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

Percentage Accurate: 99.8% → 99.8%

Time: 17.8s

Alternatives: 18

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

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (- b 0.5) (log c) (+ t (fma x (log y) (+ z 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), (t + fma(x, log(y), (z + a)))));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(y, i, fma(Float64(b - 0.5), log(c), Float64(t + fma(x, log(y), Float64(z + 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[(t + N[(x * N[Log[y], $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. +-commutative 99.9%

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

   7. fma-def 99.9%

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

   8. +-commutative 99.9%

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

   9. fma-def 99.9%

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

   10. +-commutative 99.9%

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

   11. associate-+l+ 99.9%

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

   12. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+52} \lor \neg \left(x \leq 1.9 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.4e+52) (not (<= x 1.9e+125)))
   (+ (* y i) (+ a (+ z (+ (* x (log y)) (* (log c) -0.5)))))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.4e+52) || !(x <= 1.9e+125)) {
		tmp = (y * i) + (a + (z + ((x * log(y)) + (log(c) * -0.5))));
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + 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 ((x <= (-1.4d+52)) .or. (.not. (x <= 1.9d+125))) then
        tmp = (y * i) + (a + (z + ((x * log(y)) + (log(c) * (-0.5d0)))))
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (t + 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 ((x <= -1.4e+52) || !(x <= 1.9e+125)) {
		tmp = (y * i) + (a + (z + ((x * Math.log(y)) + (Math.log(c) * -0.5))));
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (t + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.4e+52) or not (x <= 1.9e+125):
		tmp = (y * i) + (a + (z + ((x * math.log(y)) + (math.log(c) * -0.5))))
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (t + z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.4e+52) || !(x <= 1.9e+125))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * -0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(t + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.4e+52) || ~((x <= 1.9e+125)))
		tmp = (y * i) + (a + (z + ((x * log(y)) + (log(c) * -0.5))));
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.4e+52], N[Not[LessEqual[x, 1.9e+125]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e52 or 1.90000000000000001e125 < 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. Taylor expanded in t around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-+r+ 89.4%

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

      3. +-commutative 89.4%

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

      4. +-commutative 89.4%

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

      5. fma-def 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in b around 0 84.4%

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

   if -1.4e52 < x < 1.90000000000000001e125

   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. Taylor expanded in x around 0 98.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+52} \lor \neg \left(x \leq 1.9 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ a (+ t (+ z (* x (log y))))) (* (- 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 ((a + (t + (z + (x * log(y))))) + ((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 = ((a + (t + (z + (x * log(y))))) + ((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 ((a + (t + (z + (x * Math.log(y))))) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

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

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((a + (t + (z + (x * log(y))))) + ((b - 0.5) * log(c))) + (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[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in b around inf 98.9%

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

   1. *-commutative 48.6%

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

4. Simplified 98.9%

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

5. Final simplification 98.9%

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

Alternative 5: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+213} \lor \neg \left(x \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.5e+213) (not (<= x 5e+153)))
   (+ (* y i) (+ (* x (log y)) (* b (log c))))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+213) || !(x <= 5e+153)) {
		tmp = (y * i) + ((x * log(y)) + (b * log(c)));
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + 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 ((x <= (-2.5d+213)) .or. (.not. (x <= 5d+153))) then
        tmp = (y * i) + ((x * log(y)) + (b * log(c)))
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (t + 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 ((x <= -2.5e+213) || !(x <= 5e+153)) {
		tmp = (y * i) + ((x * Math.log(y)) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (t + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.5e+213) or not (x <= 5e+153):
		tmp = (y * i) + ((x * math.log(y)) + (b * math.log(c)))
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (t + z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.5e+213) || !(x <= 5e+153))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(t + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.5e+213) || ~((x <= 5e+153)))
		tmp = (y * i) + ((x * log(y)) + (b * log(c)));
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.5e+213], N[Not[LessEqual[x, 5e+153]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e213 or 5.00000000000000018e153 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 85.8%

