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

Percentage Accurate: 90.0% → 96.4%

Time: 20.8s

Alternatives: 15

Speedup: 0.9×

• 47.4% 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: 90.0% 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: 96.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i))))
     (* 2.0 (* c (* i (- (- a) (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   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. Step-by-step derivation

      1. associate-*l* 98.0%

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

      2. fma-def 98.0%

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

   3. Simplified 98.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 63.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 2: 43.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 7.3 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* a (* c i))))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -2.1e+80)
     t_3
     (if (<= (* x y) -1.08e-69)
       t_1
       (if (<= (* x y) -3.9e-106)
         t_2
         (if (<= (* x y) 9.6e-234)
           t_1
           (if (<= (* x y) 8.2e+44)
             t_2
             (if (<= (* x y) 7.3e+109) t_1 t_3))))))))

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 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2.1e+80) {
		tmp = t_3;
	} else if ((x * y) <= -1.08e-69) {
		tmp = t_1;
	} else if ((x * y) <= -3.9e-106) {
		tmp = t_2;
	} else if ((x * y) <= 9.6e-234) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e+44) {
		tmp = t_2;
	} else if ((x * y) <= 7.3e+109) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-2.1d+80)) then
        tmp = t_3
    else if ((x * y) <= (-1.08d-69)) then
        tmp = t_1
    else if ((x * y) <= (-3.9d-106)) then
        tmp = t_2
    else if ((x * y) <= 9.6d-234) then
        tmp = t_1
    else if ((x * y) <= 8.2d+44) then
        tmp = t_2
    else if ((x * y) <= 7.3d+109) then
        tmp = t_1
    else
        tmp = t_3
    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 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2.1e+80) {
		tmp = t_3;
	} else if ((x * y) <= -1.08e-69) {
		tmp = t_1;
	} else if ((x * y) <= -3.9e-106) {
		tmp = t_2;
	} else if ((x * y) <= 9.6e-234) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e+44) {
		tmp = t_2;
	} else if ((x * y) <= 7.3e+109) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2.1e+80:
		tmp = t_3
	elif (x * y) <= -1.08e-69:
		tmp = t_1
	elif (x * y) <= -3.9e-106:
		tmp = t_2
	elif (x * y) <= 9.6e-234:
		tmp = t_1
	elif (x * y) <= 8.2e+44:
		tmp = t_2
	elif (x * y) <= 7.3e+109:
		tmp = t_1
	else:
		tmp = t_3
	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(a * Float64(c * i)))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+80)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.08e-69)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.9e-106)
		tmp = t_2;
	elseif (Float64(x * y) <= 9.6e-234)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.2e+44)
		tmp = t_2;
	elseif (Float64(x * y) <= 7.3e+109)
		tmp = t_1;
	else
		tmp = t_3;
	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 * (a * (c * i));
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2.1e+80)
		tmp = t_3;
	elseif ((x * y) <= -1.08e-69)
		tmp = t_1;
	elseif ((x * y) <= -3.9e-106)
		tmp = t_2;
	elseif ((x * y) <= 9.6e-234)
		tmp = t_1;
	elseif ((x * y) <= 8.2e+44)
		tmp = t_2;
	elseif ((x * y) <= 7.3e+109)
		tmp = t_1;
	else
		tmp = t_3;
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+80], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.08e-69], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.9e-106], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9.6e-234], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.2e+44], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 7.3e+109], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.10000000000000001e80 or 7.2999999999999998e109 < (*.f64 x y)

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 62.3%

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

   if -2.10000000000000001e80 < (*.f64 x y) < -1.0800000000000001e-69 or -3.9000000000000001e-106 < (*.f64 x y) < 9.5999999999999996e-234 or 8.1999999999999993e44 < (*.f64 x y) < 7.2999999999999998e109

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 47.8%

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

   if -1.0800000000000001e-69 < (*.f64 x y) < -3.9000000000000001e-106 or 9.5999999999999996e-234 < (*.f64 x y) < 8.1999999999999993e44

