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

Percentage Accurate: 99.8% → 99.8%

Time: 15.1s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+
  (+ (+ (+ (+ (* x (log y)) z) t) a) (* (* b (- 1.0 (/ 0.5 b))) (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 * (1.0 - (0.5 / b))) * 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 * (1.0d0 - (0.5d0 / b))) * 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 * (1.0 - (0.5 / b))) * 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 * (1.0 - (0.5 / b))) * 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 * Float64(1.0 - Float64(0.5 / b))) * 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 * (1.0 - (0.5 / b))) * 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 * N[(1.0 - N[(0.5 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 99.9%

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

   1. associate-*r/ 99.9%

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

   2. metadata-eval 99.9%

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

5. Simplified 99.9%

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

Alternative 2: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-68}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= i -2.3e+47)
     (+ (* y i) (+ (+ z a) (* (* b (- 1.0 (/ 0.5 b))) (log c))))
     (if (<= i 1.15e-68)
       (+ a (+ t (+ z (+ (* x (log y)) t_1))))
       (+ (* y i) (+ a (+ t (+ z t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (i <= -2.3e+47) {
		tmp = (y * i) + ((z + a) + ((b * (1.0 - (0.5 / b))) * log(c)));
	} else if (i <= 1.15e-68) {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (i <= (-2.3d+47)) then
        tmp = (y * i) + ((z + a) + ((b * (1.0d0 - (0.5d0 / b))) * log(c)))
    else if (i <= 1.15d-68) then
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    else
        tmp = (y * i) + (a + (t + (z + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (i <= -2.3e+47) {
		tmp = (y * i) + ((z + a) + ((b * (1.0 - (0.5 / b))) * Math.log(c)));
	} else if (i <= 1.15e-68) {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if i <= -2.3e+47:
		tmp = (y * i) + ((z + a) + ((b * (1.0 - (0.5 / b))) * math.log(c)))
	elif i <= 1.15e-68:
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	else:
		tmp = (y * i) + (a + (t + (z + t_1)))
	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 (i <= -2.3e+47)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(Float64(b * Float64(1.0 - Float64(0.5 / b))) * log(c))));
	elseif (i <= 1.15e-68)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	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 (i <= -2.3e+47)
		tmp = (y * i) + ((z + a) + ((b * (1.0 - (0.5 / b))) * log(c)));
	elseif (i <= 1.15e-68)
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	else
		tmp = (y * i) + (a + (t + (z + t_1)));
	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[LessEqual[i, -2.3e+47], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[(b * N[(1.0 - N[(0.5 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e-68], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.2999999999999999e47

   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 t around 0 84.7%

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

   4. Taylor expanded in x around 0 70.1%

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

      1. associate-+r+ 70.1%

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

      2. sub-neg 70.1%

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

      3. metadata-eval 70.1%

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

      4. +-commutative 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in b around inf 70.1%

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

      1. associate-*r/ 70.1%

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

      2. metadata-eval 70.1%

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

   9. Simplified 70.1%

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

   if -2.2999999999999999e47 < i < 1.14999999999999998e-68

   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 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 68.5%

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

   6. Taylor expanded in y around 0 98.0%

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

   if 1.14999999999999998e-68 < i

   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 95.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-68}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 4: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+211}:\\ \;\;\;\;t + \left(z + \left(t\_1 + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.3e+211)
     (+ t (+ z (+ t_1 (* (log c) (- b 0.5)))))
     (if (<= x 1.55e+117)
       (+ (* y i) (+ a (+ (* (* b (- 1.0 (/ 0.5 b))) (log c)) (+ z t))))
       (+ (* y i) (+ t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.3e+211) {
		tmp = t + (z + (t_1 + (log(c) * (b - 0.5))));
	} else if (x <= 1.55e+117) {
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * log(c)) + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.3d+211)) then
        tmp = t + (z + (t_1 + (log(c) * (b - 0.5d0))))
    else if (x <= 1.55d+117) then
        tmp = (y * i) + (a + (((b * (1.0d0 - (0.5d0 / b))) * log(c)) + (z + t)))
    else
        tmp = (y * i) + (t_1 + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -2.3e+211) {
		tmp = t + (z + (t_1 + (Math.log(c) * (b - 0.5))));
	} else if (x <= 1.55e+117) {
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * Math.log(c)) + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.3e+211:
		tmp = t + (z + (t_1 + (math.log(c) * (b - 0.5))))
	elif x <= 1.55e+117:
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * math.log(c)) + (z + t)))
	else:
		tmp = (y * i) + (t_1 + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.3e+211)
		tmp = Float64(t + Float64(z + Float64(t_1 + Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 1.55e+117)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(b * Float64(1.0 - Float64(0.5 / b))) * log(c)) + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.3e+211)
		tmp = t + (z + (t_1 + (log(c) * (b - 0.5))));
	elseif (x <= 1.55e+117)
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * log(c)) + (z + t)));
	else
		tmp = (y * i) + (t_1 + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+211], N[(t + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+117], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(b * N[(1.0 - N[(0.5 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.30000000000000011e211