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

   3. Taylor expanded in b around inf 85.8%

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

      1. *-commutative 26.1%

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

   5. Simplified 85.8%

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

   if -2.4999999999999999e213 < x < 5.00000000000000018e153

   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. Taylor expanded in x around 0 94.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+213} \lor \neg \left(x \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 6: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+236} \lor \neg \left(x \leq 1.2 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot \log y + t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t_1 + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (or (<= x -9.6e+236) (not (<= x 1.2e+163)))
     (+ (* x (log y)) t_1)
     (+ (* y i) (+ t_1 (+ a (+ t z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if ((x <= -9.6e+236) || !(x <= 1.2e+163)) {
		tmp = (x * log(y)) + t_1;
	} else {
		tmp = (y * i) + (t_1 + (a + (t + 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) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if ((x <= (-9.6d+236)) .or. (.not. (x <= 1.2d+163))) then
        tmp = (x * log(y)) + t_1
    else
        tmp = (y * i) + (t_1 + (a + (t + 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 t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if ((x <= -9.6e+236) || !(x <= 1.2e+163)) {
		tmp = (x * Math.log(y)) + t_1;
	} else {
		tmp = (y * i) + (t_1 + (a + (t + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if (x <= -9.6e+236) or not (x <= 1.2e+163):
		tmp = (x * math.log(y)) + t_1
	else:
		tmp = (y * i) + (t_1 + (a + (t + z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if ((x <= -9.6e+236) || !(x <= 1.2e+163))
		tmp = Float64(Float64(x * log(y)) + t_1);
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(t + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if ((x <= -9.6e+236) || ~((x <= 1.2e+163)))
		tmp = (x * log(y)) + t_1;
	else
		tmp = (y * i) + (t_1 + (a + (t + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9.6e+236], N[Not[LessEqual[x, 1.2e+163]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.60000000000000051e236 or 1.1999999999999999e163 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 85.0%

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

   3. Taylor expanded in y around 0 73.1%

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

   if -9.60000000000000051e236 < x < 1.1999999999999999e163

   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. Taylor expanded in x around 0 94.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+236} \lor \neg \left(x \leq 1.2 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot \log y + \left(b - 0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 7: 86.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237} \lor \neg \left(x \leq 1.2 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4e+237) (not (<= x 1.2e+163)))
   (* x (log y))
   (+ (* y i) (+ (* (- b 0.5) (log c)) (+ a (+ t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4e+237) || !(x <= 1.2e+163)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + 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 ((x <= (-4d+237)) .or. (.not. (x <= 1.2d+163))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + (a + (t + 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 ((x <= -4e+237) || !(x <= 1.2e+163)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + (a + (t + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4e+237) or not (x <= 1.2e+163):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + (a + (t + z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4e+237) || !(x <= 1.2e+163))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(a + Float64(t + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4e+237) || ~((x <= 1.2e+163)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + (a + (t + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4e+237], N[Not[LessEqual[x, 1.2e+163]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999976e237 or 1.1999999999999999e163 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 85.0%

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

   3. Taylor expanded in x around inf 65.4%

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

   if -3.99999999999999976e237 < x < 1.1999999999999999e163

   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. Taylor expanded in x around 0 94.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237} \lor \neg \left(x \leq 1.2 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 8: 61.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+68}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5e+68)
   (+ (* y i) (+ a (+ t (+ z (* (log c) -0.5)))))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5e+68) {
		tmp = (y * i) + (a + (t + (z + (log(c) * -0.5))));
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * 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 (z <= (-5d+68)) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (-0.5d0)))))
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * 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 (z <= -5e+68) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * -0.5))));
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5e+68:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * -0.5))))
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5e+68)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * -0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5e+68)
		tmp = (y * i) + (a + (t + (z + (log(c) * -0.5))));
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5e+68], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000004e68

   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. Taylor expanded in x around 0 84.2%

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

      1. associate-+r+ 84.2%

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

      2. sub-neg 84.2%

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

      3. metadata-eval 84.2%

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

      4. *-commutative 84.2%

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

      5. associate-+r+ 84.2%

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

      6. +-commutative 84.2%

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

      7. +-commutative 84.2%

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

      8. associate-+r+ 84.2%

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

      9. associate-+l+ 84.2%

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

      10. +-commutative 84.2%

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

      11. *-commutative 84.2%

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

      12. fma-def 84.2%

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

      13. +-commutative 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in b around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   7. Simplified 76.6%

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

   if -5.0000000000000004e68 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+68}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]

Alternative 9: 59.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3e+96)
   (+ (* y i) (+ z (* b (log c))))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3e+96) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * 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 (z <= (-3d+96)) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * 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 (z <= -3e+96) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3e+96:
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3e+96)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3e+96)
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3e+96], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e96

   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. Taylor expanded in z around inf 74.2%

