Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.8% → 94.2%

Time: 15.2s

Alternatives: 15

Speedup: 1.0×

• 48.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (fma(x, y, (z * t)) - ((a + (b * c)) * (c * i)));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

   1. fma-define 95.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. associate-*l* 97.2%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -102000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* b (* c i))))))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -3.2e+150)
     t_2
     (if (<= c -102000000000.0)
       t_1
       (if (<= c 1.7e-80)
         (* 2.0 (+ (* x y) (* z t)))
         (if (<= c 6.4e+124) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * (b * (c * i))));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.2e+150) {
		tmp = t_2;
	} else if (c <= -102000000000.0) {
		tmp = t_1;
	} else if (c <= 1.7e-80) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.4e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-3.2d+150)) then
        tmp = t_2
    else if (c <= (-102000000000.0d0)) then
        tmp = t_1
    else if (c <= 1.7d-80) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 6.4d+124) then
        tmp = t_1
    else
        tmp = t_2
    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 = 2.0 * ((x * y) - (c * (b * (c * i))));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.2e+150) {
		tmp = t_2;
	} else if (c <= -102000000000.0) {
		tmp = t_1;
	} else if (c <= 1.7e-80) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.4e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * (b * (c * i))))
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -3.2e+150:
		tmp = t_2
	elif c <= -102000000000.0:
		tmp = t_1
	elif c <= 1.7e-80:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 6.4e+124:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -3.2e+150)
		tmp = t_2;
	elseif (c <= -102000000000.0)
		tmp = t_1;
	elseif (c <= 1.7e-80)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 6.4e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (c * (b * (c * i))));
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -3.2e+150)
		tmp = t_2;
	elseif (c <= -102000000000.0)
		tmp = t_1;
	elseif (c <= 1.7e-80)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 6.4e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+150], t$95$2, If[LessEqual[c, -102000000000.0], t$95$1, If[LessEqual[c, 1.7e-80], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e+124], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.20000000000000016e150 or 6.39999999999999986e124 < c

   1. Initial program 91.2%

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

      1. fma-define 91.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 98.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 98.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 98.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 98.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in c around 0 93.8%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   8. Taylor expanded in i around inf 86.4%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 86.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

      2. neg-mul-1 86.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. distribute-rgt-in 84.9%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\left(a \cdot i + \left(b \cdot c\right) \cdot i\right)}\right) \]

      4. associate-*r* 81.8%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \left(a \cdot i + \color{blue}{b \cdot \left(c \cdot i\right)}\right)\right) \]

      5. +-commutative 81.8%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right) + a \cdot i\right)}\right) \]

      6. *-commutative 81.8%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \left(b \cdot \left(c \cdot i\right) + \color{blue}{i \cdot a}\right)\right) \]

      7. fma-undefine 81.8%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\mathsf{fma}\left(b, c \cdot i, i \cdot a\right)}\right) \]

      8. *-commutative 81.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(b, c \cdot i, i \cdot a\right) \cdot \left(-c\right)\right)} \]

      9. fma-undefine 81.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(b \cdot \left(c \cdot i\right) + i \cdot a\right)} \cdot \left(-c\right)\right) \]

      10. *-commutative 81.8%

          \[\leadsto 2 \cdot \left(\left(b \cdot \left(c \cdot i\right) + \color{blue}{a \cdot i}\right) \cdot \left(-c\right)\right) \]

      11. +-commutative 81.8%

          \[\leadsto 2 \cdot \left(\color{blue}{\left(a \cdot i + b \cdot \left(c \cdot i\right)\right)} \cdot \left(-c\right)\right) \]

      12. associate-*r* 84.9%

          \[\leadsto 2 \cdot \left(\left(a \cdot i + \color{blue}{\left(b \cdot c\right) \cdot i}\right) \cdot \left(-c\right)\right) \]

      13. distribute-rgt-in 86.4%

          \[\leadsto 2 \cdot \left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)} \cdot \left(-c\right)\right) \]

      14. *-commutative 86.4%

          \[\leadsto 2 \cdot \left(\left(i \cdot \left(a + \color{blue}{c \cdot b}\right)\right) \cdot \left(-c\right)\right) \]