   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 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 59.4%

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

   6. Taylor expanded in y around 0 84.8%

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

   7. Taylor expanded in a around 0 79.6%

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

   if -2.30000000000000011e211 < x < 1.54999999999999988e117

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.1%

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

      1. associate-+r+ 96.1%

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

      2. associate-*r/ 96.1%

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

      3. metadata-eval 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-*l* 96.1%

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

      6. *-commutative 96.1%

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

   8. Simplified 96.1%

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

   if 1.54999999999999988e117 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 92.2%

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

   4. Taylor expanded in z around inf 65.2%

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

      1. associate-/l* 65.2%

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

      2. associate-/l* 65.2%

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

      3. sub-neg 65.2%

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

      4. metadata-eval 65.2%

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

      5. +-commutative 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in x around inf 75.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+211}:\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+117}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in t around 0 82.5%

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

4. Final simplification 82.5%

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

Alternative 6: 90.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+210} \lor \neg \left(x \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.2e+210) (not (<= x 1.3e+117)))
   (+ (* y i) (+ (* x (log y)) a))
   (+ (* y i) (+ a (+ (* (* b (- 1.0 (/ 0.5 b))) (log c)) (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.2e+210) || !(x <= 1.3e+117)) {
		tmp = (y * i) + ((x * log(y)) + a);
	} else {
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * log(c)) + (z + t)));
	}
	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 <= (-2.2d+210)) .or. (.not. (x <= 1.3d+117))) then
        tmp = (y * i) + ((x * log(y)) + a)
    else
        tmp = (y * i) + (a + (((b * (1.0d0 - (0.5d0 / b))) * log(c)) + (z + t)))
    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 <= -2.2e+210) || !(x <= 1.3e+117)) {
		tmp = (y * i) + ((x * Math.log(y)) + a);
	} else {
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * Math.log(c)) + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.2e+210) or not (x <= 1.3e+117):
		tmp = (y * i) + ((x * math.log(y)) + a)
	else:
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * math.log(c)) + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.2e+210) || !(x <= 1.3e+117))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(Float64(b * Float64(1.0 - Float64(0.5 / b))) * log(c)) + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.2e+210) || ~((x <= 1.3e+117)))
		tmp = (y * i) + ((x * log(y)) + a);
	else
		tmp = (y * i) + (a + (((b * (1.0 - (0.5 / b))) * log(c)) + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.2e+210], N[Not[LessEqual[x, 1.3e+117]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(N[(b * N[(1.0 - N[(0.5 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999987e210 or 1.3e117 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.2%

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

   4. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 60.2%

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

      2. associate-/l* 60.2%

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

      3. sub-neg 60.2%

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

      4. metadata-eval 60.2%

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

      5. +-commutative 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in x around inf 76.4%

