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

Percentage Accurate: 99.8% → 99.8%

Time: 14.2s

Alternatives: 12

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

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

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]

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 98.8%

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

   1. *-commutative 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 3: 67.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+117} \lor \neg \left(b - 0.5 \leq 4 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -5e+117) (not (<= (- b 0.5) 4e+125)))
   (+ (* y i) (+ t (+ z (* (- b 0.5) (log c)))))
   (+ (* y i) (+ (+ z a) (* (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+117) || !((b - 0.5) <= 4e+125)) {
		tmp = (y * i) + (t + (z + ((b - 0.5) * log(c))));
	} else {
		tmp = (y * i) + ((z + a) + (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+117)) .or. (.not. ((b - 0.5d0) <= 4d+125))) then
        tmp = (y * i) + (t + (z + ((b - 0.5d0) * log(c))))
    else
        tmp = (y * i) + ((z + a) + (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+117) || !((b - 0.5) <= 4e+125)) {
		tmp = (y * i) + (t + (z + ((b - 0.5) * Math.log(c))));
	} else {
		tmp = (y * i) + ((z + a) + (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+117) or not ((b - 0.5) <= 4e+125):
		tmp = (y * i) + (t + (z + ((b - 0.5) * math.log(c))))
	else:
		tmp = (y * i) + ((z + a) + (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+117) || !(Float64(b - 0.5) <= 4e+125))
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + 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+117) || ~(((b - 0.5) <= 4e+125)))
		tmp = (y * i) + (t + (z + ((b - 0.5) * log(c))));
	else
		tmp = (y * i) + ((z + a) + (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+117], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 4e+125]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -4.99999999999999983e117 or 3.9999999999999997e125 < (-.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. Add Preprocessing

   3. Taylor expanded in x around 0 89.7%

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

   4. Taylor expanded in a around 0 82.8%

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

   if -4.99999999999999983e117 < (-.f64 b 1/2) < 3.9999999999999997e125

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in b around 0 79.4%

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

   5. Taylor expanded in t around 0 64.1%

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

      1. associate-+r+ 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+117} \lor \neg \left(b - 0.5 \leq 4 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+150} \lor \neg \left(b \leq 3.15 \cdot 10^{+150}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -6.1e+150) (not (<= b 3.15e+150)))
   (+ (* y i) (* b (log c)))
   (+ (* y i) (+ (+ z a) (* (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 <= -6.1e+150) || !(b <= 3.15e+150)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (y * i) + ((z + a) + (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 <= (-6.1d+150)) .or. (.not. (b <= 3.15d+150))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (y * i) + ((z + a) + (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 <= -6.1e+150) || !(b <= 3.15e+150)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (y * i) + ((z + a) + (Math.log(c) * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -6.1e+150) or not (b <= 3.15e+150):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (y * i) + ((z + a) + (math.log(c) * -0.5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -6.1e+150) || !(b <= 3.15e+150))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + 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 <= -6.1e+150) || ~((b <= 3.15e+150)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (y * i) + ((z + a) + (log(c) * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -6.1e+150], N[Not[LessEqual[b, 3.15e+150]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.10000000000000026e150 or 3.15000000000000015e150 < b

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.1%

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

   4. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   if -6.10000000000000026e150 < b < 3.15000000000000015e150

   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 81.7%

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

   4. Taylor expanded in b around 0 77.9%

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

   5. Taylor expanded in t around 0 63.6%

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

      1. associate-+r+ 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+150} \lor \neg \left(b \leq 3.15 \cdot 10^{+150}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+151} \lor \neg \left(b \leq 3.3 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -3.3e+151) (not (<= b 3.3e+154)))
   (+ (* y i) (* b (log c)))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -3.3e+151) || !(b <= 3.3e+154)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (y * i) + (z + (t + 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 ((b <= (-3.3d+151)) .or. (.not. (b <= 3.3d+154))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (y * i) + (z + (t + 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 ((b <= -3.3e+151) || !(b <= 3.3e+154)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -3.3e+151) or not (b <= 3.3e+154):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -3.3e+151) || !(b <= 3.3e+154))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -3.3e+151) || ~((b <= 3.3e+154)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -3.3e+151], N[Not[LessEqual[b, 3.3e+154]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.30000000000000025e151 or 3.3e154 < b

