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

Percentage Accurate: 99.8% → 99.8%

Time: 14.9s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+79} \lor \neg \left(t\_1 \leq 10^{+177}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= t_1 -4e+79) (not (<= t_1 1e+177)))
     (+ (* y i) (+ a (+ z t_1)))
     (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* -0.5 (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((t_1 <= -4e+79) || !(t_1 <= 1e+177)) {
		tmp = (y * i) + (a + (z + t_1));
	} else {
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (-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) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((t_1 <= (-4d+79)) .or. (.not. (t_1 <= 1d+177))) then
        tmp = (y * i) + (a + (z + t_1))
    else
        tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + ((-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 t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((t_1 <= -4e+79) || !(t_1 <= 1e+177)) {
		tmp = (y * i) + (a + (z + t_1));
	} else {
		tmp = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (-0.5 * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (t_1 <= -4e+79) or not (t_1 <= 1e+177):
		tmp = (y * i) + (a + (z + t_1))
	else:
		tmp = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (-0.5 * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((t_1 <= -4e+79) || !(t_1 <= 1e+177))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t_1)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(-0.5 * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((t_1 <= -4e+79) || ~((t_1 <= 1e+177)))
		tmp = (y * i) + (a + (z + t_1));
	else
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (-0.5 * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+79], N[Not[LessEqual[t$95$1, 1e+177]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -3.99999999999999987e79 or 1e177 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 58.4%

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

      1. sub-neg 58.4%

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

      2. metadata-eval 58.4%

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

      3. associate-/l* 58.3%

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

      4. +-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in t around 0 53.6%

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

   7. Taylor expanded in x around 0 87.8%

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

   if -3.99999999999999987e79 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1e177

   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 0 97.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -4 \cdot 10^{+79} \lor \neg \left(\log c \cdot \left(b - 0.5\right) \leq 10^{+177}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+168} \lor \neg \left(x \leq 2.7 \cdot 10^{+140}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.9e+168) (not (<= x 2.7e+140)))
   (+ (* y i) (+ a (+ z (+ (* x (log y)) (* -0.5 (log c))))))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.9e+168) || !(x <= 2.7e+140)) {
		tmp = (y * i) + (a + (z + ((x * log(y)) + (-0.5 * log(c)))));
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.9d+168)) .or. (.not. (x <= 2.7d+140))) then
        tmp = (y * i) + (a + (z + ((x * log(y)) + ((-0.5d0) * log(c)))))
    else
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.9e+168) || !(x <= 2.7e+140)) {
		tmp = (y * i) + (a + (z + ((x * Math.log(y)) + (-0.5 * Math.log(c)))));
	} else {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.9e+168) or not (x <= 2.7e+140):
		tmp = (y * i) + (a + (z + ((x * math.log(y)) + (-0.5 * math.log(c)))))
	else:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.9e+168) || !(x <= 2.7e+140))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(x * log(y)) + Float64(-0.5 * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.9e+168) || ~((x <= 2.7e+140)))
		tmp = (y * i) + (a + (z + ((x * log(y)) + (-0.5 * log(c)))));
	else
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.9e+168], N[Not[LessEqual[x, 2.7e+140]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e168 or 2.70000000000000018e140 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 92.7%

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

   4. Taylor expanded in t around 0 85.9%

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

   if -2.9e168 < x < 2.70000000000000018e140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+168} \lor \neg \left(x \leq 2.7 \cdot 10^{+140}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + b \cdot \frac{\log c}{x}\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.9e+214)
   (+ (* y i) (* x (+ (log y) (* b (/ (log c) x)))))
   (if (<= x 1.26e+171)
     (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
     (+ (* y i) (* x (+ (log y) (/ a x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.9e+214) {
		tmp = (y * i) + (x * (log(y) + (b * (log(c) / x))));
	} else if (x <= 1.26e+171) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	}
	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 <= (-1.9d+214)) then
        tmp = (y * i) + (x * (log(y) + (b * (log(c) / x))))
    else if (x <= 1.26d+171) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + (x * (log(y) + (a / x)))
    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 <= -1.9e+214) {
		tmp = (y * i) + (x * (Math.log(y) + (b * (Math.log(c) / x))));
	} else if (x <= 1.26e+171) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.9e+214:
		tmp = (y * i) + (x * (math.log(y) + (b * (math.log(c) / x))))
	elif x <= 1.26e+171:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.9e+214)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(b * Float64(log(c) / x)))));
	elseif (x <= 1.26e+171)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.9e+214)
		tmp = (y * i) + (x * (log(y) + (b * (log(c) / x))));
	elseif (x <= 1.26e+171)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + (x * (log(y) + (a / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.9e+214], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(b * N[(N[Log[c], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.26e+171], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.89999999999999999e214

