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

Percentage Accurate: 99.8% → 99.8%

Time: 17.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.8%

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

   1. associate-+l+ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+l+ 99.8%

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

   4. associate-+r+ 99.8%

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

   5. +-commutative 99.8%

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

   6. +-commutative 99.8%

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

   7. associate-+l+ 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. fma-define 99.8%

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

   11. +-commutative 99.8%

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

   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. 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: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;y \leq 350000000:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= y 350000000.0)
     (+ a (+ t (+ z (+ (* x (log y)) t_1))))
     (+ (* y i) (+ t_1 (+ a (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (y <= 350000000.0) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	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 = log(c) * (b - 0.5d0)
    if (y <= 350000000.0d0) then
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    else
        tmp = (y * i) + (t_1 + (a + (z + t)))
    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 = Math.log(c) * (b - 0.5);
	double tmp;
	if (y <= 350000000.0) {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if y <= 350000000.0:
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	else:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (y <= 350000000.0)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (y <= 350000000.0)
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	else
		tmp = (y * i) + (t_1 + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 350000000.0], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.5e8

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.1%

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

   if 3.5e8 < 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 x around 0 91.1%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 350000000:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
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 99.8%

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

3. Final simplification 99.8%

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

Alternative 4: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

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

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

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

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

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 99.8%

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

3. Taylor expanded in b around inf 98.3%

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

   1. *-commutative 98.3%

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

5. Simplified 98.3%

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

6. Final simplification 98.3%

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

Alternative 5: 94.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+46} \lor \neg \left(x \leq 2.4 \cdot 10^{+53}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.8e+46) (not (<= x 2.4e+53)))
   (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.8e+46) || !(x <= 2.4e+53)) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	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 <= (-3.8d+46)) .or. (.not. (x <= 2.4d+53))) then
        tmp = a + (t + (z + ((x * log(y)) + (y * i))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    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 <= -3.8e+46) || !(x <= 2.4e+53)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.8e+46) or not (x <= 2.4e+53):
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.8e+46) || !(x <= 2.4e+53))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.8e+46) || ~((x <= 2.4e+53)))
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.8e+46], N[Not[LessEqual[x, 2.4e+53]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999999e46 or 2.4e53 < 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 90.0%

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

   if -3.7999999999999999e46 < x < 2.4e53

   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%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+46} \lor \neg \left(x \leq 2.4 \cdot 10^{+53}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+249}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y + b \cdot \frac{\log c}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= b -3.6e+257)
     t_1
     (if (<= b 2e+249)
       (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
       (if (<= b 6.2e+273) t_1 (* i (+ y (* b (/ (log c) i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (b <= -3.6e+257) {
		tmp = t_1;
	} else if (b <= 2e+249) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else if (b <= 6.2e+273) {
		tmp = t_1;
	} else {
		tmp = i * (y + (b * (log(c) / i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (b <= (-3.6d+257)) then
        tmp = t_1
    else if (b <= 2d+249) then
        tmp = a + (t + (z + ((x * log(y)) + (y * i))))
    else if (b <= 6.2d+273) then
        tmp = t_1
    else
        tmp = i * (y + (b * (log(c) / i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (b <= -3.6e+257) {
		tmp = t_1;
	} else if (b <= 2e+249) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	} else if (b <= 6.2e+273) {
		tmp = t_1;
	} else {
		tmp = i * (y + (b * (Math.log(c) / i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if b <= -3.6e+257:
		tmp = t_1
	elif b <= 2e+249:
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	elif b <= 6.2e+273:
		tmp = t_1
	else:
		tmp = i * (y + (b * (math.log(c) / i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -3.6e+257)
		tmp = t_1;
	elseif (b <= 2e+249)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	elseif (b <= 6.2e+273)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y + Float64(b * Float64(log(c) / i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (b <= -3.6e+257)
		tmp = t_1;
	elseif (b <= 2e+249)
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	elseif (b <= 6.2e+273)
		tmp = t_1;
	else
		tmp = i * (y + (b * (log(c) / i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+257], t$95$1, If[LessEqual[b, 2e+249], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+273], t$95$1, N[(i * N[(y + N[(b * N[(N[Log[c], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.59999999999999984e257 or 1.9999999999999998e249 < b < 6.2000000000000002e273

