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

Percentage Accurate: 99.8% → 99.8%

Time: 18.8s

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, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(z - x \cdot \log \left(\frac{1}{y}\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (- z (* x (log (/ 1.0 y)))) 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 ((((z - (x * log((1.0 / y)))) + 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 = ((((z - (x * log((1.0d0 / y)))) + 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 ((((z - (x * Math.log((1.0 / y)))) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((z - (x * math.log((1.0 / y)))) + 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(z - Float64(x * log(Float64(1.0 / y)))) + 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 = ((((z - (x * log((1.0 / y)))) + 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[(z - N[(x * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

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 y around inf 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+86} \lor \neg \left(x \leq 1.2 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.6e+86) (not (<= x 1.2e+175)))
   (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) -0.5)))
   (+ (* y i) (+ a (+ t (+ z (* (- 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 ((x <= -2.6e+86) || !(x <= 1.2e+175)) {
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * -0.5));
	} else {
		tmp = (y * i) + (a + (t + (z + ((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 ((x <= (-2.6d+86)) .or. (.not. (x <= 1.2d+175))) then
        tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * (-0.5d0)))
    else
        tmp = (y * i) + (a + (t + (z + ((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 ((x <= -2.6e+86) || !(x <= 1.2e+175)) {
		tmp = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * -0.5));
	} else {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.6e+86) or not (x <= 1.2e+175):
		tmp = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * -0.5))
	else:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.6e+86) || !(x <= 1.2e+175))
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * -0.5)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + 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 ((x <= -2.6e+86) || ~((x <= 1.2e+175)))
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (log(c) * -0.5));
	else
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.6e+86], N[Not[LessEqual[x, 1.2e+175]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999998e86 or 1.2e175 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   if -2.5999999999999998e86 < x < 1.2e175

   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 97.7%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+86} \lor \neg \left(x \leq 1.2 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+87} \lor \neg \left(x \leq 2.15 \cdot 10^{+176}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+87) (not (<= x 2.15e+176)))
   (+ a (+ t (+ z (+ (* x (log y)) (* (log c) -0.5)))))
   (+ (* y i) (+ a (+ t (+ z (* (- 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 ((x <= -4.8e+87) || !(x <= 2.15e+176)) {
		tmp = a + (t + (z + ((x * log(y)) + (log(c) * -0.5))));
	} else {
		tmp = (y * i) + (a + (t + (z + ((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 ((x <= (-4.8d+87)) .or. (.not. (x <= 2.15d+176))) then
        tmp = a + (t + (z + ((x * log(y)) + (log(c) * (-0.5d0)))))
    else
        tmp = (y * i) + (a + (t + (z + ((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 ((x <= -4.8e+87) || !(x <= 2.15e+176)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (Math.log(c) * -0.5))));
	} else {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+87) or not (x <= 2.15e+176):
		tmp = a + (t + (z + ((x * math.log(y)) + (math.log(c) * -0.5))))
	else:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.8e+87) || !(x <= 2.15e+176))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * -0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + 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 ((x <= -4.8e+87) || ~((x <= 2.15e+176)))
		tmp = a + (t + (z + ((x * log(y)) + (log(c) * -0.5))));
	else
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.8e+87], N[Not[LessEqual[x, 2.15e+176]], $MachinePrecision]], N[(a + N[(t + 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[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999963e87 or 2.15000000000000013e176 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in y around 0 75.8%

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

   if -4.79999999999999963e87 < x < 2.15000000000000013e176

   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 97.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+87} \lor \neg \left(x \leq 2.15 \cdot 10^{+176}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+181} \lor \neg \left(x \leq 3.3 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.65e+181) (not (<= x 3.3e+175)))
   (+ (* y i) (+ z (+ (* x (log y)) (* (log c) -0.5))))
   (+ (* y i) (+ a (+ t (+ z (* (- 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 ((x <= -1.65e+181) || !(x <= 3.3e+175)) {
		tmp = (y * i) + (z + ((x * log(y)) + (log(c) * -0.5)));
	} else {
		tmp = (y * i) + (a + (t + (z + ((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 ((x <= (-1.65d+181)) .or. (.not. (x <= 3.3d+175))) then
        tmp = (y * i) + (z + ((x * log(y)) + (log(c) * (-0.5d0))))
    else
        tmp = (y * i) + (a + (t + (z + ((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 ((x <= -1.65e+181) || !(x <= 3.3e+175)) {
		tmp = (y * i) + (z + ((x * Math.log(y)) + (Math.log(c) * -0.5)));
	} else {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.65e+181) or not (x <= 3.3e+175):
		tmp = (y * i) + (z + ((x * math.log(y)) + (math.log(c) * -0.5)))
	else:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.65e+181) || !(x <= 3.3e+175))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * -0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + 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 ((x <= -1.65e+181) || ~((x <= 3.3e+175)))
		tmp = (y * i) + (z + ((x * log(y)) + (log(c) * -0.5)));
	else
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.65e+181], N[Not[LessEqual[x, 3.3e+175]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000008e181 or 3.3000000000000002e175 < x

