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

Percentage Accurate: 99.8% → 99.8%

Time: 27.4s

Alternatives: 21

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 99.8%

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

   13. sub-neg 99.8%

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

   14. metadata-eval 99.8%

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

   15. +-commutative 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 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 3: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z + (x * log(y)))) + (log(c) * (b - 0.5d0)))
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 + (z + (x * Math.log(y)))) + (Math.log(c) * (b - 0.5)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $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 t around 0 83.9%

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

4. Final simplification 83.9%

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

Alternative 4: 64.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(\left(z + a\right) + -0.5 \cdot \log c\right)\\ t_2 := a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -0.09:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ (+ z a) (* -0.5 (log c)))))
        (t_2 (+ a (+ (* x (log y)) (* y i)))))
   (if (<= x -6.4e+151)
     t_2
     (if (<= x -2.6e+19)
       t_1
       (if (<= x -0.09)
         t_2
         (if (<= x -7.8e-70)
           (+ a (+ z (* (log c) (- b 0.5))))
           (if (<= x 7.8e+31) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + ((z + a) + (-0.5 * log(c)));
	double t_2 = a + ((x * log(y)) + (y * i));
	double tmp;
	if (x <= -6.4e+151) {
		tmp = t_2;
	} else if (x <= -2.6e+19) {
		tmp = t_1;
	} else if (x <= -0.09) {
		tmp = t_2;
	} else if (x <= -7.8e-70) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else if (x <= 7.8e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y * i) + ((z + a) + ((-0.5d0) * log(c)))
    t_2 = a + ((x * log(y)) + (y * i))
    if (x <= (-6.4d+151)) then
        tmp = t_2
    else if (x <= (-2.6d+19)) then
        tmp = t_1
    else if (x <= (-0.09d0)) then
        tmp = t_2
    else if (x <= (-7.8d-70)) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else if (x <= 7.8d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + ((z + a) + (-0.5 * Math.log(c)));
	double t_2 = a + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (x <= -6.4e+151) {
		tmp = t_2;
	} else if (x <= -2.6e+19) {
		tmp = t_1;
	} else if (x <= -0.09) {
		tmp = t_2;
	} else if (x <= -7.8e-70) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else if (x <= 7.8e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + ((z + a) + (-0.5 * math.log(c)))
	t_2 = a + ((x * math.log(y)) + (y * i))
	tmp = 0
	if x <= -6.4e+151:
		tmp = t_2
	elif x <= -2.6e+19:
		tmp = t_1
	elif x <= -0.09:
		tmp = t_2
	elif x <= -7.8e-70:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	elif x <= 7.8e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(-0.5 * log(c))))
	t_2 = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (x <= -6.4e+151)
		tmp = t_2;
	elseif (x <= -2.6e+19)
		tmp = t_1;
	elseif (x <= -0.09)
		tmp = t_2;
	elseif (x <= -7.8e-70)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (x <= 7.8e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + ((z + a) + (-0.5 * log(c)));
	t_2 = a + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (x <= -6.4e+151)
		tmp = t_2;
	elseif (x <= -2.6e+19)
		tmp = t_1;
	elseif (x <= -0.09)
		tmp = t_2;
	elseif (x <= -7.8e-70)
		tmp = a + (z + (log(c) * (b - 0.5)));
	elseif (x <= 7.8e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+151], t$95$2, If[LessEqual[x, -2.6e+19], t$95$1, If[LessEqual[x, -0.09], t$95$2, If[LessEqual[x, -7.8e-70], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+31], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999988e151 or -2.6e19 < x < -0.089999999999999997 or 7.79999999999999999e31 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.8%

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

      8. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around inf 78.9%

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

   7. Taylor expanded in x around 0 78.9%

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

   if -6.39999999999999988e151 < x < -2.6e19 or -7.80000000000000038e-70 < x < 7.79999999999999999e31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.2%

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

      1. +-commutative 98.2%

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

      2. sub-neg 98.2%

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

      3. metadata-eval 98.2%

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

      4. fma-define 98.2%

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

      5. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in t around 0 75.1%

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

   7. Taylor expanded in b around 0 60.8%

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

      1. associate-+r+ 60.8%

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

   9. Simplified 60.8%

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

   if -0.089999999999999997 < x < -7.80000000000000038e-70

   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 x around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. fma-define 99.5%

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

      5. +-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in t around 0 92.1%

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

   7. Taylor expanded in y around 0 92.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+151}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + -0.5 \cdot \log c\right)\\ \mathbf{elif}\;x \leq -0.09:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+207}:\\ \;\;\;\;a + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-250} \lor \neg \left(z \leq -1.26 \cdot 10^{-281}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ (* y i) (+ a (+ z t)))))
   (if (<= z -3.3e+240)
     t_2
     (if (<= z -1.25e+207)
       (+ a (+ z t_1))
       (if (<= z -1.2e+117)
         t_2
         (if (or (<= z -3.7e-250) (not (<= z -1.26e-281)))
           (+ a (+ (* x (log y)) (* y i)))
           (+ (* y i) t_1)))))))