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in i around inf 52.1%

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

      1. associate-/l* 52.0%

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

      2. associate-/l* 52.0%

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

   8. Simplified 52.0%

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

   9. Taylor expanded in b around inf 95.2%

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

   if -3.59999999999999984e257 < b < 1.9999999999999998e249

   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 98.2%

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

      1. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in b around 0 88.6%

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

   if 6.2000000000000002e273 < b

   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 i around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in b around inf 100.0%

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

       1. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+257}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+249}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+273}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y + b \cdot \frac{\log c}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+145} \lor \neg \left(x \leq 2.05 \cdot 10^{+53}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.35e+145) (not (<= x 2.05e+53)))
   (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
   (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.35e+145) || !(x <= 2.05e+53)) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	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 <= (-1.35d+145)) .or. (.not. (x <= 2.05d+53))) then
        tmp = a + (t + (z + ((x * log(y)) + (y * i))))
    else
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    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 <= -1.35e+145) || !(x <= 2.05e+53)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.35e+145) or not (x <= 2.05e+53):
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	else:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.35e+145) || !(x <= 2.05e+53))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.35e+145) || ~((x <= 2.05e+53)))
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	else
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.35e+145], N[Not[LessEqual[x, 2.05e+53]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000011e145 or 2.05000000000000009e53 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in b around 0 90.7%

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

   if -1.35000000000000011e145 < x < 2.05000000000000009e53

   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 97.7%

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

      1. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around 0 96.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+145} \lor \neg \left(x \leq 2.05 \cdot 10^{+53}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+166} \lor \neg \left(x \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.25e+166) (not (<= x 3.2e+111)))
   (+ t (+ z (+ (* x (log y)) (* y i))))
   (+ 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 <= -1.25e+166) || !(x <= 3.2e+111)) {
		tmp = t + (z + ((x * log(y)) + (y * i)));
	} 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 <= (-1.25d+166)) .or. (.not. (x <= 3.2d+111))) then
        tmp = t + (z + ((x * log(y)) + (y * i)))
    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 <= -1.25e+166) || !(x <= 3.2e+111)) {
		tmp = t + (z + ((x * Math.log(y)) + (y * i)));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.25e+166) or not (x <= 3.2e+111):
		tmp = t + (z + ((x * math.log(y)) + (y * i)))
	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 <= -1.25e+166) || !(x <= 3.2e+111))
		tmp = Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i))));
	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 <= -1.25e+166) || ~((x <= 3.2e+111)))
		tmp = t + (z + ((x * log(y)) + (y * i)));
	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, -1.25e+166], N[Not[LessEqual[x, 3.2e+111]], $MachinePrecision]], N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $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 x < -1.25e166 or 3.2000000000000001e111 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in b around 0 89.3%

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

   7. Taylor expanded in a around 0 81.0%

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

   if -1.25e166 < x < 3.2000000000000001e111

   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 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in b around 0 80.9%

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

   7. Taylor expanded in x around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. *-commutative 78.5%

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

   9. Simplified 78.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+166} \lor \neg \left(x \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+155} \lor \neg \left(x \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+155) (not (<= x 8e+117)))
   (* x (+ (log y) (/ a x)))
   (+ 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 <= -4.8e+155) || !(x <= 8e+117)) {
		tmp = x * (log(y) + (a / x));
	} 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 <= (-4.8d+155)) .or. (.not. (x <= 8d+117))) then
        tmp = x * (log(y) + (a / x))
    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 <= -4.8e+155) || !(x <= 8e+117)) {
		tmp = x * (Math.log(y) + (a / x));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+155) or not (x <= 8e+117):
		tmp = x * (math.log(y) + (a / x))
	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 <= -4.8e+155) || !(x <= 8e+117))
		tmp = Float64(x * Float64(log(y) + Float64(a / x)));
	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 <= -4.8e+155) || ~((x <= 8e+117)))
		tmp = x * (log(y) + (a / x));
	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, -4.8e+155], N[Not[LessEqual[x, 8e+117]], $MachinePrecision]], N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $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 x < -4.80000000000000042e155 or 8.0000000000000004e117 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.6%

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

      1. associate-/l* 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-/l* 99.6%

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

      5. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf 66.8%

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

   if -4.80000000000000042e155 < x < 8.0000000000000004e117

   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 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in b around 0 80.8%