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in a around 0 86.1%

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

   7. Taylor expanded in t around 0 79.7%

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

   if -1.65000000000000008e181 < x < 3.3000000000000002e175

   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 95.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+181} \lor \neg \left(x \leq 3.3 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_1 + t\_2\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t\_1 + \log c \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* (- b 0.5) (log c))))
   (if (<= x -4.2e+87)
     (+ a (+ t (+ z (+ t_1 t_2))))
     (if (<= x 4.5e+175)
       (+ (* y i) (+ a (+ t (+ z t_2))))
       (+ (* y i) (+ z (+ t_1 (* (log c) -0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (x <= -4.2e+87) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 4.5e+175) {
		tmp = (y * i) + (a + (t + (z + t_2)));
	} else {
		tmp = (y * i) + (z + (t_1 + (log(c) * -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = (b - 0.5d0) * log(c)
    if (x <= (-4.2d+87)) then
        tmp = a + (t + (z + (t_1 + t_2)))
    else if (x <= 4.5d+175) then
        tmp = (y * i) + (a + (t + (z + t_2)))
    else
        tmp = (y * i) + (z + (t_1 + (log(c) * (-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 t_1 = x * Math.log(y);
	double t_2 = (b - 0.5) * Math.log(c);
	double tmp;
	if (x <= -4.2e+87) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 4.5e+175) {
		tmp = (y * i) + (a + (t + (z + t_2)));
	} else {
		tmp = (y * i) + (z + (t_1 + (Math.log(c) * -0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = (b - 0.5) * math.log(c)
	tmp = 0
	if x <= -4.2e+87:
		tmp = a + (t + (z + (t_1 + t_2)))
	elif x <= 4.5e+175:
		tmp = (y * i) + (a + (t + (z + t_2)))
	else:
		tmp = (y * i) + (z + (t_1 + (math.log(c) * -0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (x <= -4.2e+87)
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + t_2))));
	elseif (x <= 4.5e+175)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_2))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t_1 + Float64(log(c) * -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (x <= -4.2e+87)
		tmp = a + (t + (z + (t_1 + t_2)));
	elseif (x <= 4.5e+175)
		tmp = (y * i) + (a + (t + (z + t_2)));
	else
		tmp = (y * i) + (z + (t_1 + (log(c) * -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+87], N[(a + N[(t + N[(z + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+175], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e87

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 83.8%

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

   if -4.2e87 < x < 4.49999999999999989e175

   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 97.7%

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

   if 4.49999999999999989e175 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 95.3%

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

      1. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in a around 0 86.5%

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

   7. Taylor expanded in t around 0 78.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+180} \lor \neg \left(x \leq 4.8 \cdot 10^{+228}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.5e+180) (not (<= x 4.8e+228)))
   (+ t (+ z (+ (* x (log y)) (* (log c) -0.5))))
   (+ (* y i) (+ a (+ t (+ z (* (- 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 ((x <= -6.5e+180) || !(x <= 4.8e+228)) {
		tmp = t + (z + ((x * log(y)) + (log(c) * -0.5)));
	} else {
		tmp = (y * i) + (a + (t + (z + ((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 ((x <= (-6.5d+180)) .or. (.not. (x <= 4.8d+228))) then
        tmp = t + (z + ((x * log(y)) + (log(c) * (-0.5d0))))
    else
        tmp = (y * i) + (a + (t + (z + ((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 ((x <= -6.5e+180) || !(x <= 4.8e+228)) {
		tmp = t + (z + ((x * Math.log(y)) + (Math.log(c) * -0.5)));
	} else {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -6.5e+180) or not (x <= 4.8e+228):
		tmp = t + (z + ((x * math.log(y)) + (math.log(c) * -0.5)))
	else:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.5e+180) || !(x <= 4.8e+228))
		tmp = Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * -0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + 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 ((x <= -6.5e+180) || ~((x <= 4.8e+228)))
		tmp = t + (z + ((x * log(y)) + (log(c) * -0.5)));
	else
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.5e+180], N[Not[LessEqual[x, 4.8e+228]], $MachinePrecision]], N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e180 or 4.79999999999999977e228 < x

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in a around 0 89.0%

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

   7. Taylor expanded in y around 0 74.0%

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

   if -6.5e180 < x < 4.79999999999999977e228

   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 93.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+180} \lor \neg \left(x \leq 4.8 \cdot 10^{+228}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* (- b 0.5) (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 - 0.5) * 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 - 0.5d0) * 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 - 0.5) * 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 - 0.5) * 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(Float64(b - 0.5) * 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 - 0.5) * 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[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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. Final simplification 99.5%