   1. Initial program 92.3%

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

   2. Taylor expanded in a around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. *-commutative 48.4%

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

      3. associate-*l* 44.7%

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

      4. *-commutative 44.7%

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

      5. distribute-rgt-neg-in 44.7%

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

      6. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in c around 0 48.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-106}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{-234}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 7.3 \cdot 10^{+109}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 3: 43.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -9.8 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 9.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -8e+75)
     t_2
     (if (<= (* x y) -9.8e-79)
       t_1
       (if (<= (* x y) -1.35e-101)
         (* c (* -2.0 (* a i)))
         (if (<= (* x y) 8.8e-234)
           t_1
           (if (<= (* x y) 3.5e+54)
             (* -2.0 (* a (* c i)))
             (if (<= (* x y) 9.4e+107) 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 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -8e+75) {
		tmp = t_2;
	} else if ((x * y) <= -9.8e-79) {
		tmp = t_1;
	} else if ((x * y) <= -1.35e-101) {
		tmp = c * (-2.0 * (a * i));
	} else if ((x * y) <= 8.8e-234) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+54) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 9.4e+107) {
		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 = (x * y) * 2.0d0
    if ((x * y) <= (-8d+75)) then
        tmp = t_2
    else if ((x * y) <= (-9.8d-79)) then
        tmp = t_1
    else if ((x * y) <= (-1.35d-101)) then
        tmp = c * ((-2.0d0) * (a * i))
    else if ((x * y) <= 8.8d-234) then
        tmp = t_1
    else if ((x * y) <= 3.5d+54) then
        tmp = (-2.0d0) * (a * (c * i))
    else if ((x * y) <= 9.4d+107) 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 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -8e+75) {
		tmp = t_2;
	} else if ((x * y) <= -9.8e-79) {
		tmp = t_1;
	} else if ((x * y) <= -1.35e-101) {
		tmp = c * (-2.0 * (a * i));
	} else if ((x * y) <= 8.8e-234) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+54) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 9.4e+107) {
		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 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -8e+75:
		tmp = t_2
	elif (x * y) <= -9.8e-79:
		tmp = t_1
	elif (x * y) <= -1.35e-101:
		tmp = c * (-2.0 * (a * i))
	elif (x * y) <= 8.8e-234:
		tmp = t_1
	elif (x * y) <= 3.5e+54:
		tmp = -2.0 * (a * (c * i))
	elif (x * y) <= 9.4e+107:
		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(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -8e+75)
		tmp = t_2;
	elseif (Float64(x * y) <= -9.8e-79)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.35e-101)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	elseif (Float64(x * y) <= 8.8e-234)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e+54)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (Float64(x * y) <= 9.4e+107)
		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 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -8e+75)
		tmp = t_2;
	elseif ((x * y) <= -9.8e-79)
		tmp = t_1;
	elseif ((x * y) <= -1.35e-101)
		tmp = c * (-2.0 * (a * i));
	elseif ((x * y) <= 8.8e-234)
		tmp = t_1;
	elseif ((x * y) <= 3.5e+54)
		tmp = -2.0 * (a * (c * i));
	elseif ((x * y) <= 9.4e+107)
		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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8e+75], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -9.8e-79], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.35e-101], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.8e-234], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+54], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.4e+107], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -7.99999999999999941e75 or 9.4000000000000002e107 < (*.f64 x y)

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 62.3%

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

   if -7.99999999999999941e75 < (*.f64 x y) < -9.8000000000000001e-79 or -1.3500000000000001e-101 < (*.f64 x y) < 8.7999999999999996e-234 or 3.5000000000000001e54 < (*.f64 x y) < 9.4000000000000002e107

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 47.8%

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

   if -9.8000000000000001e-79 < (*.f64 x y) < -1.3500000000000001e-101

   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. Taylor expanded in a around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-*l* 63.0%

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

      4. *-commutative 63.0%

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

      5. distribute-rgt-neg-in 63.0%

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

      6. *-commutative 63.0%

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

   4. Simplified 63.0%

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

   5. Taylor expanded in c around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-*r* 63.0%

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

      4. associate-*l* 63.0%

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

   7. Simplified 63.0%

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

   if 8.7999999999999996e-234 < (*.f64 x y) < 3.5000000000000001e54

   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. Taylor expanded in a around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. *-commutative 44.3%

