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

Percentage Accurate: 99.8% → 99.8%

Time: 17.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

(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

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

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

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. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   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%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.9 \cdot 10^{+133} \lor \neg \left(x \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.9e+133) (not (<= x 3.5e-26)))
   (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* b (log c))))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.9e+133) || !(x <= 3.5e-26)) {
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-8.9d+133)) .or. (.not. (x <= 3.5d-26))) then
        tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (b * log(c)))
    else
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.9e+133) || !(x <= 3.5e-26)) {
		tmp = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.9e+133) or not (x <= 3.5e-26):
		tmp = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.9e+133) || !(x <= 3.5e-26))
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8.9e+133) || ~((x <= 3.5e-26)))
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (b * log(c)));
	else
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.9e+133], N[Not[LessEqual[x, 3.5e-26]], $MachinePrecision]], 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], 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 < -8.90000000000000025e133 or 3.49999999999999985e-26 < x

   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 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -8.90000000000000025e133 < x < 3.49999999999999985e-26

   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 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.9 \cdot 10^{+133} \lor \neg \left(x \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(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

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

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

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

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

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

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

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 4: 89.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+216} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+233}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+216) (not (<= (- b 0.5) 2e+233)))
   (+ (* y i) (* b (log c)))
   (+ (+ a (+ t (+ z (* x (log y))))) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+216) || !((b - 0.5) <= 2e+233)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-4d+216)) .or. (.not. ((b - 0.5d0) <= 2d+233))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (a + (t + (z + (x * log(y))))) + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+216) || !((b - 0.5) <= 2e+233)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (a + (t + (z + (x * Math.log(y))))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+216) or not ((b - 0.5) <= 2e+233):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (a + (t + (z + (x * math.log(y))))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+216) || !(Float64(b - 0.5) <= 2e+233))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -4e+216) || ~(((b - 0.5) <= 2e+233)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+216], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 2e+233]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -4.0000000000000001e216 or 1.99999999999999995e233 < (-.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 inf 57.9%

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

      1. associate-+r+ 57.9%

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

      2. associate-+r+ 57.9%

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

      3. sub-neg 57.9%

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

      4. metadata-eval 57.9%

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

      5. associate-/l* 57.7%

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

      6. +-commutative 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in b around inf 51.8%

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

      1. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in x around 0 85.4%

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

   if -4.0000000000000001e216 < (-.f64 b #s(literal 1/2 binary64)) < 1.99999999999999995e233

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in b around 0 88.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+216} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+233}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+134} \lor \neg \left(x \leq 3.3 \cdot 10^{+59}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.05e+134) (not (<= x 3.3e+59)))
   (+ (+ a (+ t (+ z (* x (log y))))) (* y i))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.05e+134) || !(x <= 3.3e+59)) {
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.05d+134)) .or. (.not. (x <= 3.3d+59))) 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

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.05e+134) || !(x <= 3.3e+59)) {
		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

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.05e+134) or not (x <= 3.3e+59):
		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

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.05e+134) || !(x <= 3.3e+59))
		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

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.05e+134) || ~((x <= 3.3e+59)))
		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

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.05e+134], N[Not[LessEqual[x, 3.3e+59]], $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 < -3.04999999999999989e134 or 3.2999999999999999e59 < 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 93.2%