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

Alternative 8: 21.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := b \cdot \log c\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-249}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-97}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+22}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* b (log c))))
   (if (<= a -3.1e-249)
     z
     (if (<= a -2.65e-281)
       (* y i)
       (if (<= a 4.9e-225)
         z
         (if (<= a 2.9e-130)
           t_2
           (if (<= a 9.5e-97)
             z
             (if (<= a 1.46e-21)
               t_1
               (if (<= a 3.9e+22)
                 (* y i)
                 (if (<= a 4.8e+127) t_2 (if (<= a 2.2e+145) t_1 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = b * log(c);
	double tmp;
	if (a <= -3.1e-249) {
		tmp = z;
	} else if (a <= -2.65e-281) {
		tmp = y * i;
	} else if (a <= 4.9e-225) {
		tmp = z;
	} else if (a <= 2.9e-130) {
		tmp = t_2;
	} else if (a <= 9.5e-97) {
		tmp = z;
	} else if (a <= 1.46e-21) {
		tmp = t_1;
	} else if (a <= 3.9e+22) {
		tmp = y * i;
	} else if (a <= 4.8e+127) {
		tmp = t_2;
	} else if (a <= 2.2e+145) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = b * log(c)
    if (a <= (-3.1d-249)) then
        tmp = z
    else if (a <= (-2.65d-281)) then
        tmp = y * i
    else if (a <= 4.9d-225) then
        tmp = z
    else if (a <= 2.9d-130) then
        tmp = t_2
    else if (a <= 9.5d-97) then
        tmp = z
    else if (a <= 1.46d-21) then
        tmp = t_1
    else if (a <= 3.9d+22) then
        tmp = y * i
    else if (a <= 4.8d+127) then
        tmp = t_2
    else if (a <= 2.2d+145) then
        tmp = t_1
    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 t_1 = x * Math.log(y);
	double t_2 = b * Math.log(c);
	double tmp;
	if (a <= -3.1e-249) {
		tmp = z;
	} else if (a <= -2.65e-281) {
		tmp = y * i;
	} else if (a <= 4.9e-225) {
		tmp = z;
	} else if (a <= 2.9e-130) {
		tmp = t_2;
	} else if (a <= 9.5e-97) {
		tmp = z;
	} else if (a <= 1.46e-21) {
		tmp = t_1;
	} else if (a <= 3.9e+22) {
		tmp = y * i;
	} else if (a <= 4.8e+127) {
		tmp = t_2;
	} else if (a <= 2.2e+145) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = b * math.log(c)
	tmp = 0
	if a <= -3.1e-249:
		tmp = z
	elif a <= -2.65e-281:
		tmp = y * i
	elif a <= 4.9e-225:
		tmp = z
	elif a <= 2.9e-130:
		tmp = t_2
	elif a <= 9.5e-97:
		tmp = z
	elif a <= 1.46e-21:
		tmp = t_1
	elif a <= 3.9e+22:
		tmp = y * i
	elif a <= 4.8e+127:
		tmp = t_2
	elif a <= 2.2e+145:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(b * log(c))
	tmp = 0.0
	if (a <= -3.1e-249)
		tmp = z;
	elseif (a <= -2.65e-281)
		tmp = Float64(y * i);
	elseif (a <= 4.9e-225)
		tmp = z;
	elseif (a <= 2.9e-130)
		tmp = t_2;
	elseif (a <= 9.5e-97)
		tmp = z;
	elseif (a <= 1.46e-21)
		tmp = t_1;
	elseif (a <= 3.9e+22)
		tmp = Float64(y * i);
	elseif (a <= 4.8e+127)
		tmp = t_2;
	elseif (a <= 2.2e+145)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = b * log(c);
	tmp = 0.0;
	if (a <= -3.1e-249)
		tmp = z;
	elseif (a <= -2.65e-281)
		tmp = y * i;
	elseif (a <= 4.9e-225)
		tmp = z;
	elseif (a <= 2.9e-130)
		tmp = t_2;
	elseif (a <= 9.5e-97)
		tmp = z;
	elseif (a <= 1.46e-21)
		tmp = t_1;
	elseif (a <= 3.9e+22)
		tmp = y * i;
	elseif (a <= 4.8e+127)
		tmp = t_2;
	elseif (a <= 2.2e+145)
		tmp = t_1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e-249], z, If[LessEqual[a, -2.65e-281], N[(y * i), $MachinePrecision], If[LessEqual[a, 4.9e-225], z, If[LessEqual[a, 2.9e-130], t$95$2, If[LessEqual[a, 9.5e-97], z, If[LessEqual[a, 1.46e-21], t$95$1, If[LessEqual[a, 3.9e+22], N[(y * i), $MachinePrecision], If[LessEqual[a, 4.8e+127], t$95$2, If[LessEqual[a, 2.2e+145], t$95$1, a]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.09999999999999986e-249 or -2.64999999999999997e-281 < a < 4.89999999999999971e-225 or 2.9e-130 < a < 9.5000000000000001e-97

   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 z around inf 13.5%

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

   if -3.09999999999999986e-249 < a < -2.64999999999999997e-281 or 1.46000000000000006e-21 < a < 3.90000000000000021e22

   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 y around inf 35.5%

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

      1. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   if 4.89999999999999971e-225 < a < 2.9e-130 or 3.90000000000000021e22 < a < 4.8000000000000004e127

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 21.6%

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

      1. *-commutative 21.6%

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

   5. Simplified 21.6%

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

   if 9.5000000000000001e-97 < a < 1.46000000000000006e-21 or 4.8000000000000004e127 < a < 2.20000000000000009e145