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

   3. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 32.9%

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

   5. Simplified 74.2%

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

   if -3e96 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]

Alternative 10: 42.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-192}:\\ \;\;\;\;a + \left(b - 0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9e+66)
   (+ z (* y i))
   (if (<= z -6.2e-192) (+ a (* (- b 0.5) (log c))) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9e+66) {
		tmp = z + (y * i);
	} else if (z <= -6.2e-192) {
		tmp = a + ((b - 0.5) * log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-9d+66)) then
        tmp = z + (y * i)
    else if (z <= (-6.2d-192)) then
        tmp = a + ((b - 0.5d0) * log(c))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9e+66) {
		tmp = z + (y * i);
	} else if (z <= -6.2e-192) {
		tmp = a + ((b - 0.5) * Math.log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9e+66:
		tmp = z + (y * i)
	elif z <= -6.2e-192:
		tmp = a + ((b - 0.5) * math.log(c))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9e+66)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -6.2e-192)
		tmp = Float64(a + Float64(Float64(b - 0.5) * log(c)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -9e+66)
		tmp = z + (y * i);
	elseif (z <= -6.2e-192)
		tmp = a + ((b - 0.5) * log(c));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9e+66], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-192], N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999997e66

   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. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-+r+ 85.1%

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

      3. +-commutative 85.1%

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

      4. +-commutative 85.1%

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

      5. fma-def 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around inf 60.8%

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

   if -8.9999999999999997e66 < z < -6.2000000000000001e-192

   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. Taylor expanded in a around inf 65.9%

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

   3. Taylor expanded in y around 0 48.2%

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

   if -6.2000000000000001e-192 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 48.4%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in b around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-192}:\\ \;\;\;\;a + \left(b - 0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 11: 56.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+191}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.4e+191) (+ z (* y i)) (+ (* y i) (+ a (* 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 (z <= -5.4e+191) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (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 (z <= (-5.4d+191)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + (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 (z <= -5.4e+191) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.4e+191:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.4e+191)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + 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 (z <= -5.4e+191)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.4e+191], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999992e191

   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. Taylor expanded in t around 0 90.3%

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

      1. +-commutative 90.3%

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

      2. associate-+r+ 90.3%

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

      3. +-commutative 90.3%

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

      4. +-commutative 90.3%

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

      5. fma-def 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -5.39999999999999992e191 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 51.1%

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

   3. Taylor expanded in b around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+191}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 12: 57.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(z + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= z -4.1e+96) (+ (* y i) (+ z t_1)) (+ (* 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 = b * log(c);
	double tmp;
	if (z <= -4.1e+96) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (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) :: tmp
    t_1 = b * log(c)
    if (z <= (-4.1d+96)) then
        tmp = (y * i) + (z + t_1)
    else
        tmp = (y * i) + (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 = b * Math.log(c);
	double tmp;
	if (z <= -4.1e+96) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if z <= -4.1e+96:
		tmp = (y * i) + (z + t_1)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (z <= -4.1e+96)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (z <= -4.1e+96)
		tmp = (y * i) + (z + t_1);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+96], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999998e96

   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. Taylor expanded in z around inf 74.2%

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

   3. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 32.9%

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

   5. Simplified 74.2%

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

   if -4.09999999999999998e96 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.1%

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

   3. Taylor expanded in b around inf 51.0%

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

      1. *-commutative 51.0%

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

   5. Simplified 51.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 13: 42.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+95}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-47} \lor \neg \left(z \leq -8.5 \cdot 10^{-93}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.8e+95)
   (+ z (* y i))
   (if (or (<= z -7.4e-47) (not (<= z -8.5e-93)))
     (+ a (* y i))
     (* x (log y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.8e+95) {
		tmp = z + (y * i);
	} else if ((z <= -7.4e-47) || !(z <= -8.5e-93)) {
		tmp = a + (y * i);
	} else {
		tmp = x * log(y);
	}
	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 <= (-5.8d+95)) then
        tmp = z + (y * i)
    else if ((z <= (-7.4d-47)) .or. (.not. (z <= (-8.5d-93)))) then
        tmp = a + (y * i)
    else
        tmp = x * log(y)
    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 <= -5.8e+95) {
		tmp = z + (y * i);
	} else if ((z <= -7.4e-47) || !(z <= -8.5e-93)) {
		tmp = a + (y * i);
	} else {
		tmp = x * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.8e+95:
		tmp = z + (y * i)
	elif (z <= -7.4e-47) or not (z <= -8.5e-93):
		tmp = a + (y * i)
	else:
		tmp = x * math.log(y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.8e+95)
		tmp = Float64(z + Float64(y * i));
	elseif ((z <= -7.4e-47) || !(z <= -8.5e-93))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(x * log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5.8e+95)
		tmp = z + (y * i);
	elseif ((z <= -7.4e-47) || ~((z <= -8.5e-93)))
		tmp = a + (y * i);
	else
		tmp = x * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.8e+95], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.4e-47], N[Not[LessEqual[z, -8.5e-93]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000027e95