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-/l* 99.8%

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

      4. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around inf 94.2%

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

      1. associate-/l* 94.2%

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

   8. Simplified 94.2%

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

   if -1.89999999999999999e214 < x < 1.26000000000000004e171

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.1%

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

   if 1.26000000000000004e171 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-/l* 99.7%

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

      4. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around inf 83.9%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + b \cdot \frac{\log c}{x}\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6.4e+209)
   (+ (* y i) (* x (+ (log y) (/ z x))))
   (if (<= x 1.15e+171)
     (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
     (+ (* y i) (* x (+ (log y) (/ a x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6.4e+209) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else if (x <= 1.15e+171) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-6.4d+209)) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else if (x <= 1.15d+171) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + (x * (log(y) + (a / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6.4e+209) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else if (x <= 1.15e+171) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -6.4e+209:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	elif x <= 1.15e+171:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6.4e+209)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	elseif (x <= 1.15e+171)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -6.4e+209)
		tmp = (y * i) + (x * (log(y) + (z / x)));
	elseif (x <= 1.15e+171)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + (x * (log(y) + (a / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6.4e+209], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+171], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.3999999999999999e209

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-/l* 99.8%

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

      4. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 87.9%

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

   if -6.3999999999999999e209 < x < 1.15000000000000009e171

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.1%

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

   if 1.15000000000000009e171 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-/l* 99.7%

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

      4. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around inf 83.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+153}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-198}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.3e+153)
   (+ z (* y i))
   (if (<= z -7.2e+19)
     (+ (* y i) (* x (+ (log y) (/ a x))))
     (if (<= z -5.6e-198) (+ (* (log c) (- b 0.5)) (* 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 <= -3.3e+153) {
		tmp = z + (y * i);
	} else if (z <= -7.2e+19) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else if (z <= -5.6e-198) {
		tmp = (log(c) * (b - 0.5)) + (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 <= (-3.3d+153)) then
        tmp = z + (y * i)
    else if (z <= (-7.2d+19)) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else if (z <= (-5.6d-198)) then
        tmp = (log(c) * (b - 0.5d0)) + (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 <= -3.3e+153) {
		tmp = z + (y * i);
	} else if (z <= -7.2e+19) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else if (z <= -5.6e-198) {
		tmp = (Math.log(c) * (b - 0.5)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.3e+153:
		tmp = z + (y * i)
	elif z <= -7.2e+19:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	elif z <= -5.6e-198:
		tmp = (math.log(c) * (b - 0.5)) + (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 <= -3.3e+153)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -7.2e+19)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	elseif (z <= -5.6e-198)
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + 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 <= -3.3e+153)
		tmp = z + (y * i);
	elseif (z <= -7.2e+19)
		tmp = (y * i) + (x * (log(y) + (a / x)));
	elseif (z <= -5.6e-198)
		tmp = (log(c) * (b - 0.5)) + (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, -3.3e+153], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e+19], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-198], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.29999999999999994e153

   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 68.2%

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

   if -3.29999999999999994e153 < z < -7.2e19

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 58.9%

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

      1. sub-neg 58.9%

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

      2. metadata-eval 58.9%

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

      3. associate-/l* 58.9%

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

      4. +-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 52.3%

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

   if -7.2e19 < z < -5.5999999999999998e-198

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf 91.8%

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

      1. associate-+r+ 91.8%

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

      2. associate-/l* 91.9%

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

   7. Simplified 91.9%

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

   8. Taylor expanded in z around inf 49.0%

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

   9. Taylor expanded in z around 0 48.8%

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

   if -5.5999999999999998e-198 < 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 36.4%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+153}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-198}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+210}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.8e+210)
   (+ (* y i) (* x (+ (log y) (/ z x))))
   (if (<= x 1.06e+171)
     (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))
     (+ (* y i) (* x (+ (log y) (/ a x)))))))