   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 inf 34.1%

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

   if 2.20000000000000009e145 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-249}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-97}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+22}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 21.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-91}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+58}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= a -7.4e-252)
     z
     (if (<= a -2.7e-281)
       (* y i)
       (if (<= a 5.2e-170)
         z
         (if (<= a 3.4e-130)
           t_1
           (if (<= a 2.15e-91)
             z
             (if (<= a 1.25e-21)
               t_1
               (if (<= a 3.8e+58)
                 (* y i)
                 (if (<= a 1e+137)
                   t_1
                   (if (<= a 1.15e+146) (* y i) a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (a <= -7.4e-252) {
		tmp = z;
	} else if (a <= -2.7e-281) {
		tmp = y * i;
	} else if (a <= 5.2e-170) {
		tmp = z;
	} else if (a <= 3.4e-130) {
		tmp = t_1;
	} else if (a <= 2.15e-91) {
		tmp = z;
	} else if (a <= 1.25e-21) {
		tmp = t_1;
	} else if (a <= 3.8e+58) {
		tmp = y * i;
	} else if (a <= 1e+137) {
		tmp = t_1;
	} else if (a <= 1.15e+146) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (a <= (-7.4d-252)) then
        tmp = z
    else if (a <= (-2.7d-281)) then
        tmp = y * i
    else if (a <= 5.2d-170) then
        tmp = z
    else if (a <= 3.4d-130) then
        tmp = t_1
    else if (a <= 2.15d-91) then
        tmp = z
    else if (a <= 1.25d-21) then
        tmp = t_1
    else if (a <= 3.8d+58) then
        tmp = y * i
    else if (a <= 1d+137) then
        tmp = t_1
    else if (a <= 1.15d+146) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (a <= -7.4e-252) {
		tmp = z;
	} else if (a <= -2.7e-281) {
		tmp = y * i;
	} else if (a <= 5.2e-170) {
		tmp = z;
	} else if (a <= 3.4e-130) {
		tmp = t_1;
	} else if (a <= 2.15e-91) {
		tmp = z;
	} else if (a <= 1.25e-21) {
		tmp = t_1;
	} else if (a <= 3.8e+58) {
		tmp = y * i;
	} else if (a <= 1e+137) {
		tmp = t_1;
	} else if (a <= 1.15e+146) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if a <= -7.4e-252:
		tmp = z
	elif a <= -2.7e-281:
		tmp = y * i
	elif a <= 5.2e-170:
		tmp = z
	elif a <= 3.4e-130:
		tmp = t_1
	elif a <= 2.15e-91:
		tmp = z
	elif a <= 1.25e-21:
		tmp = t_1
	elif a <= 3.8e+58:
		tmp = y * i
	elif a <= 1e+137:
		tmp = t_1
	elif a <= 1.15e+146:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (a <= -7.4e-252)
		tmp = z;
	elseif (a <= -2.7e-281)
		tmp = Float64(y * i);
	elseif (a <= 5.2e-170)
		tmp = z;
	elseif (a <= 3.4e-130)
		tmp = t_1;
	elseif (a <= 2.15e-91)
		tmp = z;
	elseif (a <= 1.25e-21)
		tmp = t_1;
	elseif (a <= 3.8e+58)
		tmp = Float64(y * i);
	elseif (a <= 1e+137)
		tmp = t_1;
	elseif (a <= 1.15e+146)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (a <= -7.4e-252)
		tmp = z;
	elseif (a <= -2.7e-281)
		tmp = y * i;
	elseif (a <= 5.2e-170)
		tmp = z;
	elseif (a <= 3.4e-130)
		tmp = t_1;
	elseif (a <= 2.15e-91)
		tmp = z;
	elseif (a <= 1.25e-21)
		tmp = t_1;
	elseif (a <= 3.8e+58)
		tmp = y * i;
	elseif (a <= 1e+137)
		tmp = t_1;
	elseif (a <= 1.15e+146)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.4e-252], z, If[LessEqual[a, -2.7e-281], N[(y * i), $MachinePrecision], If[LessEqual[a, 5.2e-170], z, If[LessEqual[a, 3.4e-130], t$95$1, If[LessEqual[a, 2.15e-91], z, If[LessEqual[a, 1.25e-21], t$95$1, If[LessEqual[a, 3.8e+58], N[(y * i), $MachinePrecision], If[LessEqual[a, 1e+137], t$95$1, If[LessEqual[a, 1.15e+146], N[(y * i), $MachinePrecision], a]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.4000000000000002e-252 or -2.6999999999999999e-281 < a < 5.2000000000000003e-170 or 3.40000000000000005e-130 < a < 2.15e-91

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 14.1%

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

   if -7.4000000000000002e-252 < a < -2.6999999999999999e-281 or 1.24999999999999993e-21 < a < 3.7999999999999999e58 or 1e137 < a < 1.15e146

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 39.8%

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

      1. *-commutative 39.8%

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

   5. Simplified 39.8%

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

   if 5.2000000000000003e-170 < a < 3.40000000000000005e-130 or 2.15e-91 < a < 1.24999999999999993e-21 or 3.7999999999999999e58 < a < 1e137

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 27.6%

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

   if 1.15e146 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.2%

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

4. Final simplification 23.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-252}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-91}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+58}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 10^{+137}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+111} \lor \neg \left(b - 0.5 \leq 10^{+99}\right):\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -5e+111) (not (<= (- b 0.5) 1e+99)))
   (+ a (+ z (* (- b 0.5) (log c))))
   (+ a (+ t (+ z (+ (* y i) (* (log c) -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) <= -5e+111) || !((b - 0.5) <= 1e+99)) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else {
		tmp = a + (t + (z + ((y * i) + (log(c) * -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) <= (-5d+111)) .or. (.not. ((b - 0.5d0) <= 1d+99))) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else
        tmp = a + (t + (z + ((y * i) + (log(c) * (-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) <= -5e+111) || !((b - 0.5) <= 1e+99)) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = a + (t + (z + ((y * i) + (Math.log(c) * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -5e+111) or not ((b - 0.5) <= 1e+99):
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	else:
		tmp = a + (t + (z + ((y * i) + (math.log(c) * -0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -5e+111) || !(Float64(b - 0.5) <= 1e+99))
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * -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) <= -5e+111) || ~(((b - 0.5) <= 1e+99)))
		tmp = a + (z + ((b - 0.5) * log(c)));
	else
		tmp = a + (t + (z + ((y * i) + (log(c) * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+111], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+99]], $MachinePrecision]], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -4.9999999999999997e111 or 9.9999999999999997e98 < (-.f64 b 1/2)