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

      3. associate-*l* 39.5%

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

      4. *-commutative 39.5%

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

      5. distribute-rgt-neg-in 39.5%

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

      6. *-commutative 39.5%

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

   4. Simplified 39.5%

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

   5. Taylor expanded in c around 0 44.3%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -9.8 \cdot 10^{-79}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.35 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{-234}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 9.4 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 4: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+128} \lor \neg \left(c \leq 3.4 \cdot 10^{+148}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* (* b (* c (* c i))) -2.0))
        (t_3 (* (* x y) 2.0)))
   (if (<= c -5.2e+48)
     t_2
     (if (<= c -1e-149)
       t_1
       (if (<= c 2.3e-288)
         t_3
         (if (<= c 5.3e-263)
           t_1
           (if (<= c 4.6e-24)
             t_3
             (if (<= c 1.2e+40)
               t_1
               (if (or (<= c 1.85e+128) (not (<= c 3.4e+148)))
                 t_2
                 (* c (* -2.0 (* a i))))))))))))

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 = (b * (c * (c * i))) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (c <= -5.2e+48) {
		tmp = t_2;
	} else if (c <= -1e-149) {
		tmp = t_1;
	} else if (c <= 2.3e-288) {
		tmp = t_3;
	} else if (c <= 5.3e-263) {
		tmp = t_1;
	} else if (c <= 4.6e-24) {
		tmp = t_3;
	} else if (c <= 1.2e+40) {
		tmp = t_1;
	} else if ((c <= 1.85e+128) || !(c <= 3.4e+148)) {
		tmp = t_2;
	} else {
		tmp = c * (-2.0 * (a * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (b * (c * (c * i))) * (-2.0d0)
    t_3 = (x * y) * 2.0d0
    if (c <= (-5.2d+48)) then
        tmp = t_2
    else if (c <= (-1d-149)) then
        tmp = t_1
    else if (c <= 2.3d-288) then
        tmp = t_3
    else if (c <= 5.3d-263) then
        tmp = t_1
    else if (c <= 4.6d-24) then
        tmp = t_3
    else if (c <= 1.2d+40) then
        tmp = t_1
    else if ((c <= 1.85d+128) .or. (.not. (c <= 3.4d+148))) then
        tmp = t_2
    else
        tmp = c * ((-2.0d0) * (a * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (b * (c * (c * i))) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (c <= -5.2e+48) {
		tmp = t_2;
	} else if (c <= -1e-149) {
		tmp = t_1;
	} else if (c <= 2.3e-288) {
		tmp = t_3;
	} else if (c <= 5.3e-263) {
		tmp = t_1;
	} else if (c <= 4.6e-24) {
		tmp = t_3;
	} else if (c <= 1.2e+40) {
		tmp = t_1;
	} else if ((c <= 1.85e+128) || !(c <= 3.4e+148)) {
		tmp = t_2;
	} else {
		tmp = c * (-2.0 * (a * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (b * (c * (c * i))) * -2.0
	t_3 = (x * y) * 2.0
	tmp = 0
	if c <= -5.2e+48:
		tmp = t_2
	elif c <= -1e-149:
		tmp = t_1
	elif c <= 2.3e-288:
		tmp = t_3
	elif c <= 5.3e-263:
		tmp = t_1
	elif c <= 4.6e-24:
		tmp = t_3
	elif c <= 1.2e+40:
		tmp = t_1
	elif (c <= 1.85e+128) or not (c <= 3.4e+148):
		tmp = t_2
	else:
		tmp = c * (-2.0 * (a * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0)
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (c <= -5.2e+48)
		tmp = t_2;
	elseif (c <= -1e-149)
		tmp = t_1;
	elseif (c <= 2.3e-288)
		tmp = t_3;
	elseif (c <= 5.3e-263)
		tmp = t_1;
	elseif (c <= 4.6e-24)
		tmp = t_3;
	elseif (c <= 1.2e+40)
		tmp = t_1;
	elseif ((c <= 1.85e+128) || !(c <= 3.4e+148))
		tmp = t_2;
	else
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	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 = (b * (c * (c * i))) * -2.0;
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if (c <= -5.2e+48)
		tmp = t_2;
	elseif (c <= -1e-149)
		tmp = t_1;
	elseif (c <= 2.3e-288)
		tmp = t_3;
	elseif (c <= 5.3e-263)
		tmp = t_1;
	elseif (c <= 4.6e-24)
		tmp = t_3;
	elseif (c <= 1.2e+40)
		tmp = t_1;
	elseif ((c <= 1.85e+128) || ~((c <= 3.4e+148)))
		tmp = t_2;
	else
		tmp = c * (-2.0 * (a * i));
	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[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -5.2e+48], t$95$2, If[LessEqual[c, -1e-149], t$95$1, If[LessEqual[c, 2.3e-288], t$95$3, If[LessEqual[c, 5.3e-263], t$95$1, If[LessEqual[c, 4.6e-24], t$95$3, If[LessEqual[c, 1.2e+40], t$95$1, If[Or[LessEqual[c, 1.85e+128], N[Not[LessEqual[c, 3.4e+148]], $MachinePrecision]], t$95$2, N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.1999999999999999e48 or 1.2e40 < c < 1.85e128 or 3.4000000000000003e148 < c