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

   if -3.04999999999999989e134 < x < 3.2999999999999999e59

   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 99.4%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+134} \lor \neg \left(x \leq 3.3 \cdot 10^{+59}\right):\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;y \leq 28000000:\\ \;\;\;\;a + \left(t + t\_1\right)\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+54}:\\ \;\;\;\;a + t\_1\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* (log c) (- b 0.5)))))
   (if (<= y 28000000.0)
     (+ a (+ t t_1))
     (if (<= y 3.55e+22)
       (+ (* x (log y)) (* y i))
       (if (<= y 5.6e+54) (+ a t_1) (+ a (+ t (+ z (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (log(c) * (b - 0.5));
	double tmp;
	if (y <= 28000000.0) {
		tmp = a + (t + t_1);
	} else if (y <= 3.55e+22) {
		tmp = (x * log(y)) + (y * i);
	} else if (y <= 5.6e+54) {
		tmp = a + t_1;
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (log(c) * (b - 0.5d0))
    if (y <= 28000000.0d0) then
        tmp = a + (t + t_1)
    else if (y <= 3.55d+22) then
        tmp = (x * log(y)) + (y * i)
    else if (y <= 5.6d+54) then
        tmp = a + t_1
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (Math.log(c) * (b - 0.5));
	double tmp;
	if (y <= 28000000.0) {
		tmp = a + (t + t_1);
	} else if (y <= 3.55e+22) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (y <= 5.6e+54) {
		tmp = a + t_1;
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (math.log(c) * (b - 0.5))
	tmp = 0
	if y <= 28000000.0:
		tmp = a + (t + t_1)
	elif y <= 3.55e+22:
		tmp = (x * math.log(y)) + (y * i)
	elif y <= 5.6e+54:
		tmp = a + t_1
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(log(c) * Float64(b - 0.5)))
	tmp = 0.0
	if (y <= 28000000.0)
		tmp = Float64(a + Float64(t + t_1));
	elseif (y <= 3.55e+22)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (y <= 5.6e+54)
		tmp = Float64(a + t_1);
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (log(c) * (b - 0.5));
	tmp = 0.0;
	if (y <= 28000000.0)
		tmp = a + (t + t_1);
	elseif (y <= 3.55e+22)
		tmp = (x * log(y)) + (y * i);
	elseif (y <= 5.6e+54)
		tmp = a + t_1;
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 28000000.0], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.55e+22], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+54], N[(a + t$95$1), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 2.8e7

   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 79.2%

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

   4. Taylor expanded in y around 0 76.3%

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

   if 2.8e7 < y < 3.5500000000000001e22

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate-+r+ 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate-/l* 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 85.2%

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

   if 3.5500000000000001e22 < y < 5.6000000000000003e54

   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 77.7%

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

   4. Taylor expanded in y around 0 78.1%

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

   5. Taylor expanded in t around 0 67.0%

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

   if 5.6000000000000003e54 < y

   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 b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 87.0%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 28000000:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+54}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;y \leq 25000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ z (* (log c) (- b 0.5))))))
   (if (<= y 25000000.0)
     t_1
     (if (<= y 4.5e+22)
       (+ (* x (log y)) (* y i))
       (if (<= y 5.2e+54) t_1 (+ a (+ t (+ z (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + (log(c) * (b - 0.5)));
	double tmp;
	if (y <= 25000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e+22) {
		tmp = (x * log(y)) + (y * i);
	} else if (y <= 5.2e+54) {
		tmp = t_1;
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z + (log(c) * (b - 0.5d0)))
    if (y <= 25000000.0d0) then
        tmp = t_1
    else if (y <= 4.5d+22) then
        tmp = (x * log(y)) + (y * i)
    else if (y <= 5.2d+54) then
        tmp = t_1
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + (Math.log(c) * (b - 0.5)));
	double tmp;
	if (y <= 25000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e+22) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (y <= 5.2e+54) {
		tmp = t_1;
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (z + (math.log(c) * (b - 0.5)))
	tmp = 0
	if y <= 25000000.0:
		tmp = t_1
	elif y <= 4.5e+22:
		tmp = (x * math.log(y)) + (y * i)
	elif y <= 5.2e+54:
		tmp = t_1
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (y <= 25000000.0)
		tmp = t_1;
	elseif (y <= 4.5e+22)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (y <= 5.2e+54)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (z + (log(c) * (b - 0.5)));
	tmp = 0.0;
	if (y <= 25000000.0)
		tmp = t_1;
	elseif (y <= 4.5e+22)
		tmp = (x * log(y)) + (y * i);
	elseif (y <= 5.2e+54)
		tmp = t_1;
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 25000000.0], t$95$1, If[LessEqual[y, 4.5e+22], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+54], t$95$1, N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.5e7 or 4.4999999999999998e22 < y < 5.20000000000000013e54

   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 79.1%

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

   4. Taylor expanded in y around 0 76.4%

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

   5. Taylor expanded in t around 0 60.7%

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

   if 2.5e7 < y < 4.4999999999999998e22

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate-+r+ 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate-/l* 99.7%

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

      6. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 85.2%

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

   if 5.20000000000000013e54 < y

   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 b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 87.0%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 25000000:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+54}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+212} \lor \neg \left(b \leq 2.45 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -3.1e+212) (not (<= b 2.45e+213)))
   (+ (* y i) (* b (log c)))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.1e+212) || !(b <= 2.45e+213)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-3.1d+212)) .or. (.not. (b <= 2.45d+213))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.1e+212) || !(b <= 2.45e+213)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -3.1e+212) or not (b <= 2.45e+213):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -3.1e+212) || !(b <= 2.45e+213))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -3.1e+212) || ~((b <= 2.45e+213)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -3.1e+212], N[Not[LessEqual[b, 2.45e+213]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.09999999999999998e212 or 2.44999999999999998e213 < 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 inf 57.5%

