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

Percentage Accurate: 99.8% → 99.8%

Time: 18.5s

Alternatives: 16

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{+126}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.25e+126)
   (+ (* y i) (+ t (+ z (+ (* x (log y)) (* b (log c))))))
   (+ (* y i) (+ a (+ (+ z t) (* (log c) (+ b -0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e+126) {
		tmp = (y * i) + (t + (z + ((x * log(y)) + (b * log(c)))));
	} else {
		tmp = (y * i) + (a + ((z + t) + (log(c) * (b + -0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.25d+126) then
        tmp = (y * i) + (t + (z + ((x * log(y)) + (b * log(c)))))
    else
        tmp = (y * i) + (a + ((z + t) + (log(c) * (b + (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e+126) {
		tmp = (y * i) + (t + (z + ((x * Math.log(y)) + (b * Math.log(c)))));
	} else {
		tmp = (y * i) + (a + ((z + t) + (Math.log(c) * (b + -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.25e+126:
		tmp = (y * i) + (t + (z + ((x * math.log(y)) + (b * math.log(c)))))
	else:
		tmp = (y * i) + (a + ((z + t) + (math.log(c) * (b + -0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.25e+126)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(b * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.25e+126)
		tmp = (y * i) + (t + (z + ((x * log(y)) + (b * log(c)))));
	else
		tmp = (y * i) + (a + ((z + t) + (log(c) * (b + -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.25e+126], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.24999999999999987e126

   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 96.9%

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

      1. *-commutative 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in a around 0 83.1%

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

   if 2.24999999999999987e126 < 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 94.3%

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

      1. associate-+r+ 94.3%

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

      2. sub-neg 94.3%

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

      3. metadata-eval 94.3%

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

      4. +-commutative 94.3%

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

   5. Simplified 94.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{+126}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 97.4%

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

   1. *-commutative 97.4%

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

5. Simplified 97.4%

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

6. Final simplification 97.4%

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

Alternative 4: 89.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+194}:\\ \;\;\;\;y \cdot i + \left(z + t_1\right)\\ \mathbf{elif}\;b - 0.5 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c))))
   (if (<= (- b 0.5) -1e+194)
     (+ (* y i) (+ z t_1))
     (if (<= (- b 0.5) 2e+149)
       (+ (+ a (+ t (+ (* x (log y)) z))) (* y i))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * log(c);
	double tmp;
	if ((b - 0.5) <= -1e+194) {
		tmp = (y * i) + (z + t_1);
	} else if ((b - 0.5) <= 2e+149) {
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    if ((b - 0.5d0) <= (-1d+194)) then
        tmp = (y * i) + (z + t_1)
    else if ((b - 0.5d0) <= 2d+149) then
        tmp = (a + (t + ((x * log(y)) + z))) + (y * i)
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (b - 0.5) * Math.log(c);
	double tmp;
	if ((b - 0.5) <= -1e+194) {
		tmp = (y * i) + (z + t_1);
	} else if ((b - 0.5) <= 2e+149) {
		tmp = (a + (t + ((x * Math.log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	tmp = 0
	if (b - 0.5) <= -1e+194:
		tmp = (y * i) + (z + t_1)
	elif (b - 0.5) <= 2e+149:
		tmp = (a + (t + ((x * math.log(y)) + z))) + (y * i)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+194)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (Float64(b - 0.5) <= 2e+149)
		tmp = Float64(Float64(a + Float64(t + Float64(Float64(x * log(y)) + z))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	tmp = 0.0;
	if ((b - 0.5) <= -1e+194)
		tmp = (y * i) + (z + t_1);
	elseif ((b - 0.5) <= 2e+149)
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+194], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 2e+149], N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b 1/2) < -9.99999999999999945e193

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 96.0%

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

      1. associate-+r+ 96.0%

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

      2. sub-neg 96.0%

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

      3. metadata-eval 96.0%

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

      4. +-commutative 96.0%

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

   8. Simplified 96.0%

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

   9. Taylor expanded in a around 0 72.2%

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

   if -9.99999999999999945e193 < (-.f64 b 1/2) < 2.0000000000000001e149

   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 96.9%

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

      1. *-commutative 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in b around 0 93.7%

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

   if 2.0000000000000001e149 < (-.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 91.5%