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 t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (z <= -3.3e+240) {
		tmp = t_2;
	} else if (z <= -1.25e+207) {
		tmp = a + (z + t_1);
	} else if (z <= -1.2e+117) {
		tmp = t_2;
	} else if ((z <= -3.7e-250) || !(z <= -1.26e-281)) {
		tmp = a + ((x * log(y)) + (y * i));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = (y * i) + (a + (z + t))
    if (z <= (-3.3d+240)) then
        tmp = t_2
    else if (z <= (-1.25d+207)) then
        tmp = a + (z + t_1)
    else if (z <= (-1.2d+117)) then
        tmp = t_2
    else if ((z <= (-3.7d-250)) .or. (.not. (z <= (-1.26d-281)))) then
        tmp = a + ((x * log(y)) + (y * i))
    else
        tmp = (y * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (z <= -3.3e+240) {
		tmp = t_2;
	} else if (z <= -1.25e+207) {
		tmp = a + (z + t_1);
	} else if (z <= -1.2e+117) {
		tmp = t_2;
	} else if ((z <= -3.7e-250) || !(z <= -1.26e-281)) {
		tmp = a + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = (y * i) + (a + (z + t))
	tmp = 0
	if z <= -3.3e+240:
		tmp = t_2
	elif z <= -1.25e+207:
		tmp = a + (z + t_1)
	elif z <= -1.2e+117:
		tmp = t_2
	elif (z <= -3.7e-250) or not (z <= -1.26e-281):
		tmp = a + ((x * math.log(y)) + (y * i))
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(y * i) + Float64(a + Float64(z + t)))
	tmp = 0.0
	if (z <= -3.3e+240)
		tmp = t_2;
	elseif (z <= -1.25e+207)
		tmp = Float64(a + Float64(z + t_1));
	elseif (z <= -1.2e+117)
		tmp = t_2;
	elseif ((z <= -3.7e-250) || !(z <= -1.26e-281))
		tmp = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = (y * i) + (a + (z + t));
	tmp = 0.0;
	if (z <= -3.3e+240)
		tmp = t_2;
	elseif (z <= -1.25e+207)
		tmp = a + (z + t_1);
	elseif (z <= -1.2e+117)
		tmp = t_2;
	elseif ((z <= -3.7e-250) || ~((z <= -1.26e-281)))
		tmp = a + ((x * log(y)) + (y * i));
	else
		tmp = (y * i) + t_1;
	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]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+240], t$95$2, If[LessEqual[z, -1.25e+207], N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e+117], t$95$2, If[Or[LessEqual[z, -3.7e-250], N[Not[LessEqual[z, -1.26e-281]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2999999999999998e240 or -1.25e207 < z < -1.1999999999999999e117

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.2%

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

      1. +-commutative 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. fma-define 96.2%

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

      5. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in z around inf 83.8%

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

   if -3.2999999999999998e240 < z < -1.25e207

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. sub-neg 76.2%

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

      3. metadata-eval 76.2%

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

      4. fma-define 76.2%

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

      5. +-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around 0 76.2%

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

   7. Taylor expanded in y around 0 76.2%

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

   if -1.1999999999999999e117 < z < -3.6999999999999998e-250 or -1.26e-281 < 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 x around inf 71.3%

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

      1. associate-+r+ 71.3%

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

      2. +-commutative 71.3%

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

      3. +-commutative 71.3%

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

      4. sub-neg 71.3%

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

      5. metadata-eval 71.3%

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

      6. associate-/l* 71.3%

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

      7. fma-define 71.3%

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

      8. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in a around inf 48.0%

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

   7. Taylor expanded in x around 0 58.5%

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

   if -3.6999999999999998e-250 < z < -1.26e-281

   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 x around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. sub-neg 89.4%

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

      3. metadata-eval 89.4%

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

      4. fma-define 89.4%

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

      5. +-commutative 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in t around 0 77.9%

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

   7. Taylor expanded in a around inf 68.1%

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

      1. associate-+r+ 68.1%

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

      2. sub-neg 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in z around 0 68.1%

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

       1. sub-neg 68.1%

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

       2. metadata-eval 68.1%

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

       3. associate-*r/ 67.9%

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

   12. Simplified 67.9%

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

   13. Taylor expanded in a around 0 78.4%

       \[\leadsto \color{blue}{\log c \cdot \left(b - 0.5\right)} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+207}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-250} \lor \neg \left(z \leq -1.26 \cdot 10^{-281}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \log c \cdot \left(b - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;a + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-253} \lor \neg \left(z \leq -1.26 \cdot 10^{-281}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ (* y i) (+ a (+ z t)))))
   (if (<= z -3.3e+240)
     t_2
     (if (<= z -1.3e+207)
       (+ a (+ z t_1))
       (if (<= z -7.8e+117)
         t_2
         (if (or (<= z -4.3e-253) (not (<= z -1.26e-281)))
           (+ a (+ (* x (log y)) (* y i)))
           (+ a t_1)))))))

