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

Percentage Accurate: 99.8% → 99.8%

Time: 16.2s

Alternatives: 14

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 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Step-by-step derivation

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

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
 (+ (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))) (* 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 ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (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 = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (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 ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5))) + (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 ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5))) + (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(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))) + 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 = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (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[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 3: 97.9% accurate, 1.0× speedup

Math

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

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) (+ (+ a (+ t (+ z (* x (log y))))) (* b (log c)))))

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) + ((a + (t + (z + (x * log(y))))) + (b * log(c)));
}

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) + ((a + (t + (z + (x * log(y))))) + (b * log(c)))
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) + ((a + (t + (z + (x * Math.log(y))))) + (b * Math.log(c)));
}

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) + ((a + (t + (z + (x * math.log(y))))) + (b * math.log(c)))

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(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(b * log(c))))
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) + ((a + (t + (z + (x * log(y))))) + (b * log(c)));
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[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 98.6%

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

   1. *-commutative 98.6%

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

5. Simplified 98.6%

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

6. Final simplification 98.6%

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

Alternative 4: 94.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+101} \lor \neg \left(x \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

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 (or (<= x -2.15e+101) (not (<= x 9e+152)))
   (+ (+ a (+ t (+ z (* x (log y))))) (* y i))
   (+ (* y i) (+ a (+ t (+ 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 ((x <= -2.15e+101) || !(x <= 9e+152)) {
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	} else {
		tmp = (y * i) + (a + (t + (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 ((x <= (-2.15d+101)) .or. (.not. (x <= 9d+152))) then
        tmp = (a + (t + (z + (x * log(y))))) + (y * i)
    else
        tmp = (y * i) + (a + (t + (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 ((x <= -2.15e+101) || !(x <= 9e+152)) {
		tmp = (a + (t + (z + (x * Math.log(y))))) + (y * i);
	} else {
		tmp = (y * i) + (a + (t + (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 (x <= -2.15e+101) or not (x <= 9e+152):
		tmp = (a + (t + (z + (x * math.log(y))))) + (y * i)
	else:
		tmp = (y * i) + (a + (t + (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 ((x <= -2.15e+101) || !(x <= 9e+152))
		tmp = Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + 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 ((x <= -2.15e+101) || ~((x <= 9e+152)))
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	else
		tmp = (y * i) + (a + (t + (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[Or[LessEqual[x, -2.15e+101], N[Not[LessEqual[x, 9e+152]], $MachinePrecision]], N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e101 or 9.0000000000000002e152 < x

   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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 92.3%

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

      1. +-commutative 92.3%

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

   8. Simplified 92.3%

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

   if -2.15e101 < x < 9.0000000000000002e152

   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 98.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+101} \lor \neg \left(x \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+101} \lor \neg \left(x \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

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 (or (<= x -2.6e+101) (not (<= x 9e+152)))
   (+ (+ a (+ t (+ z (* x (log y))))) (* y i))
   (+ (* 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 ((x <= -2.6e+101) || !(x <= 9e+152)) {
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	} 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 ((x <= (-2.6d+101)) .or. (.not. (x <= 9d+152))) then
        tmp = (a + (t + (z + (x * log(y))))) + (y * i)
    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 ((x <= -2.6e+101) || !(x <= 9e+152)) {
		tmp = (a + (t + (z + (x * Math.log(y))))) + (y * i);
	} 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 (x <= -2.6e+101) or not (x <= 9e+152):
		tmp = (a + (t + (z + (x * math.log(y))))) + (y * i)
	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 ((x <= -2.6e+101) || !(x <= 9e+152))
		tmp = Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(y * i));
	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 ((x <= -2.6e+101) || ~((x <= 9e+152)))
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	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[Or[LessEqual[x, -2.6e+101], N[Not[LessEqual[x, 9e+152]], $MachinePrecision]], N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $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 x < -2.6e101 or 9.0000000000000002e152 < x

   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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 92.3%