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

   7. Taylor expanded in x around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. *-commutative 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+155} \lor \neg \left(x \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+173} \lor \neg \left(x \leq 4 \cdot 10^{+152}\right):\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.4e+173) (not (<= x 4e+152)))
   (* x (+ (log y) (/ z x)))
   (+ 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 <= -2.4e+173) || !(x <= 4e+152)) {
		tmp = x * (log(y) + (z / x));
	} 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 <= (-2.4d+173)) .or. (.not. (x <= 4d+152))) then
        tmp = x * (log(y) + (z / x))
    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 <= -2.4e+173) || !(x <= 4e+152)) {
		tmp = x * (Math.log(y) + (z / x));
	} else {
		tmp = a + (t + (z + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.4e+173) or not (x <= 4e+152):
		tmp = x * (math.log(y) + (z / x))
	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 <= -2.4e+173) || !(x <= 4e+152))
		tmp = Float64(x * Float64(log(y) + Float64(z / x)));
	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 <= -2.4e+173) || ~((x <= 4e+152)))
		tmp = x * (log(y) + (z / x));
	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, -2.4e+173], N[Not[LessEqual[x, 4e+152]], $MachinePrecision]], N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $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 x < -2.3999999999999999e173 or 4.0000000000000002e152 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-/l* 99.6%

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

      5. +-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 67.9%

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

   if -2.3999999999999999e173 < x < 4.0000000000000002e152

   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 b around inf 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in b around 0 80.7%

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

   7. Taylor expanded in x around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. *-commutative 77.1%

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

   9. Simplified 77.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+173} \lor \neg \left(x \leq 4 \cdot 10^{+152}\right):\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+214} \lor \neg \left(x \leq 5 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.1e+214) (not (<= x 5e+157)))
   (* 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 <= -2.1e+214) || !(x <= 5e+157)) {
		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 <= (-2.1d+214)) .or. (.not. (x <= 5d+157))) 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 <= -2.1e+214) || !(x <= 5e+157)) {
		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 <= -2.1e+214) or not (x <= 5e+157):
		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 <= -2.1e+214) || !(x <= 5e+157))
		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 <= -2.1e+214) || ~((x <= 5e+157)))
		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, -2.1e+214], N[Not[LessEqual[x, 5e+157]], $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 < -2.1000000000000001e214 or 4.99999999999999976e157 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 71.7%

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

   if -2.1000000000000001e214 < x < 4.99999999999999976e157

   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 98.0%

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

      1. *-commutative 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in b around 0 81.3%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. *-commutative 76.3%

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

   9. Simplified 76.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+214} \lor \neg \left(x \leq 5 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.6% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-63} \lor \neg \left(z \leq -6.2 \cdot 10^{-154}\right) \land z \leq -1.52 \cdot 10^{-195}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.65e+106)
   z
   (if (or (<= z -6.2e-63) (and (not (<= z -6.2e-154)) (<= z -1.52e-195)))
     (* y i)
     a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.65e+106) {
		tmp = z;
	} else if ((z <= -6.2e-63) || (!(z <= -6.2e-154) && (z <= -1.52e-195))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.65d+106)) then
        tmp = z
    else if ((z <= (-6.2d-63)) .or. (.not. (z <= (-6.2d-154))) .and. (z <= (-1.52d-195))) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.65e+106) {
		tmp = z;
	} else if ((z <= -6.2e-63) || (!(z <= -6.2e-154) && (z <= -1.52e-195))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.65e+106:
		tmp = z
	elif (z <= -6.2e-63) or (not (z <= -6.2e-154) and (z <= -1.52e-195)):
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.65e+106)
		tmp = z;
	elseif ((z <= -6.2e-63) || (!(z <= -6.2e-154) && (z <= -1.52e-195)))
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.65e+106)
		tmp = z;
	elseif ((z <= -6.2e-63) || (~((z <= -6.2e-154)) && (z <= -1.52e-195)))
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.65e+106], z, If[Or[LessEqual[z, -6.2e-63], And[N[Not[LessEqual[z, -6.2e-154]], $MachinePrecision], LessEqual[z, -1.52e-195]]], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000004e106

   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 z around inf 35.3%

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

   if -1.65000000000000004e106 < z < -6.19999999999999968e-63 or -6.19999999999999963e-154 < z < -1.5200000000000001e-195

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 30.1%

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

      1. *-commutative 30.1%

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

   5. Simplified 30.1%

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

   if -6.19999999999999968e-63 < z < -6.19999999999999963e-154 or -1.5200000000000001e-195 < 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 20.8%