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 t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (z <= -3.3e+240) {
		tmp = t_2;
	} else if (z <= -1.3e+207) {
		tmp = a + (z + t_1);
	} else if (z <= -7.8e+117) {
		tmp = t_2;
	} else if ((z <= -4.3e-253) || !(z <= -1.26e-281)) {
		tmp = a + ((x * log(y)) + (y * i));
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = (y * i) + (a + (z + t))
    if (z <= (-3.3d+240)) then
        tmp = t_2
    else if (z <= (-1.3d+207)) then
        tmp = a + (z + t_1)
    else if (z <= (-7.8d+117)) then
        tmp = t_2
    else if ((z <= (-4.3d-253)) .or. (.not. (z <= (-1.26d-281)))) then
        tmp = a + ((x * log(y)) + (y * i))
    else
        tmp = a + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double t_2 = (y * i) + (a + (z + t));
	double tmp;
	if (z <= -3.3e+240) {
		tmp = t_2;
	} else if (z <= -1.3e+207) {
		tmp = a + (z + t_1);
	} else if (z <= -7.8e+117) {
		tmp = t_2;
	} else if ((z <= -4.3e-253) || !(z <= -1.26e-281)) {
		tmp = a + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = (y * i) + (a + (z + t))
	tmp = 0
	if z <= -3.3e+240:
		tmp = t_2
	elif z <= -1.3e+207:
		tmp = a + (z + t_1)
	elif z <= -7.8e+117:
		tmp = t_2
	elif (z <= -4.3e-253) or not (z <= -1.26e-281):
		tmp = a + ((x * math.log(y)) + (y * i))
	else:
		tmp = a + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(y * i) + Float64(a + Float64(z + t)))
	tmp = 0.0
	if (z <= -3.3e+240)
		tmp = t_2;
	elseif (z <= -1.3e+207)
		tmp = Float64(a + Float64(z + t_1));
	elseif (z <= -7.8e+117)
		tmp = t_2;
	elseif ((z <= -4.3e-253) || !(z <= -1.26e-281))
		tmp = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = (y * i) + (a + (z + t));
	tmp = 0.0;
	if (z <= -3.3e+240)
		tmp = t_2;
	elseif (z <= -1.3e+207)
		tmp = a + (z + t_1);
	elseif (z <= -7.8e+117)
		tmp = t_2;
	elseif ((z <= -4.3e-253) || ~((z <= -1.26e-281)))
		tmp = a + ((x * log(y)) + (y * i));
	else
		tmp = a + t_1;
	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]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+240], t$95$2, If[LessEqual[z, -1.3e+207], N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e+117], t$95$2, If[Or[LessEqual[z, -4.3e-253], N[Not[LessEqual[z, -1.26e-281]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2999999999999998e240 or -1.2999999999999999e207 < z < -7.79999999999999981e117

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.2%

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

      1. +-commutative 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. fma-define 96.2%

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

      5. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in z around inf 83.8%

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

   if -3.2999999999999998e240 < z < -1.2999999999999999e207

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. sub-neg 76.2%

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

      3. metadata-eval 76.2%

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

      4. fma-define 76.2%

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

      5. +-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around 0 76.2%

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

   7. Taylor expanded in y around 0 76.2%

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

   if -7.79999999999999981e117 < z < -4.3000000000000002e-253 or -1.26e-281 < 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 x around inf 71.4%