   10. Simplified 86.4%

       \[\leadsto 2 \cdot \color{blue}{\left(\left(i \cdot \left(a + c \cdot b\right)\right) \cdot \left(-c\right)\right)} \]

   if -3.20000000000000016e150 < c < -1.02e11 or 1.7e-80 < c < 6.39999999999999986e124

   1. Initial program 94.0%

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

      1. fma-define 94.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 95.1%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 95.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 95.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 95.1%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in c around 0 89.2%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   8. Taylor expanded in z around 0 74.5%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 74.6%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i + \color{blue}{\left(b \cdot c\right) \cdot i}\right)\right) \]

      2. distribute-rgt-in 78.2%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. *-commutative 78.2%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + \color{blue}{c \cdot b}\right)\right)\right) \]

   10. Simplified 78.2%

       \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)} \]

   11. Taylor expanded in a around 0 70.9%

       \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   if -1.02e11 < c < 1.7e-80

   1. Initial program 98.1%

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

   3. Taylor expanded in c around 0 72.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+150}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -102000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.95 \cdot 10^{-264}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(-a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= (* x y) -4.7e+70)
     t_2
     (if (<= (* x y) -6e-133)
       t_1
       (if (<= (* x y) -1.95e-264)
         (* 2.0 (* i (- (* a c))))
         (if (<= (* x y) 4.1e+34) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -4.7e+70) {
		tmp = t_2;
	} else if ((x * y) <= -6e-133) {
		tmp = t_1;
	} else if ((x * y) <= -1.95e-264) {
		tmp = 2.0 * (i * -(a * c));
	} else if ((x * y) <= 4.1e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if ((x * y) <= (-4.7d+70)) then
        tmp = t_2
    else if ((x * y) <= (-6d-133)) then
        tmp = t_1
    else if ((x * y) <= (-1.95d-264)) then
        tmp = 2.0d0 * (i * -(a * c))
    else if ((x * y) <= 4.1d+34) then
        tmp = t_1
    else
        tmp = t_2
    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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -4.7e+70) {
		tmp = t_2;
	} else if ((x * y) <= -6e-133) {
		tmp = t_1;
	} else if ((x * y) <= -1.95e-264) {
		tmp = 2.0 * (i * -(a * c));
	} else if ((x * y) <= 4.1e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -4.7e+70:
		tmp = t_2
	elif (x * y) <= -6e-133:
		tmp = t_1
	elif (x * y) <= -1.95e-264:
		tmp = 2.0 * (i * -(a * c))
	elif (x * y) <= 4.1e+34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -4.7e+70)
		tmp = t_2;
	elseif (Float64(x * y) <= -6e-133)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.95e-264)
		tmp = Float64(2.0 * Float64(i * Float64(-Float64(a * c))));
	elseif (Float64(x * y) <= 4.1e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -4.7e+70)
		tmp = t_2;
	elseif ((x * y) <= -6e-133)
		tmp = t_1;
	elseif ((x * y) <= -1.95e-264)
		tmp = 2.0 * (i * -(a * c));
	elseif ((x * y) <= 4.1e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.7e+70], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6e-133], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.95e-264], N[(2.0 * N[(i * (-N[(a * c), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.6999999999999998e70 or 4.0999999999999998e34 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 57.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -4.6999999999999998e70 < (*.f64 x y) < -6.00000000000000038e-133 or -1.9499999999999999e-264 < (*.f64 x y) < 4.0999999999999998e34

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 39.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -6.00000000000000038e-133 < (*.f64 x y) < -1.9499999999999999e-264

   1. Initial program 99.7%

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

      1. fma-define 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 99.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in a around inf 42.3%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. associate-*r* 42.3%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(a \cdot c\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 42.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 42.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot a\right)} \cdot \left(-i\right)\right) \]