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+210) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else if (x <= 1.06e+171) {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	}
	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+210)) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else if (x <= 1.06d+171) then
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (x * (log(y) + (a / x)))
    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+210) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else if (x <= 1.06e+171) {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.8e+210:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	elif x <= 1.06e+171:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.8e+210)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	elseif (x <= 1.06e+171)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.8e+210)
		tmp = (y * i) + (x * (log(y) + (z / x)));
	elseif (x <= 1.06e+171)
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (x * (log(y) + (a / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.8e+210], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+171], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8000000000000001e210

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-/l* 99.8%

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

      4. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 87.9%

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

   if -1.8000000000000001e210 < x < 1.06000000000000001e171

   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 inf 66.2%

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

      1. sub-neg 66.2%

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

      2. metadata-eval 66.2%

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

      3. associate-/l* 66.2%

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

      4. +-commutative 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in t around 0 54.9%

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

   7. Taylor expanded in x around 0 76.5%

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

   if 1.06000000000000001e171 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-/l* 99.7%

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

      4. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around inf 83.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+210}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+171}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-198}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.75e+158)
   (+ z (* y i))
   (if (<= z -5.5e-198) (+ (* (log c) (- b 0.5)) (* y i)) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.75e+158) {
		tmp = z + (y * i);
	} else if (z <= -5.5e-198) {
		tmp = (log(c) * (b - 0.5)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.75d+158)) then
        tmp = z + (y * i)
    else if (z <= (-5.5d-198)) then
        tmp = (log(c) * (b - 0.5d0)) + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.75e+158) {
		tmp = z + (y * i);
	} else if (z <= -5.5e-198) {
		tmp = (Math.log(c) * (b - 0.5)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.75e+158:
		tmp = z + (y * i)
	elif z <= -5.5e-198:
		tmp = (math.log(c) * (b - 0.5)) + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.75e+158)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -5.5e-198)
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.75e+158)
		tmp = z + (y * i);
	elseif (z <= -5.5e-198)
		tmp = (log(c) * (b - 0.5)) + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.75e+158], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-198], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e158

   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 68.2%

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

   if -1.7500000000000001e158 < z < -5.5000000000000001e-198

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf 90.7%

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

      1. associate-+r+ 90.7%

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

      2. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

   8. Taylor expanded in z around inf 46.8%

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

   9. Taylor expanded in z around 0 46.6%

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

   if -5.5000000000000001e-198 < 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 36.4%

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

Alternative 10: 44.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-195}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.8e+158)
   (+ z (* y i))
   (if (<= z -9e-195) (+ (* y i) (* b (log c))) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+158) {
		tmp = z + (y * i);
	} else if (z <= -9e-195) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.8d+158)) then
        tmp = z + (y * i)
    else if (z <= (-9d-195)) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+158) {
		tmp = z + (y * i);
	} else if (z <= -9e-195) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+158:
		tmp = z + (y * i)
	elif z <= -9e-195:
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.8e+158)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -9e-195)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.8e+158)
		tmp = z + (y * i);
	elseif (z <= -9e-195)
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.8e+158], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-195], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000001e158

   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 68.2%

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

   if -2.80000000000000001e158 < z < -9e-195

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 77.6%

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

      1. sub-neg 77.6%

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

      2. metadata-eval 77.6%

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

      3. associate-/l* 77.6%

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

      4. +-commutative 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in b around inf 41.6%

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

      1. *-commutative 41.6%

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

   8. Simplified 41.6%

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

   if -9e-195 < 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 36.4%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+158}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-195}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.75 \cdot 10^{+221}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.75e+221) (+ (* y i) (+ z (* (log c) (- b 0.5)))) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.75e+221) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.75d+221) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.75e+221) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.75e+221:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.75e+221)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.75e+221)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.75e+221], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.7500000000000001e221