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

      1. associate-+r+ 71.4%

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

      2. +-commutative 71.4%

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

      3. +-commutative 71.4%

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

      4. sub-neg 71.4%

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

      5. metadata-eval 71.4%

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

      6. associate-/l* 71.4%

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

      7. fma-define 71.4%

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

      8. +-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in a around inf 48.2%

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

   7. Taylor expanded in x around 0 58.7%

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

   if -4.3000000000000002e-253 < z < -1.26e-281

   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 x around 0 88.1%

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

      1. +-commutative 88.1%

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

      2. sub-neg 88.1%

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

      3. metadata-eval 88.1%

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

      4. fma-define 88.1%

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

      5. +-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around 0 75.1%

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

   7. Taylor expanded in y around 0 50.5%

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

   8. Taylor expanded in z around 0 50.5%

      \[\leadsto \color{blue}{a + \log c \cdot \left(b - 0.5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-253} \lor \neg \left(z \leq -1.26 \cdot 10^{-281}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(a + \left(z + t\right)\right)\\ t_2 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{+70}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+127} \lor \neg \left(x \leq 2.25 \cdot 10^{+216}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ a (+ z t)))) (t_2 (+ (* x (log y)) (* y i))))
   (if (<= x -8.5e+192)
     t_2
     (if (<= x -1.45e+80)
       t_1
       (if (<= x 1e+70)
         (+ a (+ z (* (log c) (- b 0.5))))
         (if (or (<= x 7.2e+127) (not (<= x 2.25e+216))) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (z + t));
	double t_2 = (x * log(y)) + (y * i);
	double tmp;
	if (x <= -8.5e+192) {
		tmp = t_2;
	} else if (x <= -1.45e+80) {
		tmp = t_1;
	} else if (x <= 1e+70) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else if ((x <= 7.2e+127) || !(x <= 2.25e+216)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) + (a + (z + t))
    t_2 = (x * log(y)) + (y * i)
    if (x <= (-8.5d+192)) then
        tmp = t_2
    else if (x <= (-1.45d+80)) then
        tmp = t_1
    else if (x <= 1d+70) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else if ((x <= 7.2d+127) .or. (.not. (x <= 2.25d+216))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (a + (z + t));
	double t_2 = (x * Math.log(y)) + (y * i);
	double tmp;
	if (x <= -8.5e+192) {
		tmp = t_2;
	} else if (x <= -1.45e+80) {
		tmp = t_1;
	} else if (x <= 1e+70) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else if ((x <= 7.2e+127) || !(x <= 2.25e+216)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (a + (z + t))
	t_2 = (x * math.log(y)) + (y * i)
	tmp = 0
	if x <= -8.5e+192:
		tmp = t_2
	elif x <= -1.45e+80:
		tmp = t_1
	elif x <= 1e+70:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	elif (x <= 7.2e+127) or not (x <= 2.25e+216):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(a + Float64(z + t)))
	t_2 = Float64(Float64(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -8.5e+192)
		tmp = t_2;
	elseif (x <= -1.45e+80)
		tmp = t_1;
	elseif (x <= 1e+70)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif ((x <= 7.2e+127) || !(x <= 2.25e+216))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (a + (z + t));
	t_2 = (x * log(y)) + (y * i);
	tmp = 0.0;
	if (x <= -8.5e+192)
		tmp = t_2;
	elseif (x <= -1.45e+80)
		tmp = t_1;
	elseif (x <= 1e+70)
		tmp = a + (z + (log(c) * (b - 0.5)));
	elseif ((x <= 7.2e+127) || ~((x <= 2.25e+216)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+192], t$95$2, If[LessEqual[x, -1.45e+80], t$95$1, If[LessEqual[x, 1e+70], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 7.2e+127], N[Not[LessEqual[x, 2.25e+216]], $MachinePrecision]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999965e192 or 1.00000000000000007e70 < x < 7.19999999999999958e127 or 2.25000000000000012e216 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 86.6%

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

   if -8.49999999999999965e192 < x < -1.44999999999999993e80 or 7.19999999999999958e127 < x < 2.25000000000000012e216

   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 80.5%

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

      1. +-commutative 80.5%

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

      2. sub-neg 80.5%

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

      3. metadata-eval 80.5%

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

      4. fma-define 80.5%

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

      5. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around inf 74.1%

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

   if -1.44999999999999993e80 < x < 1.00000000000000007e70

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. sub-neg 96.6%

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

      3. metadata-eval 96.6%

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

      4. fma-define 96.6%

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

      5. +-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around 0 75.0%

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

   7. Taylor expanded in y around 0 58.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{elif}\;x \leq 10^{+70}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+127} \lor \neg \left(x \leq 2.25 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+130} \lor \neg \left(z \leq -3.8 \cdot 10^{-250}\right) \land z \leq -8.8 \cdot 10^{-283}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -3.7e+130) (and (not (<= z -3.8e-250)) (<= z -8.8e-283)))
   (+ t (+ z (+ (* y i) (* (log c) (- b 0.5)))))
   (+ a (+ (* 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 ((z <= -3.7e+130) || (!(z <= -3.8e-250) && (z <= -8.8e-283))) {
		tmp = t + (z + ((y * i) + (log(c) * (b - 0.5))));
	} else {
		tmp = a + ((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 ((z <= (-3.7d+130)) .or. (.not. (z <= (-3.8d-250))) .and. (z <= (-8.8d-283))) then
        tmp = t + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    else
        tmp = a + ((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 ((z <= -3.7e+130) || (!(z <= -3.8e-250) && (z <= -8.8e-283))) {
		tmp = t + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = a + ((x * Math.log(y)) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -3.7e+130) or (not (z <= -3.8e-250) and (z <= -8.8e-283)):
		tmp = t + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	else:
		tmp = a + ((x * math.log(y)) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -3.7e+130) || (!(z <= -3.8e-250) && (z <= -8.8e-283)))
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(a + Float64(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 ((z <= -3.7e+130) || (~((z <= -3.8e-250)) && (z <= -8.8e-283)))
		tmp = t + (z + ((y * i) + (log(c) * (b - 0.5))));
	else
		tmp = a + ((x * log(y)) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -3.7e+130], And[N[Not[LessEqual[z, -3.8e-250]], $MachinePrecision], LessEqual[z, -8.8e-283]]], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000001e130 or -3.79999999999999971e-250 < z < -8.7999999999999992e-283