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

   if -2.19999999999999987e210 < x < 1.3e117

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.1%

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

      1. associate-+r+ 96.1%

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

      2. associate-*r/ 96.1%

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

      3. metadata-eval 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-*l* 96.1%

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

      6. *-commutative 96.1%

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

   8. Simplified 96.1%

      \[\leadsto \color{blue}{\left(a + \left(\left(t + z\right) + \log c \cdot \left(b \cdot \left(1 - \frac{0.5}{b}\right)\right)\right)\right)} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+210} \lor \neg \left(x \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(\left(b \cdot \left(1 - \frac{0.5}{b}\right)\right) \cdot \log c + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+210} \lor \neg \left(x \leq 1.25 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.2e+210) (not (<= x 1.25e+117)))
   (+ (* y i) (+ (* x (log y)) a))
   (+ (* 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 <= -2.2e+210) || !(x <= 1.25e+117)) {
		tmp = (y * i) + ((x * log(y)) + a);
	} 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 <= (-2.2d+210)) .or. (.not. (x <= 1.25d+117))) then
        tmp = (y * i) + ((x * log(y)) + a)
    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 <= -2.2e+210) || !(x <= 1.25e+117)) {
		tmp = (y * i) + ((x * Math.log(y)) + a);
	} 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 <= -2.2e+210) or not (x <= 1.25e+117):
		tmp = (y * i) + ((x * math.log(y)) + a)
	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 <= -2.2e+210) || !(x <= 1.25e+117))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + a));
	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 <= -2.2e+210) || ~((x <= 1.25e+117)))
		tmp = (y * i) + ((x * log(y)) + a);
	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, -2.2e+210], N[Not[LessEqual[x, 1.25e+117]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $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 < -2.19999999999999987e210 or 1.24999999999999996e117 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.2%

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

   4. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 60.2%

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

      2. associate-/l* 60.2%

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

      3. sub-neg 60.2%

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

      4. metadata-eval 60.2%

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

      5. +-commutative 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in x around inf 76.4%

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

   if -2.19999999999999987e210 < x < 1.24999999999999996e117

   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 96.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+210} \lor \neg \left(x \leq 1.25 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+211} \lor \neg \left(x \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1e+211) (not (<= x 1.3e+117)))
   (+ (* y i) (+ (* x (log y)) a))
   (+ (* y i) (+ (+ z a) (* (log c) (+ b -0.5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+211) || !(x <= 1.3e+117)) {
		tmp = (y * i) + ((x * log(y)) + a);
	} else {
		tmp = (y * i) + ((z + a) + (log(c) * (b + -0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1d+211)) .or. (.not. (x <= 1.3d+117))) then
        tmp = (y * i) + ((x * log(y)) + a)
    else
        tmp = (y * i) + ((z + a) + (log(c) * (b + (-0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+211) || !(x <= 1.3e+117)) {
		tmp = (y * i) + ((x * Math.log(y)) + a);
	} else {
		tmp = (y * i) + ((z + a) + (Math.log(c) * (b + -0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1e+211) or not (x <= 1.3e+117):
		tmp = (y * i) + ((x * math.log(y)) + a)
	else:
		tmp = (y * i) + ((z + a) + (math.log(c) * (b + -0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1e+211) || !(x <= 1.3e+117))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + a));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(log(c) * Float64(b + -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1e+211) || ~((x <= 1.3e+117)))
		tmp = (y * i) + ((x * log(y)) + a);
	else
		tmp = (y * i) + ((z + a) + (log(c) * (b + -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1e+211], N[Not[LessEqual[x, 1.3e+117]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999996e210 or 1.3e117 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.2%

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

   4. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 60.2%

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

      2. associate-/l* 60.2%

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

      3. sub-neg 60.2%

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

      4. metadata-eval 60.2%

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

      5. +-commutative 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in x around inf 76.4%

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

   if -9.9999999999999996e210 < x < 1.3e117

   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 t around 0 80.0%

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

   4. Taylor expanded in x around 0 76.3%

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

      1. associate-+r+ 76.3%

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

      2. sub-neg 76.3%

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

      3. metadata-eval 76.3%

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

      4. +-commutative 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+211} \lor \neg \left(x \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+210} \lor \neg \left(x \leq 4.2 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.2e+210) (not (<= x 4.2e+233)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.2e+210) || !(x <= 4.2e+233)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.2d+210)) .or. (.not. (x <= 4.2d+233))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.2e+210) || !(x <= 4.2e+233)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.2e+210) or not (x <= 4.2e+233):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.2e+210) || !(x <= 4.2e+233))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.2e+210) || ~((x <= 4.2e+233)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.2e+210], N[Not[LessEqual[x, 4.2e+233]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2000000000000002e210 or 4.19999999999999993e233 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 81.1%