   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. Step-by-step derivation

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. associate-+l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-def 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-def 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.2%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. associate-+r+ 80.3%

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

      2. sub-neg 80.3%

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

      3. metadata-eval 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in y around 0 66.5%

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

   if -4.9999999999999997e111 < (-.f64 b 1/2) < 9.9999999999999997e98

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+r+ 99.3%

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

      6. associate-+l+ 99.3%

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

      7. +-commutative 99.3%

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

      8. associate-+l+ 99.3%

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

      9. +-commutative 99.3%

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

      10. fma-def 99.3%

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

      11. +-commutative 99.3%

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

      12. fma-def 99.3%

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

      13. sub-neg 99.3%

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

      14. metadata-eval 99.3%

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

      15. +-commutative 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 79.8%

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

   6. Taylor expanded in b around 0 78.0%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+111} \lor \neg \left(b - 0.5 \leq 10^{+99}\right):\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot -0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+111} \lor \neg \left(b - 0.5 \leq 10^{+99}\right):\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -5e+111) (not (<= (- b 0.5) 1e+99)))
   (+ a (+ z (* (- b 0.5) (log c))))
   (+ a (+ z (+ (* y i) (* (log c) -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) <= -5e+111) || !((b - 0.5) <= 1e+99)) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else {
		tmp = a + (z + ((y * i) + (log(c) * -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) <= (-5d+111)) .or. (.not. ((b - 0.5d0) <= 1d+99))) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else
        tmp = a + (z + ((y * i) + (log(c) * (-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) <= -5e+111) || !((b - 0.5) <= 1e+99)) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = a + (z + ((y * i) + (Math.log(c) * -0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -5e+111) or not ((b - 0.5) <= 1e+99):
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	else:
		tmp = a + (z + ((y * i) + (math.log(c) * -0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -5e+111) || !(Float64(b - 0.5) <= 1e+99))
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(log(c) * -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) <= -5e+111) || ~(((b - 0.5) <= 1e+99)))
		tmp = a + (z + ((b - 0.5) * log(c)));
	else
		tmp = a + (z + ((y * i) + (log(c) * -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+111], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+99]], $MachinePrecision]], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -4.9999999999999997e111 or 9.9999999999999997e98 < (-.f64 b 1/2)

   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. Step-by-step derivation

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. associate-+l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-def 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-def 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.2%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. associate-+r+ 80.3%

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

      2. sub-neg 80.3%

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

      3. metadata-eval 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in y around 0 66.5%

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

   if -4.9999999999999997e111 < (-.f64 b 1/2) < 9.9999999999999997e98

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+r+ 99.3%

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

      6. associate-+l+ 99.3%

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

      7. +-commutative 99.3%

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

      8. associate-+l+ 99.3%

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

      9. +-commutative 99.3%

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

      10. fma-def 99.3%

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

      11. +-commutative 99.3%

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

      12. fma-def 99.3%

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

      13. sub-neg 99.3%

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

      14. metadata-eval 99.3%

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

      15. +-commutative 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 79.8%

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

   6. Taylor expanded in b around 0 78.0%

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

   7. Taylor expanded in t around 0 63.4%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+111} \lor \neg \left(b - 0.5 \leq 10^{+99}\right):\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+184}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+287}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6.6e+184)
   (* (log (/ 1.0 y)) (- x))
   (if (<= x 1.8e+287)
     (+ (* y i) (+ a (+ t (+ z (* (- b 0.5) (log c))))))
     (* 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 (x <= -6.6e+184) {
		tmp = log((1.0 / y)) * -x;
	} else if (x <= 1.8e+287) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	} 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 (x <= (-6.6d+184)) then
        tmp = log((1.0d0 / y)) * -x
    else if (x <= 1.8d+287) then
        tmp = (y * i) + (a + (t + (z + ((b - 0.5d0) * log(c)))))
    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 (x <= -6.6e+184) {
		tmp = Math.log((1.0 / y)) * -x;
	} else if (x <= 1.8e+287) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	} else {
		tmp = x * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -6.6e+184:
		tmp = math.log((1.0 / y)) * -x
	elif x <= 1.8e+287:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	else:
		tmp = x * math.log(y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6.6e+184)
		tmp = Float64(log(Float64(1.0 / y)) * Float64(-x));
	elseif (x <= 1.8e+287)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))))));
	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 (x <= -6.6e+184)
		tmp = log((1.0 / y)) * -x;
	elseif (x <= 1.8e+287)
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	else
		tmp = x * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6.6e+184], N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, 1.8e+287], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5999999999999996e184