   9. Simplified 42.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-133}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.95 \cdot 10^{-264}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(-a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.1 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= (* x y) -3.2e+71)
     t_2
     (if (<= (* x y) -1.25e-132)
       t_1
       (if (<= (* x y) -1.1e-269)
         (* a (* (* c i) -2.0))
         (if (<= (* x y) 1.36e+34) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -3.2e+71) {
		tmp = t_2;
	} else if ((x * y) <= -1.25e-132) {
		tmp = t_1;
	} else if ((x * y) <= -1.1e-269) {
		tmp = a * ((c * i) * -2.0);
	} else if ((x * y) <= 1.36e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if ((x * y) <= (-3.2d+71)) then
        tmp = t_2
    else if ((x * y) <= (-1.25d-132)) then
        tmp = t_1
    else if ((x * y) <= (-1.1d-269)) then
        tmp = a * ((c * i) * (-2.0d0))
    else if ((x * y) <= 1.36d+34) then
        tmp = t_1
    else
        tmp = t_2
    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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -3.2e+71) {
		tmp = t_2;
	} else if ((x * y) <= -1.25e-132) {
		tmp = t_1;
	} else if ((x * y) <= -1.1e-269) {
		tmp = a * ((c * i) * -2.0);
	} else if ((x * y) <= 1.36e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -3.2e+71:
		tmp = t_2
	elif (x * y) <= -1.25e-132:
		tmp = t_1
	elif (x * y) <= -1.1e-269:
		tmp = a * ((c * i) * -2.0)
	elif (x * y) <= 1.36e+34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+71)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.25e-132)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.1e-269)
		tmp = Float64(a * Float64(Float64(c * i) * -2.0));
	elseif (Float64(x * y) <= 1.36e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.2e+71)
		tmp = t_2;
	elseif ((x * y) <= -1.25e-132)
		tmp = t_1;
	elseif ((x * y) <= -1.1e-269)
		tmp = a * ((c * i) * -2.0);
	elseif ((x * y) <= 1.36e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+71], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.25e-132], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.1e-269], N[(a * N[(N[(c * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.36e+34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.20000000000000023e71 or 1.36e34 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 57.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -3.20000000000000023e71 < (*.f64 x y) < -1.25e-132 or -1.09999999999999992e-269 < (*.f64 x y) < 1.36e34

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 39.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -1.25e-132 < (*.f64 x y) < -1.09999999999999992e-269

   1. Initial program 99.7%

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

      1. fma-define 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 99.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in a around inf 42.3%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. associate-*r* 42.3%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(a \cdot c\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 42.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 42.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot a\right)} \cdot \left(-i\right)\right) \]

   9. Simplified 42.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot a\right) \cdot \left(-i\right)\right)} \]

   10. Taylor expanded in c around 0 42.3%

       \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 42.3%

          \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

       2. associate-*l* 42.3%

          \[\leadsto \color{blue}{a \cdot \left(\left(c \cdot i\right) \cdot -2\right)} \]

   12. Simplified 42.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.1 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{+34}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-126}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -3.2e+66)
     t_1
     (if (<= c 4.1e-126)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 3e-15)
         (* 2.0 (- (* x y) (* a (* c i))))
         (if (<= c 5.9e-15) (* 2.0 (* z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.2e+66) {
		tmp = t_1;
	} else if (c <= 4.1e-126) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 3e-15) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 5.9e-15) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 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 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-3.2d+66)) then
        tmp = t_1
    else if (c <= 4.1d-126) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 3d-15) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if (c <= 5.9d-15) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 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 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.2e+66) {
		tmp = t_1;
	} else if (c <= 4.1e-126) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 3e-15) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 5.9e-15) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -3.2e+66:
		tmp = t_1
	elif c <= 4.1e-126:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 3e-15:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif c <= 5.9e-15:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -3.2e+66)
		tmp = t_1;
	elseif (c <= 4.1e-126)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 3e-15)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (c <= 5.9e-15)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -3.2e+66)
		tmp = t_1;
	elseif (c <= 4.1e-126)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 3e-15)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif (c <= 5.9e-15)
		tmp = 2.0 * (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+66], t$95$1, If[LessEqual[c, 4.1e-126], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e-15], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.9e-15], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.2e66 or 5.89999999999999963e-15 < c

   1. Initial program 90.8%

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

      1. fma-define 90.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 96.5%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 96.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 96.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 96.5%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in c around 0 92.9%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   8. Taylor expanded in i around inf 74.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 74.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

      2. neg-mul-1 74.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      3. distribute-rgt-in 72.2%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\left(a \cdot i + \left(b \cdot c\right) \cdot i\right)}\right) \]

      4. associate-*r* 72.0%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \left(a \cdot i + \color{blue}{b \cdot \left(c \cdot i\right)}\right)\right) \]