   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 91.9%

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

      1. +-commutative 91.9%

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

      2. sub-neg 91.9%

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

      3. metadata-eval 91.9%

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

      4. fma-define 91.9%

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

      5. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in a around 0 89.2%

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

   if -3.7000000000000001e130 < z < -3.79999999999999971e-250 or -8.7999999999999992e-283 < 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 x around inf 71.4%

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

      1. associate-+r+ 71.4%

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

      2. +-commutative 71.4%

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

      3. +-commutative 71.4%

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

      4. sub-neg 71.4%

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

      5. metadata-eval 71.4%

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

      6. associate-/l* 71.4%

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

      7. fma-define 71.4%

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

      8. +-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in a around inf 47.6%

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

   7. Taylor expanded in x around 0 58.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+130} \lor \neg \left(z \leq -3.8 \cdot 10^{-250}\right) \land z \leq -8.8 \cdot 10^{-283}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+230} \lor \neg \left(x \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3e+230) (not (<= x 1.8e+67)))
   (+ a (+ (* 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 <= -3e+230) || !(x <= 1.8e+67)) {
		tmp = a + ((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 <= (-3d+230)) .or. (.not. (x <= 1.8d+67))) then
        tmp = a + ((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 <= -3e+230) || !(x <= 1.8e+67)) {
		tmp = a + ((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 <= -3e+230) or not (x <= 1.8e+67):
		tmp = a + ((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 <= -3e+230) || !(x <= 1.8e+67))
		tmp = Float64(a + Float64(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 <= -3e+230) || ~((x <= 1.8e+67)))
		tmp = a + ((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, -3e+230], N[Not[LessEqual[x, 1.8e+67]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $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 < -3.00000000000000008e230 or 1.7999999999999999e67 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.8%

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

      8. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around inf 83.5%

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

   7. Taylor expanded in x around 0 83.5%

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

   if -3.00000000000000008e230 < x < 1.7999999999999999e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+230} \lor \neg \left(x \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+230} \lor \neg \left(x \leq 1.15 \cdot 10^{+67}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3e+230) (not (<= x 1.15e+67)))
   (+ a (+ (* x (log y)) (* y i)))
   (+ (* y i) (+ a (+ 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 <= -3e+230) || !(x <= 1.15e+67)) {
		tmp = a + ((x * log(y)) + (y * i));
	} else {
		tmp = (y * i) + (a + (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 <= (-3d+230)) .or. (.not. (x <= 1.15d+67))) then
        tmp = a + ((x * log(y)) + (y * i))
    else
        tmp = (y * i) + (a + (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 <= -3e+230) || !(x <= 1.15e+67)) {
		tmp = a + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3e+230) or not (x <= 1.15e+67):
		tmp = a + ((x * math.log(y)) + (y * i))
	else:
		tmp = (y * i) + (a + (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 <= -3e+230) || !(x <= 1.15e+67))
		tmp = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3e+230) || ~((x <= 1.15e+67)))
		tmp = a + ((x * log(y)) + (y * i));
	else
		tmp = (y * i) + (a + (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, -3e+230], N[Not[LessEqual[x, 1.15e+67]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000008e230 or 1.1499999999999999e67 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.8%

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

      8. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around inf 83.5%

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

   7. Taylor expanded in x around 0 83.5%

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

   if -3.00000000000000008e230 < x < 1.1499999999999999e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.3%

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

      1. +-commutative 95.3%

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

      2. sub-neg 95.3%

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

      3. metadata-eval 95.3%

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

      4. fma-define 95.3%

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

      5. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around 0 75.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+230} \lor \neg \left(x \leq 1.15 \cdot 10^{+67}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+272}:\\ \;\;\;\;a + t\_1\\ \mathbf{elif}\;b - 0.5 \leq 10^{+212}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= (- b 0.5) -1e+272)
     (+ a t_1)
     (if (<= (- b 0.5) 1e+212) (+ (* y i) (+ a (+ z t))) t_1))))