   1. Initial program 82.6%

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

   2. Taylor expanded in b around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r* 69.5%

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

      3. unpow2 69.5%

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

      4. associate-*l* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-*r* 73.5%

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

      7. distribute-rgt-neg-in 73.5%

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

      8. associate-*r* 76.4%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in c around 0 73.4%

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

      1. unpow2 73.4%

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

      2. associate-*r* 77.4%

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

   7. Simplified 77.4%

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

   if -5.1999999999999999e48 < c < -9.99999999999999979e-150 or 2.3e-288 < c < 5.2999999999999997e-263 or 4.6000000000000002e-24 < c < 1.2e40

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -9.99999999999999979e-150 < c < 2.3e-288 or 5.2999999999999997e-263 < c < 4.6000000000000002e-24

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf 51.4%

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

   if 1.85e128 < c < 3.4000000000000003e148

   1. Initial program 67.2%

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

   2. Taylor expanded in a around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*l* 83.8%

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

      4. *-commutative 83.8%

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

      5. distribute-rgt-neg-in 83.8%

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

      6. *-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in c around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*r* 83.8%

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

      4. associate-*l* 83.8%

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

   7. Simplified 83.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot a\right) \cdot -2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-288}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{-263}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+128} \lor \neg \left(c \leq 3.4 \cdot 10^{+148}\right):\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-20} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -1e-20) (not (<= (* z t) 5e-66)))
   (* 2.0 (- (+ (* x y) (* z t)) (* b (* c (* c i)))))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -1e-20) || !((z * t) <= 5e-66)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (b * (c * (c * i))));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((z * t) <= (-1d-20)) .or. (.not. ((z * t) <= 5d-66))) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (b * (c * (c * i))))
    else
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -1e-20) || !((z * t) <= 5e-66)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (b * (c * (c * i))));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -1e-20) or not ((z * t) <= 5e-66):
		tmp = 2.0 * (((x * y) + (z * t)) - (b * (c * (c * i))))
	else:
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -1e-20) || !(Float64(z * t) <= 5e-66))
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(b * Float64(c * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((z * t) <= -1e-20) || ~(((z * t) <= 5e-66)))
		tmp = 2.0 * (((x * y) + (z * t)) - (b * (c * (c * i))));
	else
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e-20], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-66]], $MachinePrecision]], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999945e-21 or 4.99999999999999962e-66 < (*.f64 z t)

   1. Initial program 89.1%

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

   2. Taylor expanded in a around 0 86.0%

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

      1. unpow2 86.0%

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

      2. associate-*r* 88.5%

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

   4. Simplified 88.5%

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

   if -9.99999999999999945e-21 < (*.f64 z t) < 4.99999999999999962e-66

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 94.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-20} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* (* b (* c (* c i))) -2.0)))
   (if (<= c -9.2e+61)
     t_2
     (if (<= c 1.95e+62)
       t_1
       (if (<= c 1.55e+76)
         t_2
         (if (<= c 8.4e+95)
           t_1
           (if (<= c 1.7e+153)
             (* 2.0 (- (* z t) (* a (* c i))))
             (* c (* (* c i) (* b -2.0))))))))))