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 96.8%

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

   4. Taylor expanded in x around inf 60.7%

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

   if -6.5999999999999996e184 < x < 1.7999999999999999e287

   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 92.3%

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

   if 1.7999999999999999e287 < x

   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 inf 100.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+184}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+287}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+287}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.25e+185)
   (* (log (/ 1.0 y)) (- x))
   (if (<= x 1.8e+287)
     (+ a (+ z (+ (* y i) (* (- b 0.5) (log c)))))
     (* 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 (x <= -1.25e+185) {
		tmp = log((1.0 / y)) * -x;
	} else if (x <= 1.8e+287) {
		tmp = a + (z + ((y * i) + ((b - 0.5) * log(c))));
	} 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 (x <= (-1.25d+185)) then
        tmp = log((1.0d0 / y)) * -x
    else if (x <= 1.8d+287) then
        tmp = a + (z + ((y * i) + ((b - 0.5d0) * log(c))))
    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 (x <= -1.25e+185) {
		tmp = Math.log((1.0 / y)) * -x;
	} else if (x <= 1.8e+287) {
		tmp = a + (z + ((y * i) + ((b - 0.5) * Math.log(c))));
	} else {
		tmp = x * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.25e+185:
		tmp = math.log((1.0 / y)) * -x
	elif x <= 1.8e+287:
		tmp = a + (z + ((y * i) + ((b - 0.5) * math.log(c))))
	else:
		tmp = x * math.log(y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.25e+185)
		tmp = Float64(log(Float64(1.0 / y)) * Float64(-x));
	elseif (x <= 1.8e+287)
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(Float64(b - 0.5) * log(c)))));
	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 (x <= -1.25e+185)
		tmp = log((1.0 / y)) * -x;
	elseif (x <= 1.8e+287)
		tmp = a + (z + ((y * i) + ((b - 0.5) * log(c))));
	else
		tmp = x * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.25e+185], N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, 1.8e+287], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999997e185

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 96.8%

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

   4. Taylor expanded in x around inf 60.7%

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

   if -1.24999999999999997e185 < x < 1.7999999999999999e287

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.3%

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

   6. Taylor expanded in t around 0 77.8%

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

   if 1.7999999999999999e287 < x

   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 inf 100.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+287}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+217} \lor \neg \left(b \leq 1.15 \cdot 10^{+240}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -6.2e+217) (not (<= b 1.15e+240)))
   (* b (log c))
   (+ a (+ t (+ z (* (log c) -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 <= -6.2e+217) || !(b <= 1.15e+240)) {
		tmp = b * log(c);
	} else {
		tmp = a + (t + (z + (log(c) * -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 <= (-6.2d+217)) .or. (.not. (b <= 1.15d+240))) then
        tmp = b * log(c)
    else
        tmp = a + (t + (z + (log(c) * (-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 <= -6.2e+217) || !(b <= 1.15e+240)) {
		tmp = b * Math.log(c);
	} else {
		tmp = a + (t + (z + (Math.log(c) * -0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -6.2e+217) or not (b <= 1.15e+240):
		tmp = b * math.log(c)
	else:
		tmp = a + (t + (z + (math.log(c) * -0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -6.2e+217) || !(b <= 1.15e+240))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -6.2e+217) || ~((b <= 1.15e+240)))
		tmp = b * log(c);
	else
		tmp = a + (t + (z + (log(c) * -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -6.2e+217], N[Not[LessEqual[b, 1.15e+240]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2000000000000003e217 or 1.15000000000000001e240 < 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 b around inf 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -6.2000000000000003e217 < b < 1.15000000000000001e240

   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. Step-by-step derivation

      1. associate-+l+ 99.4%

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

      2. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. +-commutative 99.4%

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

      5. associate-+r+ 99.4%

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

      6. associate-+l+ 99.4%

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

      7. +-commutative 99.4%

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

      8. associate-+l+ 99.4%

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

      9. +-commutative 99.4%

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

      10. fma-def 99.4%

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

      11. +-commutative 99.4%

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

      12. fma-def 99.4%

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

      13. sub-neg 99.4%

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

      14. metadata-eval 99.4%

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

      15. +-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 81.2%

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

   6. Taylor expanded in b around 0 74.9%

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

   7. Taylor expanded in i around 0 51.1%

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

      1. *-commutative 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+217} \lor \neg \left(b \leq 1.15 \cdot 10^{+240}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+176}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.25e+185)
   (* (log (/ 1.0 y)) (- x))
   (if (<= x 2.7e+176) (+ a (+ z (* (- b 0.5) (log c)))) (* 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 (x <= -1.25e+185) {
		tmp = log((1.0 / y)) * -x;
	} else if (x <= 2.7e+176) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} 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 (x <= (-1.25d+185)) then
        tmp = log((1.0d0 / y)) * -x
    else if (x <= 2.7d+176) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    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 (x <= -1.25e+185) {
		tmp = Math.log((1.0 / y)) * -x;
	} else if (x <= 2.7e+176) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = x * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.25e+185:
		tmp = math.log((1.0 / y)) * -x
	elif x <= 2.7e+176:
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	else:
		tmp = x * math.log(y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.25e+185)
		tmp = Float64(log(Float64(1.0 / y)) * Float64(-x));
	elseif (x <= 2.7e+176)
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	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 (x <= -1.25e+185)
		tmp = log((1.0 / y)) * -x;
	elseif (x <= 2.7e+176)
		tmp = a + (z + ((b - 0.5) * log(c)));
	else
		tmp = x * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.25e+185], N[(N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, 2.7e+176], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999997e185