      5. +-commutative 72.0%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right) + a \cdot i\right)}\right) \]

      6. *-commutative 72.0%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \left(b \cdot \left(c \cdot i\right) + \color{blue}{i \cdot a}\right)\right) \]

      7. fma-undefine 72.9%

         \[\leadsto 2 \cdot \left(\left(-c\right) \cdot \color{blue}{\mathsf{fma}\left(b, c \cdot i, i \cdot a\right)}\right) \]

      8. *-commutative 72.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\mathsf{fma}\left(b, c \cdot i, i \cdot a\right) \cdot \left(-c\right)\right)} \]

      9. fma-undefine 72.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(b \cdot \left(c \cdot i\right) + i \cdot a\right)} \cdot \left(-c\right)\right) \]

      10. *-commutative 72.0%

          \[\leadsto 2 \cdot \left(\left(b \cdot \left(c \cdot i\right) + \color{blue}{a \cdot i}\right) \cdot \left(-c\right)\right) \]

      11. +-commutative 72.0%

          \[\leadsto 2 \cdot \left(\color{blue}{\left(a \cdot i + b \cdot \left(c \cdot i\right)\right)} \cdot \left(-c\right)\right) \]

      12. associate-*r* 72.2%

          \[\leadsto 2 \cdot \left(\left(a \cdot i + \color{blue}{\left(b \cdot c\right) \cdot i}\right) \cdot \left(-c\right)\right) \]

      13. distribute-rgt-in 74.8%

          \[\leadsto 2 \cdot \left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)} \cdot \left(-c\right)\right) \]

      14. *-commutative 74.8%

          \[\leadsto 2 \cdot \left(\left(i \cdot \left(a + \color{blue}{c \cdot b}\right)\right) \cdot \left(-c\right)\right) \]

   10. Simplified 74.8%

       \[\leadsto 2 \cdot \color{blue}{\left(\left(i \cdot \left(a + c \cdot b\right)\right) \cdot \left(-c\right)\right)} \]

   if -3.2e66 < c < 4.0999999999999997e-126

   1. Initial program 98.2%

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

   3. Taylor expanded in c around 0 72.4%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 4.0999999999999997e-126 < c < 3e-15

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 84.7%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 84.7%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in z around 0 77.4%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - a \cdot \left(c \cdot i\right)\right)} \]

   if 3e-15 < c < 5.89999999999999963e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-126}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+25} \lor \neg \left(b \leq 15500000000\right):\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= b -7.5e+25) (not (<= b 15500000000.0)))
     (* 2.0 (- t_1 (* c (* b (* c i)))))
     (* 2.0 (- t_1 (* i (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((b <= -7.5e+25) || !(b <= 15500000000.0)) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((b <= (-7.5d+25)) .or. (.not. (b <= 15500000000.0d0))) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((b <= -7.5e+25) || !(b <= 15500000000.0)) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (b <= -7.5e+25) or not (b <= 15500000000.0):
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	else:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((b <= -7.5e+25) || !(b <= 15500000000.0))
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((b <= -7.5e+25) || ~((b <= 15500000000.0)))
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	else
		tmp = 2.0 * (t_1 - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -7.5e+25], N[Not[LessEqual[b, 15500000000.0]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999993e25 or 1.55e10 < b

   1. Initial program 93.2%

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

      1. fma-define 93.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 97.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 97.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 97.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 97.3%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in c around 0 92.0%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   8. Taylor expanded in a around 0 91.1%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   if -7.49999999999999993e25 < b < 1.55e10

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 87.4%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 87.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+25} \lor \neg \left(b \leq 15500000000\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+17} \lor \neg \left(c \leq 1.7 \cdot 10^{+49}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6e+17) (not (<= c 1.7e+49)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6e+17) || !(c <= 1.7e+49)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-6d+17)) .or. (.not. (c <= 1.7d+49))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6e+17) || !(c <= 1.7e+49)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -6e+17) or not (c <= 1.7e+49):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -6e+17) || !(c <= 1.7e+49))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -6e+17) || ~((c <= 1.7e+49)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -6e+17], N[Not[LessEqual[c, 1.7e+49]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6e17 or 1.7e49 < c