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.1%

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

   4. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   if -3.30000000000000025e151 < b < 3.3e154

   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 81.7%

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

      1. add-cube-cbrt 81.6%

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

      2. pow3 81.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

      3. *-un-lft-identity 81.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(1 \cdot \left(b - 0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      4. sub-neg 81.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\left(1 \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      5. *-un-lft-identity 81.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

      6. metadata-eval 81.6%

         \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   5. Applied egg-rr 81.6%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

   6. Taylor expanded in b around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-+r+ 77.0%

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

      3. +-commutative 77.0%

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

      4. associate-+l+ 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+151} \lor \neg \left(b \leq 3.3 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 83.3%

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

4. Final simplification 83.3%

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

Alternative 7: 68.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 83.3%

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

4. Taylor expanded in t around 0 70.1%

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

   1. associate-+r+ 70.1%

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

   2. sub-neg 70.1%

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

   3. metadata-eval 70.1%

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

6. Simplified 70.1%

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

7. Final simplification 70.1%

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

Alternative 8: 42.1% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.2e+43) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+43) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.2d+43)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.2e+43) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.2e+43:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.2e+43)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.2e+43)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.2e+43], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000014e43

   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 90.9%

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

   4. Taylor expanded in b around 0 82.6%

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

   5. Taylor expanded in z around inf 59.9%

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

   if -3.20000000000000014e43 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 81.2%

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

   4. Taylor expanded in a around inf 40.0%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.7% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 83.3%

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

   1. add-cube-cbrt 83.1%

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

   2. pow3 83.1%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b - 0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

   3. *-un-lft-identity 83.1%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(1 \cdot \left(b - 0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   4. sub-neg 83.1%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\left(1 \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   5. *-un-lft-identity 83.1%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\color{blue}{\left(b + \left(-0.5\right)\right)} \cdot \log c}\right)}^{3}\right) + y \cdot i \]

   6. metadata-eval 83.1%

      \[\leadsto \left(\left(\left(z + t\right) + a\right) + {\left(\sqrt[3]{\left(b + \color{blue}{-0.5}\right) \cdot \log c}\right)}^{3}\right) + y \cdot i \]

5. Applied egg-rr 83.1%

   \[\leadsto \left(\left(\left(z + t\right) + a\right) + \color{blue}{{\left(\sqrt[3]{\left(b + -0.5\right) \cdot \log c}\right)}^{3}}\right) + y \cdot i \]

6. Taylor expanded in b around inf 66.7%

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

   1. +-commutative 66.7%

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

   2. associate-+r+ 66.7%

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

   3. +-commutative 66.7%

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

   4. associate-+l+ 66.7%

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

8. Simplified 66.7%

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

9. Final simplification 66.7%

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

Alternative 10: 27.0% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.8e+108) (* 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 <= 1.8e+108) {
		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 <= 1.8d+108) 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 <= 1.8e+108) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.8e+108:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.8e+108)
		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 <= 1.8e+108)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.8e+108], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 1.8e108

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in a around inf 33.6%

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

   5. Taylor expanded in a around 0 24.6%

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

      1. *-commutative 24.6%

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

   7. Simplified 24.6%

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

   if 1.8e108 < 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 x around 0 89.1%

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

   4. Taylor expanded in a around inf 60.8%

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

   5. Taylor expanded in a around inf 50.9%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.6% accurate, 43.8× speedup

Math

\[\begin{array}{l} \\ a + y \cdot i \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 83.3%

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

4. Taylor expanded in a around inf 38.2%

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

5. Final simplification 38.2%

   \[\leadsto a + y \cdot i \]
6. Add Preprocessing

Alternative 12: 16.1% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 83.3%

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

4. Taylor expanded in a around inf 38.2%

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

5. Taylor expanded in a around inf 18.0%

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

6. Final simplification 18.0%

   \[\leadsto a \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024043 
(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)))