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

   if -3.2000000000000002e210 < x < 4.19999999999999993e233

   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 t around 0 80.5%

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

   4. Taylor expanded in z around inf 72.6%

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

      1. associate-/l* 72.6%

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

      2. associate-/l* 72.6%

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

      3. sub-neg 72.6%

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

      4. metadata-eval 72.6%

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

      5. +-commutative 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in z around inf 59.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+210} \lor \neg \left(x \leq 4.2 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{+47}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1e+47) (+ (* y i) (+ z (* (log c) (- b 0.5)))) (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1e+47) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1d+47) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1e+47) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1e+47:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1e+47)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1e+47)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1e+47], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1e47

   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 t around 0 83.2%

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

   4. Taylor expanded in x around 0 70.2%

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

      1. associate-+r+ 70.2%

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

      2. sub-neg 70.2%

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

      3. metadata-eval 70.2%

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

      4. +-commutative 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in a around 0 59.1%

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

   if 1e47 < 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 t around 0 79.3%

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

   4. Taylor expanded in z around inf 54.9%

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

      1. associate-/l* 54.9%

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

      2. associate-/l* 54.9%

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

      3. sub-neg 54.9%

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

      4. metadata-eval 54.9%

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

      5. +-commutative 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in z around inf 60.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+47}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4.6e+122)
   (+ a (+ (+ z t) (* (log c) (+ b -0.5))))
   (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.6e+122) {
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 4.6d+122) then
        tmp = a + ((z + t) + (log(c) * (b + (-0.5d0))))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.6e+122) {
		tmp = a + ((z + t) + (Math.log(c) * (b + -0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4.6e+122:
		tmp = a + ((z + t) + (math.log(c) * (b + -0.5)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4.6e+122)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(log(c) * Float64(b + -0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4.6e+122)
		tmp = a + ((z + t) + (log(c) * (b + -0.5)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4.6e+122], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6000000000000001e122

   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 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 54.7%

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

   6. Taylor expanded in y around 0 92.1%

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

   7. Taylor expanded in x around 0 75.9%

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

      1. associate-+r+ 75.9%

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

      2. +-commutative 75.9%

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

      3. sub-neg 75.9%

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

      4. metadata-eval 75.9%

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

   9. Simplified 75.9%

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

   if 4.6000000000000001e122 < y

   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 t around 0 88.8%

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

   4. Taylor expanded in z around inf 80.2%

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

      1. associate-/l* 80.2%

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

      2. associate-/l* 80.2%

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

      3. sub-neg 80.2%

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

      4. metadata-eval 80.2%

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

      5. +-commutative 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in z around inf 75.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;a + \left(\left(z + t\right) + \log c \cdot \left(b + -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+238} \lor \neg \left(x \leq 9.5 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3e+238) (not (<= x 9.5e+221)))
   (+ (* x (log y)) a)
   (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3e+238) || !(x <= 9.5e+221)) {
		tmp = (x * log(y)) + a;
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3d+238)) .or. (.not. (x <= 9.5d+221))) then
        tmp = (x * log(y)) + a
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3e+238) || !(x <= 9.5e+221)) {
		tmp = (x * Math.log(y)) + a;
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3e+238) or not (x <= 9.5e+221):
		tmp = (x * math.log(y)) + a
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3e+238) || !(x <= 9.5e+221))
		tmp = Float64(Float64(x * log(y)) + a);
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3e+238) || ~((x <= 9.5e+221)))
		tmp = (x * log(y)) + a;
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3e+238], N[Not[LessEqual[x, 9.5e+221]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e238 or 9.50000000000000044e221 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 93.9%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. associate-/l* 58.8%

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

      2. associate-/l* 58.8%

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

      3. sub-neg 58.8%

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

      4. metadata-eval 58.8%

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

      5. +-commutative 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in x around inf 82.3%