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 ((b - 0.5) <= -1e+272) {
		tmp = a + t_1;
	} else if ((b - 0.5) <= 1e+212) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((b - 0.5d0) <= (-1d+272)) then
        tmp = a + t_1
    else if ((b - 0.5d0) <= 1d+212) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((b - 0.5) <= -1e+272) {
		tmp = a + t_1;
	} else if ((b - 0.5) <= 1e+212) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (b - 0.5) <= -1e+272:
		tmp = a + t_1
	elif (b - 0.5) <= 1e+212:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = t_1
	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 (Float64(b - 0.5) <= -1e+272)
		tmp = Float64(a + t_1);
	elseif (Float64(b - 0.5) <= 1e+212)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = t_1;
	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 ((b - 0.5) <= -1e+272)
		tmp = a + t_1;
	elseif ((b - 0.5) <= 1e+212)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = t_1;
	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[N[(b - 0.5), $MachinePrecision], -1e+272], N[(a + t$95$1), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+212], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -1.0000000000000001e272

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. fma-define 99.8%

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

      5. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 87.1%

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

   7. Taylor expanded in y around 0 72.8%

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

   8. Taylor expanded in z around 0 72.8%

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

   if -1.0000000000000001e272 < (-.f64 b #s(literal 1/2 binary64)) < 9.9999999999999991e211

   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 79.4%

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

      1. +-commutative 79.4%

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

      2. sub-neg 79.4%

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

      3. metadata-eval 79.4%

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

      4. fma-define 79.4%

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

      5. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 69.3%

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

   if 9.9999999999999991e211 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. sub-neg 93.3%

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

      3. metadata-eval 93.3%

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

      4. fma-define 93.3%

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

      5. +-commutative 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in t around 0 93.3%

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

   7. Taylor expanded in a around inf 56.4%

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

      1. associate-+r+ 56.4%

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

      2. sub-neg 56.4%

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

      3. metadata-eval 56.4%

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

      4. associate-/l* 56.4%

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

   9. Simplified 56.4%

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

   10. Taylor expanded in z around 0 50.6%

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

       1. sub-neg 50.6%

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

       2. metadata-eval 50.6%

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

       3. associate-*r/ 50.6%

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

   12. Simplified 50.6%

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

   13. Taylor expanded in a around 0 74.8%

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

   14. Taylor expanded in y around 0 61.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+272}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+212}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+256}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 10^{+212}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (- b 0.5) -1e+256)
   (* b (log c))
   (if (<= (- b 0.5) 1e+212) (+ (* y i) (+ a (+ z t))) (* (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 ((b - 0.5) <= -1e+256) {
		tmp = b * log(c);
	} else if ((b - 0.5) <= 1e+212) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = 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 ((b - 0.5d0) <= (-1d+256)) then
        tmp = b * log(c)
    else if ((b - 0.5d0) <= 1d+212) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = 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 ((b - 0.5) <= -1e+256) {
		tmp = b * Math.log(c);
	} else if ((b - 0.5) <= 1e+212) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = Math.log(c) * (b - 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b - 0.5) <= -1e+256:
		tmp = b * math.log(c)
	elif (b - 0.5) <= 1e+212:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = math.log(c) * (b - 0.5)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+256)
		tmp = Float64(b * log(c));
	elseif (Float64(b - 0.5) <= 1e+212)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = 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 ((b - 0.5) <= -1e+256)
		tmp = b * log(c);
	elseif ((b - 0.5) <= 1e+212)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = log(c) * (b - 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+256], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+212], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -1e256

   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 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. fma-define 99.8%

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

      5. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 79.8%

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

   7. Taylor expanded in a around inf 54.2%

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

      1. associate-+r+ 54.2%

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

      2. sub-neg 54.2%

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

      3. metadata-eval 54.2%

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

      4. associate-/l* 54.2%

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

   9. Simplified 54.2%

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

   10. Taylor expanded in z around 0 54.2%

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

       1. sub-neg 54.2%

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

       2. metadata-eval 54.2%

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

       3. associate-*r/ 54.2%

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

   12. Simplified 54.2%

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

   13. Taylor expanded in a around 0 77.1%

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

   14. Taylor expanded in b around inf 67.1%

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

       1. *-commutative 67.1%

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

   16. Simplified 67.1%

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

   if -1e256 < (-.f64 b #s(literal 1/2 binary64)) < 9.9999999999999991e211

   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. Step-by-step derivation

      1. +-commutative 79.1%

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

      2. sub-neg 79.1%

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

      3. metadata-eval 79.1%

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

      4. fma-define 79.1%

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

      5. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 70.1%

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

   if 9.9999999999999991e211 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. sub-neg 93.3%

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

      3. metadata-eval 93.3%

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

      4. fma-define 93.3%

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

      5. +-commutative 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in t around 0 93.3%