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 86.7%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if -6e17 < c < 1.7e49

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 86.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 86.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+17} \lor \neg \left(c \leq 1.7 \cdot 10^{+49}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-107} \lor \neg \left(c \leq 3 \cdot 10^{-129}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.3e-107) (not (<= c 3e-129)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.3e-107) || !(c <= 3e-129)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (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 ((c <= (-2.3d-107)) .or. (.not. (c <= 3d-129))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) + (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 ((c <= -2.3e-107) || !(c <= 3e-129)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.3e-107) or not (c <= 3e-129):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.3e-107) || !(c <= 3e-129))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.3e-107) || ~((c <= 3e-129)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.3e-107], N[Not[LessEqual[c, 3e-129]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.30000000000000003e-107 or 2.9999999999999998e-129 < c

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 81.2%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if -2.30000000000000003e-107 < c < 2.9999999999999998e-129

   1. Initial program 98.6%

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

   3. Taylor expanded in c around 0 77.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-107} \lor \neg \left(c \leq 3 \cdot 10^{-129}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+71} \lor \neg \left(x \cdot y \leq 10^{+34}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i))))
   (if (or (<= (* x y) -5e+71) (not (<= (* x y) 1e+34)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double tmp;
	if (((x * y) <= -5e+71) || !((x * y) <= 1e+34)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - 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 = a * (c * i)
    if (((x * y) <= (-5d+71)) .or. (.not. ((x * y) <= 1d+34))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - 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 = a * (c * i);
	double tmp;
	if (((x * y) <= -5e+71) || !((x * y) <= 1e+34)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	tmp = 0
	if ((x * y) <= -5e+71) or not ((x * y) <= 1e+34):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	tmp = 0.0
	if ((Float64(x * y) <= -5e+71) || !(Float64(x * y) <= 1e+34))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	tmp = 0.0;
	if (((x * y) <= -5e+71) || ~(((x * y) <= 1e+34)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+71], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+34]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999972e71 or 9.99999999999999946e33 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf 81.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 81.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 81.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in z around 0 73.9%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - a \cdot \left(c \cdot i\right)\right)} \]

   if -4.99999999999999972e71 < (*.f64 x y) < 9.99999999999999946e33

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 62.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 62.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in x around 0 58.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+71} \lor \neg \left(x \cdot y \leq 10^{+34}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-97}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-23}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + \frac{z \cdot t}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e-97)
   (* 2.0 (+ (* x y) (* z t)))
   (if (<= (* x y) 1e-23)
     (* 2.0 (- (* z t) (* a (* c i))))
     (* 2.0 (* y (+ x (/ (* z t) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e-97) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 1e-23) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + ((z * t) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d-97)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if ((x * y) <= 1d-23) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = 2.0d0 * (y * (x + ((z * t) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e-97) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 1e-23) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + ((z * t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e-97:
		tmp = 2.0 * ((x * y) + (z * t))
	elif (x * y) <= 1e-23:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = 2.0 * (y * (x + ((z * t) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e-97)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 1e-23)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(y * Float64(x + Float64(Float64(z * t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e-97)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif ((x * y) <= 1e-23)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = 2.0 * (y * (x + ((z * t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-97], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-23], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000004e-97

   1. Initial program 95.9%

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

   3. Taylor expanded in c around 0 64.9%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if -1.00000000000000004e-97 < (*.f64 x y) < 9.9999999999999996e-24

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 63.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 63.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 63.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in x around 0 61.8%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - a \cdot \left(c \cdot i\right)\right)} \]

   if 9.9999999999999996e-24 < (*.f64 x y)

   1. Initial program 90.1%

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

      1. fma-define 91.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 93.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 92.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 92.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 92.5%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in c around 0 88.8%

      \[\leadsto 2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   8. Taylor expanded in y around inf 86.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot \left(\left(x + \frac{t \cdot z}{y}\right) - \frac{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}{y}\right)\right)} \]