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)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -9.2e+61) {
		tmp = t_2;
	} else if (c <= 1.95e+62) {
		tmp = t_1;
	} else if (c <= 1.55e+76) {
		tmp = t_2;
	} else if (c <= 8.4e+95) {
		tmp = t_1;
	} else if (c <= 1.7e+153) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = c * ((c * i) * (b * -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (b * (c * (c * i))) * (-2.0d0)
    if (c <= (-9.2d+61)) then
        tmp = t_2
    else if (c <= 1.95d+62) then
        tmp = t_1
    else if (c <= 1.55d+76) then
        tmp = t_2
    else if (c <= 8.4d+95) then
        tmp = t_1
    else if (c <= 1.7d+153) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = c * ((c * i) * (b * (-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 t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -9.2e+61) {
		tmp = t_2;
	} else if (c <= 1.95e+62) {
		tmp = t_1;
	} else if (c <= 1.55e+76) {
		tmp = t_2;
	} else if (c <= 8.4e+95) {
		tmp = t_1;
	} else if (c <= 1.7e+153) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = c * ((c * i) * (b * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = (b * (c * (c * i))) * -2.0
	tmp = 0
	if c <= -9.2e+61:
		tmp = t_2
	elif c <= 1.95e+62:
		tmp = t_1
	elif c <= 1.55e+76:
		tmp = t_2
	elif c <= 8.4e+95:
		tmp = t_1
	elif c <= 1.7e+153:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = c * ((c * i) * (b * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0)
	tmp = 0.0
	if (c <= -9.2e+61)
		tmp = t_2;
	elseif (c <= 1.95e+62)
		tmp = t_1;
	elseif (c <= 1.55e+76)
		tmp = t_2;
	elseif (c <= 8.4e+95)
		tmp = t_1;
	elseif (c <= 1.7e+153)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(c * Float64(Float64(c * i) * Float64(b * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = (b * (c * (c * i))) * -2.0;
	tmp = 0.0;
	if (c <= -9.2e+61)
		tmp = t_2;
	elseif (c <= 1.95e+62)
		tmp = t_1;
	elseif (c <= 1.55e+76)
		tmp = t_2;
	elseif (c <= 8.4e+95)
		tmp = t_1;
	elseif (c <= 1.7e+153)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = c * ((c * i) * (b * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -9.2e+61], t$95$2, If[LessEqual[c, 1.95e+62], t$95$1, If[LessEqual[c, 1.55e+76], t$95$2, If[LessEqual[c, 8.4e+95], t$95$1, If[LessEqual[c, 1.7e+153], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(c * i), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.1999999999999998e61 or 1.95e62 < c < 1.55000000000000006e76

   1. Initial program 87.1%

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

   2. Taylor expanded in b around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-*r* 74.5%

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

      3. unpow2 74.5%

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

      4. associate-*l* 76.3%

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

      5. *-commutative 76.3%

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

      6. associate-*r* 78.1%

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

      7. distribute-rgt-neg-in 78.1%

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

      8. associate-*r* 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in c around 0 78.1%

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

      1. unpow2 78.1%

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

      2. associate-*r* 83.5%

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

   7. Simplified 83.5%

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

   if -9.1999999999999998e61 < c < 1.95e62 or 1.55000000000000006e76 < c < 8.4e95

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 8.4e95 < c < 1.6999999999999999e153

   1. Initial program 48.1%

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

   2. Taylor expanded in a around inf 32.5%

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

      1. *-commutative 32.5%

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

   4. Simplified 32.5%

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

   5. Taylor expanded in x around 0 60.0%

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

   if 1.6999999999999999e153 < c

   1. Initial program 83.7%

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

   2. Taylor expanded in b around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. associate-*r* 88.2%

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

      3. unpow2 88.2%

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

      4. associate-*l* 92.0%

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

      5. *-commutative 92.0%

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

      6. associate-*r* 92.1%

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

      7. distribute-rgt-neg-in 92.1%

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

      8. associate-*r* 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in c around 0 88.2%

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

      1. unpow2 88.2%

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

      2. associate-*r* 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in b around 0 88.2%

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

      1. unpow2 88.2%

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

      2. associate-*r* 92.0%

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

      3. associate-*r* 92.0%

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

      4. *-commutative 92.0%

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

      5. associate-*l* 92.1%

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

   10. Simplified 92.1%

       \[\leadsto \color{blue}{c \cdot \left(\left(c \cdot i\right) \cdot \left(-2 \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+95}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]