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

      1. +-commutative 92.3%

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

   8. Simplified 92.3%

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

   if -2.6e101 < x < 9.0000000000000002e152

   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 98.9%

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

   4. Taylor expanded in t around 0 76.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+101} \lor \neg \left(x \leq 9 \cdot 10^{+152}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

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 (* x (log y))))
   (if (<= x -4.5e+215)
     (+ (* y i) (+ z t_1))
     (if (<= x 1.05e+158)
       (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))
       (+ (* y i) (+ a 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 = x * log(y);
	double tmp;
	if (x <= -4.5e+215) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 1.05e+158) {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + 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 = x * log(y)
    if (x <= (-4.5d+215)) then
        tmp = (y * i) + (z + t_1)
    else if (x <= 1.05d+158) then
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (a + 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 = x * Math.log(y);
	double tmp;
	if (x <= -4.5e+215) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 1.05e+158) {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + 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 = x * math.log(y)
	tmp = 0
	if x <= -4.5e+215:
		tmp = (y * i) + (z + t_1)
	elif x <= 1.05e+158:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (a + 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(x * log(y))
	tmp = 0.0
	if (x <= -4.5e+215)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (x <= 1.05e+158)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + 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 = x * log(y);
	tmp = 0.0;
	if (x <= -4.5e+215)
		tmp = (y * i) + (z + t_1);
	elseif (x <= 1.05e+158)
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (a + 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[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+215], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+158], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5000000000000002e215

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 68.6%

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

      1. sub-neg 68.6%

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

      2. metadata-eval 68.6%

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

      3. associate-/l* 68.6%

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

      4. +-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. associate-*r/ 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in z around 0 71.0%

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

   if -4.5000000000000002e215 < x < 1.0499999999999999e158

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.6%

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

   4. Taylor expanded in t around 0 76.1%

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

   if 1.0499999999999999e158 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in a around inf 85.1%

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

   5. Taylor expanded in x around 0 85.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + b \cdot \frac{\log c}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

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 (<= z -9.2e+125)
   (+ (* y i) (* z (+ 1.0 (* b (/ (log c) z)))))
   (+ (* y i) (+ a (* x (log y))))))

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 <= -9.2e+125) {
		tmp = (y * i) + (z * (1.0 + (b * (log(c) / z))));
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	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 <= (-9.2d+125)) then
        tmp = (y * i) + (z * (1.0d0 + (b * (log(c) / z))))
    else
        tmp = (y * i) + (a + (x * log(y)))
    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 <= -9.2e+125) {
		tmp = (y * i) + (z * (1.0 + (b * (Math.log(c) / z))));
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	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 <= -9.2e+125:
		tmp = (y * i) + (z * (1.0 + (b * (math.log(c) / z))))
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	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 <= -9.2e+125)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(1.0 + Float64(b * Float64(log(c) / z)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	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 <= -9.2e+125)
		tmp = (y * i) + (z * (1.0 + (b * (log(c) / z))));
	else
		tmp = (y * i) + (a + (x * log(y)));
	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, -9.2e+125], N[(N[(y * i), $MachinePrecision] + N[(z * N[(1.0 + N[(b * N[(N[Log[c], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000051e125

   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 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-/l* 99.7%

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

      4. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in b around inf 79.0%

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

      1. associate-/l* 78.9%

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

   8. Simplified 78.9%

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

   if -9.20000000000000051e125 < z

   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 inf 70.0%

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

   4. Taylor expanded in a around inf 51.1%

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

   5. Taylor expanded in x around 0 58.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i + z \cdot \left(1 + b \cdot \frac{\log c}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+213} \lor \neg \left(b \leq 1.9 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

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 -1.75e+213) (not (<= b 1.9e+119)))
   (+ (* y i) (* b (log c)))
   (+ (* 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) {
	double tmp;
	if ((b <= -1.75e+213) || !(b <= 1.9e+119)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (y * i) + (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 <= (-1.75d+213)) .or. (.not. (b <= 1.9d+119))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (y * i) + (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 <= -1.75e+213) || !(b <= 1.9e+119)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (y * i) + (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 <= -1.75e+213) or not (b <= 1.9e+119):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (y * i) + (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 <= -1.75e+213) || !(b <= 1.9e+119))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + 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 <= -1.75e+213) || ~((b <= 1.9e+119)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (y * i) + (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, -1.75e+213], N[Not[LessEqual[b, 1.9e+119]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7499999999999999e213 or 1.89999999999999995e119 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 60.3%