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 96.8%

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

   4. Taylor expanded in x around inf 60.7%

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

   if -1.24999999999999997e185 < x < 2.6999999999999998e176

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.4%

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

   6. Taylor expanded in t around 0 80.7%

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

      1. associate-+r+ 80.7%

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

      2. sub-neg 80.7%

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

      3. metadata-eval 80.7%

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

   8. Simplified 80.7%

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

   9. Taylor expanded in y around 0 58.2%

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

   if 2.6999999999999998e176 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 57.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+176}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \log c \cdot -0.5\\ \mathbf{if}\;y \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;a + t\_1\\ \mathbf{else}:\\ \;\;\;\;z + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* (log c) -0.5))))
   (if (<= y 4.5e+67)
     (+ a (+ z (* (- b 0.5) (log c))))
     (if (<= y 3.4e+123) (+ a t_1) (+ z 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) + (log(c) * -0.5);
	double tmp;
	if (y <= 4.5e+67) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else if (y <= 3.4e+123) {
		tmp = a + t_1;
	} else {
		tmp = z + 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 = (y * i) + (log(c) * (-0.5d0))
    if (y <= 4.5d+67) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else if (y <= 3.4d+123) then
        tmp = a + t_1
    else
        tmp = z + 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) + (Math.log(c) * -0.5);
	double tmp;
	if (y <= 4.5e+67) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else if (y <= 3.4e+123) {
		tmp = a + t_1;
	} else {
		tmp = z + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (math.log(c) * -0.5)
	tmp = 0
	if y <= 4.5e+67:
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	elif y <= 3.4e+123:
		tmp = a + t_1
	else:
		tmp = z + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(log(c) * -0.5))
	tmp = 0.0
	if (y <= 4.5e+67)
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	elseif (y <= 3.4e+123)
		tmp = Float64(a + t_1);
	else
		tmp = Float64(z + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (log(c) * -0.5);
	tmp = 0.0;
	if (y <= 4.5e+67)
		tmp = a + (z + ((b - 0.5) * log(c)));
	elseif (y <= 3.4e+123)
		tmp = a + t_1;
	else
		tmp = z + 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[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 4.5e+67], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+123], N[(a + t$95$1), $MachinePrecision], N[(z + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.4999999999999998e67

   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. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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-def 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-def 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. Taylor expanded in x around 0 80.3%

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

   6. Taylor expanded in t around 0 66.1%

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

      1. associate-+r+ 66.1%

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

      2. sub-neg 66.1%

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

      3. metadata-eval 66.1%

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

   8. Simplified 66.1%

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

   9. Taylor expanded in y around 0 59.2%

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

   if 4.4999999999999998e67 < y < 3.40000000000000001e123

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.0%

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

   6. Taylor expanded in b around 0 85.3%

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

   7. Taylor expanded in t around 0 74.4%

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

   8. Taylor expanded in z around 0 63.2%

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

   if 3.40000000000000001e123 < y

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-+l+ 98.5%

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

      3. +-commutative 98.5%

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

      4. +-commutative 98.5%

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

      5. associate-+r+ 98.5%

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

      6. associate-+l+ 98.5%

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

      7. +-commutative 98.5%

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

      8. associate-+l+ 98.5%

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

      9. +-commutative 98.5%

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

      10. fma-def 98.5%

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

      11. +-commutative 98.5%

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

      12. fma-def 98.5%

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

      13. sub-neg 98.5%

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

      14. metadata-eval 98.5%

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

      15. +-commutative 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around 0 86.8%

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

   6. Taylor expanded in b around 0 80.9%

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

   7. Taylor expanded in t around 0 70.9%

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

   8. Taylor expanded in a around 0 56.7%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+67}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(y \cdot i + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+215} \lor \neg \left(b \leq 1.2 \cdot 10^{+240}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -2.6e+215) (not (<= b 1.2e+240)))
   (* b (log c))
   (+ a (+ z (* (log c) -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 <= -2.6e+215) || !(b <= 1.2e+240)) {
		tmp = b * log(c);
	} else {
		tmp = a + (z + (log(c) * -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 <= (-2.6d+215)) .or. (.not. (b <= 1.2d+240))) then
        tmp = b * log(c)
    else
        tmp = a + (z + (log(c) * (-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 <= -2.6e+215) || !(b <= 1.2e+240)) {
		tmp = b * Math.log(c);
	} else {
		tmp = a + (z + (Math.log(c) * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -2.6e+215) or not (b <= 1.2e+240):
		tmp = b * math.log(c)
	else:
		tmp = a + (z + (math.log(c) * -0.5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -2.6e+215) || !(b <= 1.2e+240))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(a + Float64(z + Float64(log(c) * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -2.6e+215) || ~((b <= 1.2e+240)))
		tmp = b * log(c);
	else
		tmp = a + (z + (log(c) * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -2.6e+215], N[Not[LessEqual[b, 1.2e+240]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6e215 or 1.1999999999999999e240 < 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 b around inf 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -2.6e215 < b < 1.1999999999999999e240

