8e+71)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.8e+71], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000002e71

   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 39.3%

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

   if -2.80000000000000002e71 < 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 16.6%

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

4. Final simplification 20.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+71}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.9% accurate, 219.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ a \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 a)

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	return a

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 15.5%

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

4. Final simplification 15.5%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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)))