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

4. Final simplification 24.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-63} \lor \neg \left(z \leq -6.2 \cdot 10^{-154}\right) \land z \leq -1.52 \cdot 10^{-195}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.6% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+254}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(y + \frac{z}{i}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.4e+254)
   z
   (if (<= z -8.6e+57)
     (* i (+ y (/ z i)))
     (if (<= z -1.1e-270) (* i (+ y (/ a i))) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.4e+254) {
		tmp = z;
	} else if (z <= -8.6e+57) {
		tmp = i * (y + (z / i));
	} else if (z <= -1.1e-270) {
		tmp = i * (y + (a / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.4d+254)) then
        tmp = z
    else if (z <= (-8.6d+57)) then
        tmp = i * (y + (z / i))
    else if (z <= (-1.1d-270)) then
        tmp = i * (y + (a / i))
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.4e+254) {
		tmp = z;
	} else if (z <= -8.6e+57) {
		tmp = i * (y + (z / i));
	} else if (z <= -1.1e-270) {
		tmp = i * (y + (a / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.4e+254:
		tmp = z
	elif z <= -8.6e+57:
		tmp = i * (y + (z / i))
	elif z <= -1.1e-270:
		tmp = i * (y + (a / i))
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.4e+254)
		tmp = z;
	elseif (z <= -8.6e+57)
		tmp = Float64(i * Float64(y + Float64(z / i)));
	elseif (z <= -1.1e-270)
		tmp = Float64(i * Float64(y + Float64(a / i)));
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.4e+254)
		tmp = z;
	elseif (z <= -8.6e+57)
		tmp = i * (y + (z / i));
	elseif (z <= -1.1e-270)
		tmp = i * (y + (a / i));
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.4e+254], z, If[LessEqual[z, -8.6e+57], N[(i * N[(y + N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-270], N[(i * N[(y + N[(a / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], a]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3999999999999998e254

   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 z around inf 93.0%

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

   if -2.3999999999999998e254 < z < -8.60000000000000066e57

   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 i around inf 70.4%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in z around inf 37.9%

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

   if -8.60000000000000066e57 < z < -1.0999999999999999e-270

   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 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in i around inf 82.4%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in a around inf 43.5%

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

   if -1.0999999999999999e-270 < 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 22.6%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+254}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(y + \frac{z}{i}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.5% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.4e+106) z (if (<= z -1e-270) (* i (+ y (/ a i))) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.4e+106) {
		tmp = z;
	} else if (z <= -1e-270) {
		tmp = i * (y + (a / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.4d+106)) then
        tmp = z
    else if (z <= (-1d-270)) then
        tmp = i * (y + (a / i))
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.4e+106) {
		tmp = z;
	} else if (z <= -1e-270) {
		tmp = i * (y + (a / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.4e+106:
		tmp = z
	elif z <= -1e-270:
		tmp = i * (y + (a / i))
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.4e+106)
		tmp = z;
	elseif (z <= -1e-270)
		tmp = Float64(i * Float64(y + Float64(a / i)));
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.4e+106)
		tmp = z;
	elseif (z <= -1e-270)
		tmp = i * (y + (a / i));
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.4e+106], z, If[LessEqual[z, -1e-270], N[(i * N[(y + N[(a / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -1.39999999999999996e106

   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 z around inf 35.3%

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

   if -1.39999999999999996e106 < z < -1e-270

   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 98.2%

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

      1. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in i around inf 79.9%

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

      1. associate-/l* 79.9%

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

      2. associate-/l* 79.8%

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

   8. Simplified 79.8%

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

   9. Taylor expanded in a around inf 41.6%

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

   if -1e-270 < 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 22.6%

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

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.1% 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 99.8%

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

3. Taylor expanded in b around inf 98.3%

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

   1. *-commutative 98.3%

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

5. Simplified 98.3%

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

6. Taylor expanded in b around 0 83.0%

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

7. Taylor expanded in x around 0 66.3%

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

   1. +-commutative 66.3%

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

   2. *-commutative 66.3%

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

9. Simplified 66.3%

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

10. Final simplification 66.3%

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

Alternative 16: 21.3% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+105}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.3e+105) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e+105) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.3d+105)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e+105) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.3e+105:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.3e+105)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.3e+105)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.3e+105], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e105

   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 z around inf 35.3%

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

   if -1.3000000000000001e105 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 20.9%

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

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+105}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 16.3% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around inf 19.0%

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

4. Final simplification 19.0%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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)))