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

   8. Taylor expanded in y around 0 65.4%

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

   if -3e238 < x < 9.50000000000000044e221

   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 t around 0 80.8%

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

   4. Taylor expanded in z around inf 71.7%

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

      1. associate-/l* 71.7%

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

      2. associate-/l* 71.6%

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

      3. sub-neg 71.6%

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

      4. metadata-eval 71.6%

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

      5. +-commutative 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in z around inf 59.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+238} \lor \neg \left(x \leq 9.5 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.9 \cdot 10^{+122}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4.9e+122) (+ a (+ z (* (log c) (- b 0.5)))) (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.9e+122) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 4.9d+122) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.9e+122) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4.9e+122:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4.9e+122)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4.9e+122)
		tmp = a + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4.9e+122], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8999999999999998e122

   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 t around 0 79.2%

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

   4. Taylor expanded in x around 0 63.6%

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

      1. associate-+r+ 63.6%

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

      2. sub-neg 63.6%

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

      3. metadata-eval 63.6%

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

      4. +-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in i around inf 44.8%

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

      1. associate-/l* 44.8%

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

      2. sub-neg 44.8%

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

      3. metadata-eval 44.8%

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

   9. Simplified 44.8%

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

   10. Taylor expanded in i around 0 56.0%

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

   if 4.8999999999999998e122 < y

   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 t around 0 88.8%

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

   4. Taylor expanded in z around inf 80.2%

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

      1. associate-/l* 80.2%

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

      2. associate-/l* 80.2%

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

      3. sub-neg 80.2%

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

      4. metadata-eval 80.2%

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

      5. +-commutative 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in z around inf 75.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.9 \cdot 10^{+122}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+244} \lor \neg \left(x \leq 2.9 \cdot 10^{+243}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.1e+244) (not (<= x 2.9e+243)))
   (* x (log y))
   (+ (* y i) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+244) || !(x <= 2.9e+243)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.1d+244)) .or. (.not. (x <= 2.9d+243))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+244) || !(x <= 2.9e+243)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.1e+244) or not (x <= 2.9e+243):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.1e+244) || !(x <= 2.9e+243))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.1e+244) || ~((x <= 2.9e+243)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.1e+244], N[Not[LessEqual[x, 2.9e+243]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e244 or 2.90000000000000006e243 < x

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 61.1%

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

   6. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \log \left(\frac{1}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 65.9%

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

      2. log-rec 65.9%

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

   8. Applied egg-rr 65.9%

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

   if -2.1000000000000001e244 < x < 2.90000000000000006e243

   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 t around 0 80.7%

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

   4. Taylor expanded in z around inf 71.9%

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

      1. associate-/l* 71.8%

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

      2. associate-/l* 71.8%

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

      3. sub-neg 71.8%

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

      4. metadata-eval 71.8%

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

      5. +-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in z around inf 59.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+244} \lor \neg \left(x \leq 2.9 \cdot 10^{+243}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+54}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.6e+54) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.6e+54) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.6d+54)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.6e+54) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.6e+54:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.6e+54)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.6e+54)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.6e+54], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.4%

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

   if -1.6e54 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 42.4%

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

Alternative 16: 27.6% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 8.5e+49) (* 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 <= 8.5e+49) {
		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 <= 8.5d+49) 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 <= 8.5e+49) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8.5e+49:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8.5e+49)
		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 <= 8.5e+49)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8.5e+49], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 8.4999999999999996e49

   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 y around inf 25.8%

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

      1. *-commutative 25.8%

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

   7. Simplified 25.8%

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

   if 8.4999999999999996e49 < 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 48.0%

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

   4. Taylor expanded in a around inf 35.3%

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

Alternative 17: 53.1% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in t around 0 82.5%

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

4. Taylor expanded in z around inf 70.0%

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

   1. associate-/l* 70.0%

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

   2. associate-/l* 69.9%

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

   3. sub-neg 69.9%

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

   4. metadata-eval 69.9%

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

   5. +-commutative 69.9%

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

6. Simplified 69.9%

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

7. Taylor expanded in z around inf 55.5%

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

8. Final simplification 55.5%

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

Alternative 18: 38.5% accurate, 43.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 38.4%

   \[\leadsto \color{blue}{a} + y \cdot i \]
4. Add Preprocessing

Alternative 19: 15.9% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 38.4%

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

4. Taylor expanded in a around inf 16.7%

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

Reproduce

herbie shell --seed 2024135 
(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)))