   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. Step-by-step derivation

      1. associate-+l+ 99.4%

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

      2. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. +-commutative 99.4%

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

      5. associate-+r+ 99.4%

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

      6. associate-+l+ 99.4%

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

      7. +-commutative 99.4%

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

      8. associate-+l+ 99.4%

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

      9. +-commutative 99.4%

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

      10. fma-def 99.4%

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

      11. +-commutative 99.4%

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

      12. fma-def 99.4%

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

      13. sub-neg 99.4%

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

      14. metadata-eval 99.4%

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

      15. +-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 81.2%

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

   6. Taylor expanded in b around 0 74.9%

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

   7. Taylor expanded in t around 0 59.8%

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

   8. Taylor expanded in i around 0 36.4%

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

      1. *-commutative 36.4%

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

   10. Simplified 36.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+215} \lor \neg \left(b \leq 1.2 \cdot 10^{+240}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.95e+67)
   (+ a (+ z (* (- b 0.5) (log c))))
   (+ a (+ (* y i) (* (log c) -0.5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.95e+67) {
		tmp = a + (z + ((b - 0.5) * log(c)));
	} else {
		tmp = a + ((y * i) + (log(c) * -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 (y <= 1.95d+67) then
        tmp = a + (z + ((b - 0.5d0) * log(c)))
    else
        tmp = a + ((y * i) + (log(c) * (-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 (y <= 1.95e+67) {
		tmp = a + (z + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = a + ((y * i) + (Math.log(c) * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.95e+67:
		tmp = a + (z + ((b - 0.5) * math.log(c)))
	else:
		tmp = a + ((y * i) + (math.log(c) * -0.5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.95e+67)
		tmp = Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.95e+67)
		tmp = a + (z + ((b - 0.5) * log(c)));
	else
		tmp = a + ((y * i) + (log(c) * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.95e+67], N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.95000000000000003e67

   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. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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-def 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-def 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. Taylor expanded in x around 0 80.3%

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

   6. Taylor expanded in t around 0 66.1%

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

      1. associate-+r+ 66.1%

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

      2. sub-neg 66.1%

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

      3. metadata-eval 66.1%

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

   8. Simplified 66.1%

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

   9. Taylor expanded in y around 0 59.2%

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

   if 1.95000000000000003e67 < y

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. associate-+l+ 98.9%

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

      3. +-commutative 98.9%

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

      4. +-commutative 98.9%

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

      5. associate-+r+ 98.9%

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

      6. associate-+l+ 98.9%

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

      7. +-commutative 98.9%

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

      8. associate-+l+ 98.9%

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

      9. +-commutative 98.9%

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

      10. fma-def 98.9%

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

      11. +-commutative 98.9%

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

      12. fma-def 98.9%

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

      13. sub-neg 98.9%

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

      14. metadata-eval 98.9%

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

      15. +-commutative 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 88.2%

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

   6. Taylor expanded in b around 0 82.1%

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

   7. Taylor expanded in t around 0 71.8%

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

   8. Taylor expanded in z around 0 63.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.6% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -1.1e-241)
   z
   (if (<= a -8.5e-281)
     (* y i)
     (if (<= a 1.26e-33) z (if (<= a 5.8e+145) (* y i) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.1e-241) {
		tmp = z;
	} else if (a <= -8.5e-281) {
		tmp = y * i;
	} else if (a <= 1.26e-33) {
		tmp = z;
	} else if (a <= 5.8e+145) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-1.1d-241)) then
        tmp = z
    else if (a <= (-8.5d-281)) then
        tmp = y * i
    else if (a <= 1.26d-33) then
        tmp = z
    else if (a <= 5.8d+145) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.1e-241) {
		tmp = z;
	} else if (a <= -8.5e-281) {
		tmp = y * i;
	} else if (a <= 1.26e-33) {
		tmp = z;
	} else if (a <= 5.8e+145) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -1.1e-241:
		tmp = z
	elif a <= -8.5e-281:
		tmp = y * i
	elif a <= 1.26e-33:
		tmp = z
	elif a <= 5.8e+145:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -1.1e-241)
		tmp = z;
	elseif (a <= -8.5e-281)
		tmp = Float64(y * i);
	elseif (a <= 1.26e-33)
		tmp = z;
	elseif (a <= 5.8e+145)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -1.1e-241)
		tmp = z;
	elseif (a <= -8.5e-281)
		tmp = y * i;
	elseif (a <= 1.26e-33)
		tmp = z;
	elseif (a <= 5.8e+145)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -1.1e-241], z, If[LessEqual[a, -8.5e-281], N[(y * i), $MachinePrecision], If[LessEqual[a, 1.26e-33], z, If[LessEqual[a, 5.8e+145], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e-241 or -8.4999999999999994e-281 < a < 1.26000000000000005e-33

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 15.1%

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

   if -1.1e-241 < a < -8.4999999999999994e-281 or 1.26000000000000005e-33 < a < 5.8000000000000001e145

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 32.7%

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

      1. *-commutative 32.7%

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

   5. Simplified 32.7%

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

   if 5.8000000000000001e145 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.2%

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

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-281}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.4% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.3 \cdot 10^{+110}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4.3e+110) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.3e+110) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.3d+110) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.3e+110) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.3e+110:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.3e+110)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.3e+110)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.3e+110], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 4.30000000000000007e110

   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 z around inf 14.8%

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

   if 4.30000000000000007e110 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 47.4%

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

4. Final simplification 19.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.3 \cdot 10^{+110}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 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 99.5%

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

3. Taylor expanded in a around inf 19.5%

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

4. Final simplification 19.5%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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)))