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

   7. Taylor expanded in a around inf 56.4%

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

      1. associate-+r+ 56.4%

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

      2. sub-neg 56.4%

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

      3. metadata-eval 56.4%

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

      4. associate-/l* 56.4%

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

   9. Simplified 56.4%

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

   10. Taylor expanded in z around 0 50.6%

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

       1. sub-neg 50.6%

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

       2. metadata-eval 50.6%

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

       3. associate-*r/ 50.6%

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

   12. Simplified 50.6%

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

   13. Taylor expanded in a around 0 74.8%

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

   14. Taylor expanded in y around 0 61.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+256}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq 10^{+212}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+188} \lor \neg \left(x \leq 2.55 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.6e+188) (not (<= x 2.55e+216)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ 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 <= -5.6e+188) || !(x <= 2.55e+216)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (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 <= (-5.6d+188)) .or. (.not. (x <= 2.55d+216))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (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 <= -5.6e+188) || !(x <= 2.55e+216)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5.6e+188) or not (x <= 2.55e+216):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.6e+188) || !(x <= 2.55e+216))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + 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 <= -5.6e+188) || ~((x <= 2.55e+216)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.6e+188], N[Not[LessEqual[x, 2.55e+216]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5999999999999996e188 or 2.55e216 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 89.5%

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

   if -5.5999999999999996e188 < x < 2.55e216

   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 91.6%

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

      1. +-commutative 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

      4. fma-define 91.6%

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

      5. +-commutative 91.6%

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

   5. Simplified 91.6%

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

   6. Taylor expanded in z around inf 73.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+188} \lor \neg \left(x \leq 2.55 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+265}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+192}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -4.6e+265)
   (+ a (* (log c) (- b 0.5)))
   (if (<= b 2.25e+192) (+ (* y i) (+ a (+ z t))) (+ t (+ z (* b (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -4.6e+265) {
		tmp = a + (log(c) * (b - 0.5));
	} else if (b <= 2.25e+192) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t + (z + (b * log(c)));
	}
	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 <= (-4.6d+265)) then
        tmp = a + (log(c) * (b - 0.5d0))
    else if (b <= 2.25d+192) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = t + (z + (b * log(c)))
    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 <= -4.6e+265) {
		tmp = a + (Math.log(c) * (b - 0.5));
	} else if (b <= 2.25e+192) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t + (z + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -4.6e+265:
		tmp = a + (math.log(c) * (b - 0.5))
	elif b <= 2.25e+192:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = t + (z + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -4.6e+265)
		tmp = Float64(a + Float64(log(c) * Float64(b - 0.5)));
	elseif (b <= 2.25e+192)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(t + Float64(z + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -4.6e+265)
		tmp = a + (log(c) * (b - 0.5));
	elseif (b <= 2.25e+192)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = t + (z + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -4.6e+265], N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+192], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5999999999999999e265

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. fma-define 99.8%

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

      5. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 87.1%

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

   7. Taylor expanded in y around 0 72.8%

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

   8. Taylor expanded in z around 0 72.8%

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

   if -4.5999999999999999e265 < b < 2.25e192

   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 79.0%

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

      1. +-commutative 79.0%

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

      2. sub-neg 79.0%

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

      3. metadata-eval 79.0%

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

      4. fma-define 79.0%

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

      5. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around inf 68.7%

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

   if 2.25e192 < b

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. sub-neg 94.7%

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

      3. metadata-eval 94.7%

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

      4. fma-define 94.7%

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

      5. +-commutative 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in a around 0 84.7%

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

   7. Taylor expanded in b around inf 58.7%

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

      1. *-commutative 58.7%

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

   9. Simplified 58.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+265}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+192}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+249} \lor \neg \left(b \leq 1.05 \cdot 10^{+213}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.56e+249) (not (<= b 1.05e+213)))
   (* b (log c))
   (+ (* y i) (+ 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 ((b <= -1.56e+249) || !(b <= 1.05e+213)) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (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 ((b <= (-1.56d+249)) .or. (.not. (b <= 1.05d+213))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (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 ((b <= -1.56e+249) || !(b <= 1.05e+213)) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.56e+249) or not (b <= 1.05e+213):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.56e+249) || !(b <= 1.05e+213))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + 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 ((b <= -1.56e+249) || ~((b <= 1.05e+213)))
		tmp = b * log(c);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.56e+249], N[Not[LessEqual[b, 1.05e+213]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.56e249 or 1.05e213 < b

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. sub-neg 95.9%

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

      3. metadata-eval 95.9%

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

      4. fma-define 95.9%

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

      5. +-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in t around 0 87.9%

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

   7. Taylor expanded in a around inf 55.5%

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

      1. associate-+r+ 55.5%

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

      2. sub-neg 55.5%

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

      3. metadata-eval 55.5%

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

      4. associate-/l* 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in z around 0 52.0%