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

      1. associate-+r+ 91.5%

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

      2. sub-neg 91.5%

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

      3. metadata-eval 91.5%

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

      4. +-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around 0 88.3%

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

      1. associate-+r+ 88.3%

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

      2. sub-neg 88.3%

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

      3. metadata-eval 88.3%

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

      4. +-commutative 88.3%

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

   8. Simplified 88.3%

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

   9. Taylor expanded in z around 0 82.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+194}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;b - 0.5 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+165} \lor \neg \left(z \leq -2.35 \cdot 10^{+142}\right) \land z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -8.5e+165) (and (not (<= z -2.35e+142)) (<= z -2.9e+87)))
   (+ (* y i) (+ z a))
   (+ (* y i) (+ a (* (- b 0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -8.5e+165) || (!(z <= -2.35e+142) && (z <= -2.9e+87))) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-8.5d+165)) .or. (.not. (z <= (-2.35d+142))) .and. (z <= (-2.9d+87))) then
        tmp = (y * i) + (z + a)
    else
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -8.5e+165) || (!(z <= -2.35e+142) && (z <= -2.9e+87))) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -8.5e+165) or (not (z <= -2.35e+142) and (z <= -2.9e+87)):
		tmp = (y * i) + (z + a)
	else:
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -8.5e+165) || (!(z <= -2.35e+142) && (z <= -2.9e+87)))
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -8.5e+165) || (~((z <= -2.35e+142)) && (z <= -2.9e+87)))
		tmp = (y * i) + (z + a);
	else
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -8.5e+165], And[N[Not[LessEqual[z, -2.35e+142]], $MachinePrecision], LessEqual[z, -2.9e+87]]], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000001e165 or -2.35e142 < z < -2.8999999999999998e87

   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 92.6%

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

      1. associate-+r+ 92.6%

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

      2. sub-neg 92.6%

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

      3. metadata-eval 92.6%

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

      4. +-commutative 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in z around inf 73.0%

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

   if -8.5000000000000001e165 < z < -2.35e142 or -2.8999999999999998e87 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.7%

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

      1. associate-+r+ 84.7%

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

      2. sub-neg 84.7%

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

      3. metadata-eval 84.7%

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

      4. +-commutative 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in t around 0 72.4%

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

      1. associate-+r+ 72.4%

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

      2. sub-neg 72.4%

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

      3. metadata-eval 72.4%

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

      4. +-commutative 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in z around 0 61.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+165} \lor \neg \left(z \leq -2.35 \cdot 10^{+142}\right) \land z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+81} \lor \neg \left(x \leq 5.1 \cdot 10^{+33}\right):\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1e+81) (not (<= x 5.1e+33)))
   (+ (+ a (+ t (+ (* x (log y)) z))) (* y i))
   (+ (* y i) (+ a (+ (+ z t) (* (log c) (+ b -0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+81) || !(x <= 5.1e+33)) {
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (a + ((z + t) + (log(c) * (b + -0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1d+81)) .or. (.not. (x <= 5.1d+33))) then
        tmp = (a + (t + ((x * log(y)) + z))) + (y * i)
    else
        tmp = (y * i) + (a + ((z + t) + (log(c) * (b + (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+81) || !(x <= 5.1e+33)) {
		tmp = (a + (t + ((x * Math.log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + (a + ((z + t) + (Math.log(c) * (b + -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1e+81) or not (x <= 5.1e+33):
		tmp = (a + (t + ((x * math.log(y)) + z))) + (y * i)
	else:
		tmp = (y * i) + (a + ((z + t) + (math.log(c) * (b + -0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1e+81) || !(x <= 5.1e+33))
		tmp = Float64(Float64(a + Float64(t + Float64(Float64(x * log(y)) + z))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1e+81) || ~((x <= 5.1e+33)))
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	else
		tmp = (y * i) + (a + ((z + t) + (log(c) * (b + -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1e+81], N[Not[LessEqual[x, 5.1e+33]], $MachinePrecision]], N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999921e80 or 5.0999999999999999e33 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 89.5%