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

      1. associate-+r+ 57.5%

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

      2. associate-+r+ 57.5%

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

      3. sub-neg 57.5%

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

      4. metadata-eval 57.5%

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

      5. associate-/l* 57.4%

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

      6. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf 49.7%

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

      1. *-commutative 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in x around 0 82.8%

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

   if -3.09999999999999998e212 < b < 2.44999999999999998e213

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in b around 0 89.0%

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

   7. Taylor expanded in x around 0 71.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+212} \lor \neg \left(b \leq 2.45 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+54}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 5.1e+54) (+ a (+ t (+ z (* x (log y))))) (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.1e+54) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 5.1d+54) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.1e+54) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 5.1e+54:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 5.1e+54)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 5.1e+54)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 5.1e+54], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.10000000000000009e54

   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 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in b around 0 71.6%

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

   7. Taylor expanded in y around 0 68.4%

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

   if 5.10000000000000009e54 < y

   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 b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 87.0%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+54}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+220} \lor \neg \left(x \leq 1.2 \cdot 10^{+199}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.8e+220) (not (<= x 1.2e+199)))
   (* x (log y))
   (+ a (+ t (+ z (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.8e+220) || !(x <= 1.2e+199)) {
		tmp = x * log(y);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-5.8d+220)) .or. (.not. (x <= 1.2d+199))) then
        tmp = x * log(y)
    else
        tmp = a + (t + (z + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.8e+220) || !(x <= 1.2e+199)) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5.8e+220) or not (x <= 1.2e+199):
		tmp = x * math.log(y)
	else:
		tmp = a + (t + (z + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.8e+220) || !(x <= 1.2e+199))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5.8e+220) || ~((x <= 1.2e+199)))
		tmp = x * log(y);
	else
		tmp = a + (t + (z + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.8e+220], N[Not[LessEqual[x, 1.2e+199]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999983e220 or 1.20000000000000007e199 < x

   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 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around 0 95.1%

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

   7. Taylor expanded in x around inf 67.2%

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

   if -5.79999999999999983e220 < x < 1.20000000000000007e199

   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 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in b around 0 75.9%

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

   7. Taylor expanded in x around 0 68.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+220} \lor \neg \left(x \leq 1.2 \cdot 10^{+199}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7 \cdot 10^{+153}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7e+153) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7e+153) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 7d+153) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7e+153) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7e+153:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7e+153)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7e+153)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7e+153], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.9999999999999998e153

   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 43.9%

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

   if 6.9999999999999998e153 < 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 49.8%

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

Alternative 12: 41.1% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+200}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.5e+200) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.5e+200) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.5d+200)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.5e+200) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.5e+200:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.5e+200)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.5e+200)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.5e+200], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000009e200

   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 b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0 87.2%

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

   7. Taylor expanded in z around inf 65.3%

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

   if -2.50000000000000009e200 < 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 a around inf 37.9%

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

Alternative 13: 67.4% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ a + \left(t + \left(z + y \cdot i\right)\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + N[(t + N[(z + N[(y * i), $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 96.2%

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

   1. *-commutative 96.2%

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

5. Simplified 96.2%

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

6. Taylor expanded in b around 0 78.4%

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

7. Taylor expanded in x around 0 63.4%

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

8. Final simplification 63.4%

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

Alternative 14: 30.4% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= y 2.45e+63) z (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.45e+63) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 2.45d+63) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.45e+63) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.45e+63:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.45e+63)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 2.45e+63)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.45e+63], z, N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4499999999999998e63

   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 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in b around 0 72.0%

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

   7. Taylor expanded in z around inf 22.6%

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

   if 2.4499999999999998e63 < y

   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 58.7%

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

   4. Taylor expanded in a around 0 51.6%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{+150}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.2e+150) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.2e+150) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.2d+150) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.2e+150) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.2e+150:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.2e+150)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.2e+150)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.2e+150], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 2.19999999999999999e150

   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 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in b around 0 76.9%

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

   7. Taylor expanded in z around inf 18.3%

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

   if 2.19999999999999999e150 < 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 49.8%

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

   4. Taylor expanded in a around inf 39.6%

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

Alternative 16: 16.2% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 34.9%

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

4. Taylor expanded in a around inf 11.7%

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

Reproduce

herbie shell --seed 2024100 
(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)))