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

       1. sub-neg 52.0%

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

       2. metadata-eval 52.0%

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

       3. associate-*r/ 52.0%

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

   12. Simplified 52.0%

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

   13. Taylor expanded in a around 0 75.7%

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

   14. Taylor expanded in b around inf 63.7%

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

       1. *-commutative 63.7%

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

   16. Simplified 63.7%

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

   if -1.56e249 < b < 1.05e213

   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. Step-by-step derivation

      1. +-commutative 79.1%

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

      2. sub-neg 79.1%

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

      3. metadata-eval 79.1%

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

      4. fma-define 79.1%

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

      5. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 70.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+249} \lor \neg \left(b \leq 1.05 \cdot 10^{+213}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.8% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+145} \lor \neg \left(i \leq 1.45 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -7.5e+145) (not (<= i 1.45e+65))) (* y i) z))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -7.5e+145) || !(i <= 1.45e+65)) {
		tmp = y * i;
	} else {
		tmp = z;
	}
	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 ((i <= (-7.5d+145)) .or. (.not. (i <= 1.45d+65))) then
        tmp = y * i
    else
        tmp = z
    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 ((i <= -7.5e+145) || !(i <= 1.45e+65)) {
		tmp = y * i;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -7.5e+145) or not (i <= 1.45e+65):
		tmp = y * i
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -7.5e+145) || !(i <= 1.45e+65))
		tmp = Float64(y * i);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -7.5e+145) || ~((i <= 1.45e+65)))
		tmp = y * i;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -7.5e+145], N[Not[LessEqual[i, 1.45e+65]], $MachinePrecision]], N[(y * i), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if i < -7.50000000000000006e145 or 1.45e65 < i

   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 x around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. sub-neg 90.5%

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

      3. metadata-eval 90.5%

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

      4. fma-define 90.5%

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

      5. +-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around inf 52.3%

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

   if -7.50000000000000006e145 < i < 1.45e65

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 23.3%

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

   4. Taylor expanded in i around inf 13.2%

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

   5. Taylor expanded in z around inf 12.8%

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

   6. Taylor expanded in i around 0 9.9%

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

   7. Taylor expanded in i around 0 19.9%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+145} \lor \neg \left(i \leq 1.45 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.9% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.8 \cdot 10^{+83}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.8e+83) (+ z (* y i)) (+ (+ t 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 <= 2.8e+83) {
		tmp = z + (y * i);
	} else {
		tmp = (t + 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 <= 2.8d+83) then
        tmp = z + (y * i)
    else
        tmp = (t + 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 <= 2.8e+83) {
		tmp = z + (y * i);
	} else {
		tmp = (t + a) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.8e+83:
		tmp = z + (y * i)
	else:
		tmp = (t + a) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.8e+83)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(t + 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 <= 2.8e+83)
		tmp = z + (y * i);
	else
		tmp = (t + a) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.8e+83], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.8e83

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 36.2%

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

   if 2.8e83 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. sub-neg 88.9%

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

      3. metadata-eval 88.9%

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

      4. fma-define 88.9%

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

      5. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around inf 75.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.8 \cdot 10^{+83}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.35 \cdot 10^{+110}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.35e+110) (+ 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 <= 1.35e+110) {
		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 <= 1.35d+110) 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 <= 1.35e+110) {
		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 <= 1.35e+110:
		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 <= 1.35e+110)
		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 <= 1.35e+110)
		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, 1.35e+110], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.35000000000000005e110

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 36.6%

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

   if 1.35000000000000005e110 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 67.1%

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

Alternative 19: 32.9% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -5.6e-33) 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 (t <= -5.6e-33) {
		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 (t <= (-5.6d-33)) 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 (t <= -5.6e-33) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -5.6e-33:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -5.6e-33)
		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 (t <= -5.6e-33)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -5.6e-33], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6e-33

   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 33.7%

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

   4. Taylor expanded in i around inf 25.8%

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

   5. Taylor expanded in z around inf 25.9%

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

   6. Taylor expanded in i around 0 11.6%

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

   7. Taylor expanded in i around 0 19.4%

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

   if -5.6e-33 < t

   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 38.7%

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

Alternative 20: 67.1% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

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 + (z + t))
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 + (z + t));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $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 x around 0 80.8%

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

   1. +-commutative 80.8%

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

   2. sub-neg 80.8%

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

   3. metadata-eval 80.8%

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

   4. fma-define 80.8%

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

   5. +-commutative 80.8%

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

5. Simplified 80.8%

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

6. Taylor expanded in z around inf 65.8%

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

7. Final simplification 65.8%

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

Alternative 21: 16.5% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 z around inf 35.1%

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

4. Taylor expanded in i around inf 28.3%

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

5. Taylor expanded in z around inf 27.6%

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

6. Taylor expanded in i around 0 9.7%

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

7. Taylor expanded in i around 0 16.6%

   \[\leadsto \color{blue}{z} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(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)))