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

   4. Taylor expanded in b around inf 54.8%

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

   5. Taylor expanded in x around 0 72.7%

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

   if -1.7499999999999999e213 < b < 1.89999999999999995e119

   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 75.7%

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

      1. sub-neg 75.7%

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

      2. metadata-eval 75.7%

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

      3. associate-/l* 75.7%

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

      4. +-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in a around inf 55.3%

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

   7. Taylor expanded in z around 0 62.4%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+213} \lor \neg \left(b \leq 1.9 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

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 (<= z -1.32e+125) (+ (* y i) (+ z a)) (+ (* y i) (+ a (* x (log y))))))

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 <= -1.32e+125) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	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 <= (-1.32d+125)) then
        tmp = (y * i) + (z + a)
    else
        tmp = (y * i) + (a + (x * log(y)))
    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 <= -1.32e+125) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	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 <= -1.32e+125:
		tmp = (y * i) + (z + a)
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	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 <= -1.32e+125)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	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 <= -1.32e+125)
		tmp = (y * i) + (z + a);
	else
		tmp = (y * i) + (a + (x * log(y)));
	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, -1.32e+125], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32000000000000006e125

   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 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-/l* 99.7%

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

      4. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around inf 67.9%

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

   7. Taylor expanded in z around 0 67.9%

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

   if -1.32000000000000006e125 < z

   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 inf 70.0%

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

   4. Taylor expanded in a around inf 51.1%

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

   5. Taylor expanded in x around 0 58.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+125}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.4 \cdot 10^{+119}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

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 (<= a 5.4e+119) (+ 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 (a <= 5.4e+119) {
		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 (a <= 5.4d+119) 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 (a <= 5.4e+119) {
		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 a <= 5.4e+119:
		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 (a <= 5.4e+119)
		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 (a <= 5.4e+119)
		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[a, 5.4e+119], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.3999999999999997e119

   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 39.6%

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

   if 5.3999999999999997e119 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 59.2%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.4 \cdot 10^{+119}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.9% accurate, 27.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

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 1.4e+59) 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 (y <= 1.4e+59) {
		tmp = a;
	} 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 <= 1.4d+59) then
        tmp = a
    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 <= 1.4e+59) {
		tmp = a;
	} 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 <= 1.4e+59:
		tmp = a
	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 <= 1.4e+59)
		tmp = a;
	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 <= 1.4e+59)
		tmp = a;
	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, 1.4e+59], a, N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3999999999999999e59

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 26.4%

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

   4. Taylor expanded in a around inf 21.2%

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

   if 1.3999999999999999e59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 63.3%

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

   4. Taylor expanded in a around 0 51.0%

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

      1. *-commutative 51.0%

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

   6. Simplified 51.0%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.0% 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 99.9%

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

3. Taylor expanded in z around inf 73.2%

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

   1. sub-neg 73.2%

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

   2. metadata-eval 73.2%

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

   3. associate-/l* 73.2%

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

   4. +-commutative 73.2%

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

5. Simplified 73.2%

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

6. Taylor expanded in a around inf 48.9%

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

7. Taylor expanded in z around 0 55.0%

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

8. Final simplification 55.0%

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

Alternative 13: 43.9% accurate, 43.8× speedup

Math

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

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 (+ 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) {
	return a + (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 = a + (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 a + (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 a + (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(a + 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 = a + (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[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 42.5%

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

4. Final simplification 42.5%

   \[\leadsto a + y \cdot i \]
5. Add Preprocessing

Alternative 14: 22.6% 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 99.9%

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

3. Taylor expanded in a around inf 42.5%

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

4. Taylor expanded in a around inf 18.3%

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

5. Final simplification 18.3%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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)))