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf 78.0%

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

      1. associate-+r+ 78.0%

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

      2. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in z around inf 56.8%

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

   if 1.7500000000000001e221 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 64.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.75 \cdot 10^{+221}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.4 \cdot 10^{+147}:\\ \;\;\;\;z + \log c \cdot \left(b - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.4e+147) (+ z (* (log c) (- b 0.5))) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.4e+147) {
		tmp = z + (log(c) * (b - 0.5));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.4d+147) then
        tmp = z + (log(c) * (b - 0.5d0))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.4e+147) {
		tmp = z + (Math.log(c) * (b - 0.5));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.4e+147:
		tmp = z + (math.log(c) * (b - 0.5))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.4e+147)
		tmp = Float64(z + Float64(log(c) * Float64(b - 0.5)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.4e+147)
		tmp = z + (log(c) * (b - 0.5));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.4e+147], N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.40000000000000002e147

   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. Step-by-step derivation

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf 76.6%

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

      1. associate-+r+ 76.6%

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

      2. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in z around inf 56.9%

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

   9. Taylor expanded in y around 0 38.8%

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

   if 2.40000000000000002e147 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 53.3%

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

Alternative 13: 43.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+153}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2e+153) (+ 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 <= -2e+153) {
		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 <= (-2d+153)) 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 <= -2e+153) {
		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 <= -2e+153:
		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 <= -2e+153)
		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 <= -2e+153)
		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, -2e+153], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e153

   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 68.2%

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

   if -2e153 < 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 37.4%

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

Alternative 14: 39.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \frac{z}{i}\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.2e+195) (* i (/ z 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+195) {
		tmp = i * (z / 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+195)) then
        tmp = i * (z / 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+195) {
		tmp = i * (z / 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+195:
		tmp = i * (z / 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+195)
		tmp = Float64(i * Float64(z / 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+195)
		tmp = i * (z / 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+195], N[(i * N[(z / i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999982e195

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in i around inf 59.6%

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

      1. +-commutative 59.6%

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

      2. +-commutative 59.6%

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

      3. associate-+l+ 59.6%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 36.9%

      \[\leadsto i \cdot \color{blue}{\frac{z}{i}} \]

   if -3.19999999999999982e195 < 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 36.5%

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

Alternative 15: 18.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \frac{z}{i}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.5e+120) (* i (/ z i)) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.5e+120) {
		tmp = i * (z / 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 (z <= (-1.5d+120)) then
        tmp = i * (z / 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 (z <= -1.5e+120) {
		tmp = i * (z / i);
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.5e+120:
		tmp = i * (z / i)
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.5e+120)
		tmp = Float64(i * Float64(z / 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 (z <= -1.5e+120)
		tmp = i * (z / i);
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.5e+120], N[(i * N[(z / i), $MachinePrecision]), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e120

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in i around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. +-commutative 62.3%

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

      3. associate-+l+ 62.3%

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

   7. Simplified 62.2%

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

   8. Taylor expanded in z around inf 34.4%

      \[\leadsto i \cdot \color{blue}{\frac{z}{i}} \]

   if -1.5e120 < 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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in i around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. +-commutative 65.4%

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

      3. associate-+l+ 65.4%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in a around inf 11.0%

      \[\leadsto i \cdot \color{blue}{\frac{a}{i}} \]

   9. Taylor expanded in i around 0 18.0%

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

Alternative 16: 28.9% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.15 \cdot 10^{+156}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.15e+156) (* 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 <= 2.15e+156) {
		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 <= 2.15d+156) 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 <= 2.15e+156) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.15e+156:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.15e+156)
		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 <= 2.15e+156)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.15e+156], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 2.14999999999999993e156

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 20.4%

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

      1. *-commutative 20.4%

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

   7. Simplified 20.4%

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

   if 2.14999999999999993e156 < a

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in i around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. +-commutative 54.9%

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

      3. associate-+l+ 54.9%

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

   7. Simplified 54.9%

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

   8. Taylor expanded in a around inf 18.4%

      \[\leadsto i \cdot \color{blue}{\frac{a}{i}} \]

   9. Taylor expanded in i around 0 37.9%

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

Alternative 17: 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. Step-by-step derivation

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in i around inf 64.9%

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

   1. +-commutative 64.9%

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

   2. +-commutative 64.9%

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

   3. associate-+l+ 64.9%

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

7. Simplified 64.8%

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

8. Taylor expanded in a around inf 10.4%

   \[\leadsto i \cdot \color{blue}{\frac{a}{i}} \]

9. Taylor expanded in i around 0 16.6%

   \[\leadsto \color{blue}{a} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(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)))