   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. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-+r+ 86.0%

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

      3. +-commutative 86.0%

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

      4. +-commutative 86.0%

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

      5. fma-def 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around inf 65.3%

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

   if -5.80000000000000027e95 < z < -7.4000000000000001e-47 or -8.5000000000000007e-93 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.9%

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

   3. Taylor expanded in b around inf 52.1%

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

      1. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in b around 0 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

   if -7.4000000000000001e-47 < z < -8.5000000000000007e-93

   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. Taylor expanded in x around inf 100.0%

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

   3. Taylor expanded in x around inf 67.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+95}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-47} \lor \neg \left(z \leq -8.5 \cdot 10^{-93}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 14: 41.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-192}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.5e+66)
   (+ z (* y i))
   (if (<= z -5.5e-192) (+ a (* b (log c))) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.5e+66) {
		tmp = z + (y * i);
	} else if (z <= -5.5e-192) {
		tmp = a + (b * log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-5.5d+66)) then
        tmp = z + (y * i)
    else if (z <= (-5.5d-192)) then
        tmp = a + (b * log(c))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.5e+66) {
		tmp = z + (y * i);
	} else if (z <= -5.5e-192) {
		tmp = a + (b * Math.log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.5e+66:
		tmp = z + (y * i)
	elif z <= -5.5e-192:
		tmp = a + (b * math.log(c))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.5e+66)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -5.5e-192)
		tmp = Float64(a + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5.5e+66)
		tmp = z + (y * i);
	elseif (z <= -5.5e-192)
		tmp = a + (b * log(c));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.5e+66], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-192], N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e66

   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. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-+r+ 85.1%

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

      3. +-commutative 85.1%

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

      4. +-commutative 85.1%

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

      5. fma-def 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around inf 60.8%

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

   if -5.5e66 < z < -5.49999999999999995e-192

   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. Taylor expanded in a around inf 65.9%

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

   3. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in y around 0 45.1%

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

   if -5.49999999999999995e-192 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 48.4%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in b around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-192}:\\ \;\;\;\;a + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 15: 40.9% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+232}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.2e+232) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+232) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.2d+232)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+232) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.2e+232:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.2e+232)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.2e+232)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.2e+232], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e232

   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. Taylor expanded in z around inf 93.5%

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

   3. Taylor expanded in z around inf 72.4%

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

   if -3.2000000000000002e232 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 51.3%

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

   3. Taylor expanded in b around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in b around 0 36.8%

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

      1. *-commutative 36.8%

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

   8. Simplified 36.8%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+232}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 43.4% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+97}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.3e+97) (+ 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 (z <= -1.3e+97) {
		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 (z <= (-1.3d+97)) 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 (z <= -1.3e+97) {
		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 z <= -1.3e+97:
		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 (z <= -1.3e+97)
		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 (z <= -1.3e+97)
		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[z, -1.3e+97], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e97

   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. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-+r+ 86.0%

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

      3. +-commutative 86.0%

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

      4. +-commutative 86.0%

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

      5. fma-def 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around inf 65.3%

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

   if -1.3e97 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.1%

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

   3. Taylor expanded in b around inf 51.0%

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

      1. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in b around 0 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+97}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 17: 20.7% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.32e+97) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.32e+97) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.32d+97)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.32e+97) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.32e+97:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.32e+97)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.32e+97)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.32e+97], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.31999999999999994e97

   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. Taylor expanded in z around inf 74.2%

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

   3. Taylor expanded in z around inf 42.2%

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

   if -1.31999999999999994e97 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 52.1%

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

   3. Taylor expanded in a around inf 16.8%

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

4. Final simplification 20.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 18: 16.1% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 49.6%

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

3. Taylor expanded in a around inf 15.0%

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

4. Final simplification 15.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023290 
(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)))