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

   if -9.99999999999999921e80 < x < 5.0999999999999999e33

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. associate-+r+ 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+81} \lor \neg \left(x \leq 5.1 \cdot 10^{+33}\right):\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+72} \lor \neg \left(x \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5e+72) (not (<= x 6.2e+34)))
   (+ (+ a (+ t (+ (* x (log y)) z))) (* y i))
   (+ (* y i) (+ (* (log c) (+ b -0.5)) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5e+72) || !(x <= 6.2e+34)) {
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + ((log(c) * (b + -0.5)) + (z + 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 ((x <= (-5d+72)) .or. (.not. (x <= 6.2d+34))) then
        tmp = (a + (t + ((x * log(y)) + z))) + (y * i)
    else
        tmp = (y * i) + ((log(c) * (b + (-0.5d0))) + (z + 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 ((x <= -5e+72) || !(x <= 6.2e+34)) {
		tmp = (a + (t + ((x * Math.log(y)) + z))) + (y * i);
	} else {
		tmp = (y * i) + ((Math.log(c) * (b + -0.5)) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5e+72) or not (x <= 6.2e+34):
		tmp = (a + (t + ((x * math.log(y)) + z))) + (y * i)
	else:
		tmp = (y * i) + ((math.log(c) * (b + -0.5)) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5e+72) || !(x <= 6.2e+34))
		tmp = Float64(Float64(a + Float64(t + Float64(Float64(x * log(y)) + z))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b + -0.5)) + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5e+72) || ~((x <= 6.2e+34)))
		tmp = (a + (t + ((x * log(y)) + z))) + (y * i);
	else
		tmp = (y * i) + ((log(c) * (b + -0.5)) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5e+72], N[Not[LessEqual[x, 6.2e+34]], $MachinePrecision]], N[(N[(a + N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999992e72 or 6.19999999999999955e34 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 89.5%

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

   if -4.99999999999999992e72 < x < 6.19999999999999955e34

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. associate-+r+ 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in t around 0 86.5%

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

      1. associate-+r+ 86.5%

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

      2. sub-neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. +-commutative 86.5%

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

   8. Simplified 86.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+72} \lor \neg \left(x \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;\left(a + \left(t + \left(x \cdot \log y + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+220} \lor \neg \left(x \leq 3.1 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.8e+220) (not (<= x 3.1e+218)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+220) || !(x <= 3.1e+218)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + 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 ((x <= (-1.8d+220)) .or. (.not. (x <= 3.1d+218))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (z + 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 ((x <= -1.8e+220) || !(x <= 3.1e+218)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.8e+220) or not (x <= 3.1e+218):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.8e+220) || !(x <= 3.1e+218))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.8e+220) || ~((x <= 3.1e+218)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.8e+220], N[Not[LessEqual[x, 3.1e+218]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000009e220 or 3.1000000000000002e218 < x

   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. Step-by-step derivation

      1. flip-- 86.9%

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

      2. associate-*l/ 86.9%

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

      3. fma-neg 86.9%

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

      4. metadata-eval 86.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \frac{\mathsf{fma}\left(b, b, -\color{blue}{0.25}\right) \cdot \log c}{b + 0.5}\right) + y \cdot i \]

      5. metadata-eval 86.9%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \frac{\mathsf{fma}\left(b, b, \color{blue}{-0.25}\right) \cdot \log c}{b + 0.5}\right) + y \cdot i \]

   4. Applied egg-rr 86.9%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\frac{\mathsf{fma}\left(b, b, -0.25\right) \cdot \log c}{b + 0.5}}\right) + y \cdot i \]

   5. Taylor expanded in x around inf 75.3%

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

   if -1.80000000000000009e220 < x < 3.1000000000000002e218

   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 94.1%

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

      1. associate-+r+ 94.1%

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

      2. sub-neg 94.1%

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

      3. metadata-eval 94.1%

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

      4. +-commutative 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in z around inf 65.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+220} \lor \neg \left(x \leq 3.1 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+230} \lor \neg \left(b \leq 8.2 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -2.6e+230) (not (<= b 8.2e+167)))
   (+ (* y i) (* b (log c)))
   (+ (* y i) (+ z a))))

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+230) || !(b <= 8.2e+167)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = (y * i) + (z + 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 <= (-2.6d+230)) .or. (.not. (b <= 8.2d+167))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = (y * i) + (z + 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 <= -2.6e+230) || !(b <= 8.2e+167)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -2.6e+230) or not (b <= 8.2e+167):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -2.6e+230) || !(b <= 8.2e+167))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -2.6e+230) || ~((b <= 8.2e+167)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -2.6e+230], N[Not[LessEqual[b, 8.2e+167]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5999999999999999e230 or 8.2e167 < b