   9. Taylor expanded in c around 0 63.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-97}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-23}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + \frac{z \cdot t}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+70} \lor \neg \left(x \cdot y \leq 5.9 \cdot 10^{+33}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.3e+70) (not (<= (* x y) 5.9e+33)))
   (* 2.0 (* x y))
   (* 2.0 (* 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 * y) <= -2.3e+70) || !((x * y) <= 5.9e+33)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (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 * y) <= (-2.3d+70)) .or. (.not. ((x * y) <= 5.9d+33))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (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 * y) <= -2.3e+70) || !((x * y) <= 5.9e+33)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.3e+70) or not ((x * y) <= 5.9e+33):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.3e+70) || !(Float64(x * y) <= 5.9e+33))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * 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 * y) <= -2.3e+70) || ~(((x * y) <= 5.9e+33)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.3e+70], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.9e+33]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.29999999999999994e70 or 5.90000000000000008e33 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 57.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -2.29999999999999994e70 < (*.f64 x y) < 5.90000000000000008e33

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 36.0%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+70} \lor \neg \left(x \cdot y \leq 5.9 \cdot 10^{+33}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(-a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+271}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -7.2e+179)
   (* 2.0 (* i (- (* a c))))
   (if (<= a 2.65e+271) (* 2.0 (+ (* x y) (* z t))) (* a (* (* c i) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -7.2e+179) {
		tmp = 2.0 * (i * -(a * c));
	} else if (a <= 2.65e+271) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = a * ((c * i) * -2.0);
	}
	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 <= (-7.2d+179)) then
        tmp = 2.0d0 * (i * -(a * c))
    else if (a <= 2.65d+271) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = a * ((c * i) * (-2.0d0))
    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 <= -7.2e+179) {
		tmp = 2.0 * (i * -(a * c));
	} else if (a <= 2.65e+271) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = a * ((c * i) * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -7.2e+179:
		tmp = 2.0 * (i * -(a * c))
	elif a <= 2.65e+271:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = a * ((c * i) * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -7.2e+179)
		tmp = Float64(2.0 * Float64(i * Float64(-Float64(a * c))));
	elseif (a <= 2.65e+271)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(a * Float64(Float64(c * i) * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -7.2e+179)
		tmp = 2.0 * (i * -(a * c));
	elseif (a <= 2.65e+271)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = a * ((c * i) * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -7.2e+179], N[(2.0 * N[(i * (-N[(a * c), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e+271], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.1999999999999995e179

   1. Initial program 94.2%

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

      1. fma-define 94.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 96.9%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 96.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 96.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 96.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in a around inf 63.6%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.6%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. associate-*r* 63.7%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(a \cdot c\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 63.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 63.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot a\right)} \cdot \left(-i\right)\right) \]

   9. Simplified 63.7%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot a\right) \cdot \left(-i\right)\right)} \]

   if -7.1999999999999995e179 < a < 2.6500000000000001e271

   1. Initial program 95.3%

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

   3. Taylor expanded in c around 0 58.1%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 2.6500000000000001e271 < a

   1. Initial program 91.9%

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

      1. fma-define 91.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 99.9%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   7. Taylor expanded in a around inf 90.5%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.5%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. associate-*r* 82.5%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(a \cdot c\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 82.5%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot \left(-i\right)\right)} \]

      4. *-commutative 82.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot a\right)} \cdot \left(-i\right)\right) \]

   9. Simplified 82.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot a\right) \cdot \left(-i\right)\right)} \]

   10. Taylor expanded in c around 0 90.5%

       \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 90.5%

          \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

       2. associate-*l* 90.5%

          \[\leadsto \color{blue}{a \cdot \left(\left(c \cdot i\right) \cdot -2\right)} \]

   12. Simplified 90.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+179}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(-a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+271}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * 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 = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * 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 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

   1. fma-define 95.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. associate-*l* 97.2%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-define 96.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   2. +-commutative 96.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

6. Applied egg-rr 96.8%

   \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

7. Final simplification 96.8%

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

Alternative 14: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (i * (c * (a + (b * c)))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (i * (c * (a + (b * c)))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (i * (c * (a + (b * c)))));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (i * (c * (a + (b * c)))))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * Float64(a + Float64(b * c))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (a + (b * c)))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

3. Final simplification 95.0%

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

Alternative 15: 29.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (z * t)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (z * t)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(z * t))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (z * t);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

3. Taylor expanded in z around inf 27.1%

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

4. Final simplification 27.1%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
5. Add Preprocessing

Developer target: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * 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 = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * 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 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))