   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 93.6%

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

      1. associate-+r+ 93.6%

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

      2. sub-neg 93.6%

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

      3. metadata-eval 93.6%

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

      4. +-commutative 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around 0 89.4%

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

      1. associate-+r+ 89.4%

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

      2. sub-neg 89.4%

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

      3. metadata-eval 89.4%

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

      4. +-commutative 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in b around inf 80.2%

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

       1. *-commutative 80.2%

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

   11. Simplified 80.2%

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

   if -2.5999999999999999e230 < b < 8.2e167

   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 84.5%

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

      1. associate-+r+ 84.5%

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

      2. sub-neg 84.5%

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

      3. metadata-eval 84.5%

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

      4. +-commutative 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in z around inf 65.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+230} \lor \neg \left(b \leq 8.2 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.75 \cdot 10^{+74}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.75e+74)
   (+ (* y i) (+ z (* (- b 0.5) (log c))))
   (+ (* y i) (+ 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 <= 1.75e+74) {
		tmp = (y * i) + (z + ((b - 0.5) * log(c)));
	} else {
		tmp = (y * i) + (z + 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 <= 1.75d+74) then
        tmp = (y * i) + (z + ((b - 0.5d0) * log(c)))
    else
        tmp = (y * i) + (z + 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 <= 1.75e+74) {
		tmp = (y * i) + (z + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.75e+74:
		tmp = (y * i) + (z + ((b - 0.5) * math.log(c)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.75e+74)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.75e+74)
		tmp = (y * i) + (z + ((b - 0.5) * log(c)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.75e+74], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.75000000000000007e74

   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 83.8%

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

      1. associate-+r+ 83.8%

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

      2. sub-neg 83.8%

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

      3. metadata-eval 83.8%

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

      4. +-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in t around 0 70.8%

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

      1. associate-+r+ 70.8%

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

      2. sub-neg 70.8%

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

      3. metadata-eval 70.8%

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

      4. +-commutative 70.8%

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

   8. Simplified 70.8%

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

   9. Taylor expanded in a around 0 58.4%

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

   if 1.75000000000000007e74 < 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 94.2%

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

      1. associate-+r+ 94.2%

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

      2. sub-neg 94.2%

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

      3. metadata-eval 94.2%

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

      4. +-commutative 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in z around inf 83.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.75 \cdot 10^{+74}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.1% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.2e+158) (+ z (* y i)) (+ (* y i) (+ t a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.2e+158) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (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 (z <= (-2.2d+158)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (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 (z <= -2.2e+158) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.2e+158:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.2e+158)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.2e+158)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.2e+158], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e158

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 54.2%

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

   if -2.2000000000000001e158 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.8%

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

      1. associate-+r+ 84.8%

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

      2. sub-neg 84.8%

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

      3. metadata-eval 84.8%

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

      4. +-commutative 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in t around inf 58.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.7% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.05e+158) (+ 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 <= -2.05e+158) {
		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 <= (-2.05d+158)) 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 <= -2.05e+158) {
		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 <= -2.05e+158:
		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 <= -2.05e+158)
		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 <= -2.05e+158)
		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, -2.05e+158], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05000000000000002e158

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 54.2%

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

   if -2.05000000000000002e158 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 47.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.4% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+157}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4.2e+157) (* 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 <= 4.2e+157) {
		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 <= 4.2d+157) 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 <= 4.2e+157) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.2e+157:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.2e+157)
		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 <= 4.2e+157)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.2e+157], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 4.2e157

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 39.2%

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

   4. Taylor expanded in a around 0 26.5%

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

   if 4.2e157 < 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 75.1%

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

   4. Taylor expanded in a around inf 69.7%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+157}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.3% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(z + a), $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 85.9%

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

   1. associate-+r+ 85.9%

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

   2. sub-neg 85.9%

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

   3. metadata-eval 85.9%

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

   4. +-commutative 85.9%

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

5. Simplified 85.9%

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

6. Taylor expanded in z around inf 59.6%

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

7. Final simplification 59.6%

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

Alternative 15: 37.5% 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 a around inf 44.2%

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

4. Final simplification 44.2%

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

Alternative 16: 15.8% 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 a around inf 44.2%

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

4. Taylor expanded in a around inf 22.3%

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

5. Final simplification 22.3%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(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)))