Alternative 7: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c 2.4e+100)
   (* (- (+ (* x y) (* z t)) (* (* c (+ a (* b c))) i)) 2.0)
   (* 2.0 (* c (* i (- (- a) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= 2.4e+100) {
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * 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 <= 2.4d+100) then
        tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0d0
    else
        tmp = 2.0d0 * (c * (i * (-a - (b * 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 <= 2.4e+100) {
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= 2.4e+100:
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0
	else:
		tmp = 2.0 * (c * (i * (-a - (b * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= 2.4e+100)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= 2.4e+100)
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0;
	else
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, 2.4e+100], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(i * N[((-a) - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.40000000000000012e100

   1. Initial program 94.6%

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

   if 2.40000000000000012e100 < c

   1. Initial program 71.2%

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

   2. Taylor expanded in i around inf 92.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* (* b (* c (* c i))) -2.0)))
   (if (<= c -1.65e+60)
     t_2
     (if (<= c 6e+62)
       t_1
       (if (<= c 4.4e+77)
         t_2
         (if (<= c 2.4e+100)
           t_1
           (if (<= c 3.2e+148) (* c (* -2.0 (* a i))) t_2)))))))

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)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -1.65e+60) {
		tmp = t_2;
	} else if (c <= 6e+62) {
		tmp = t_1;
	} else if (c <= 4.4e+77) {
		tmp = t_2;
	} else if (c <= 2.4e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} 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 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (b * (c * (c * i))) * (-2.0d0)
    if (c <= (-1.65d+60)) then
        tmp = t_2
    else if (c <= 6d+62) then
        tmp = t_1
    else if (c <= 4.4d+77) then
        tmp = t_2
    else if (c <= 2.4d+100) then
        tmp = t_1
    else if (c <= 3.2d+148) then
        tmp = c * ((-2.0d0) * (a * i))
    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 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -1.65e+60) {
		tmp = t_2;
	} else if (c <= 6e+62) {
		tmp = t_1;
	} else if (c <= 4.4e+77) {
		tmp = t_2;
	} else if (c <= 2.4e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = (b * (c * (c * i))) * -2.0
	tmp = 0
	if c <= -1.65e+60:
		tmp = t_2
	elif c <= 6e+62:
		tmp = t_1
	elif c <= 4.4e+77:
		tmp = t_2
	elif c <= 2.4e+100:
		tmp = t_1
	elif c <= 3.2e+148:
		tmp = c * (-2.0 * (a * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0)
	tmp = 0.0
	if (c <= -1.65e+60)
		tmp = t_2;
	elseif (c <= 6e+62)
		tmp = t_1;
	elseif (c <= 4.4e+77)
		tmp = t_2;
	elseif (c <= 2.4e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = (b * (c * (c * i))) * -2.0;
	tmp = 0.0;
	if (c <= -1.65e+60)
		tmp = t_2;
	elseif (c <= 6e+62)
		tmp = t_1;
	elseif (c <= 4.4e+77)
		tmp = t_2;
	elseif (c <= 2.4e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = c * (-2.0 * (a * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -1.65e+60], t$95$2, If[LessEqual[c, 6e+62], t$95$1, If[LessEqual[c, 4.4e+77], t$95$2, If[LessEqual[c, 2.4e+100], t$95$1, If[LessEqual[c, 3.2e+148], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.6499999999999999e60 or 6e62 < c < 4.4000000000000001e77 or 3.1999999999999999e148 < c

   1. Initial program 85.2%

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

   2. Taylor expanded in b around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. associate-*r* 76.9%

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

      3. unpow2 76.9%

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

      4. associate-*l* 79.2%

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

      5. *-commutative 79.2%

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

      6. associate-*r* 80.5%

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

      7. distribute-rgt-neg-in 80.5%

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

      8. associate-*r* 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in c around 0 80.5%

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

      1. unpow2 80.5%

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

      2. associate-*r* 85.3%

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

   7. Simplified 85.3%

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

   if -1.6499999999999999e60 < c < 6e62 or 4.4000000000000001e77 < c < 2.40000000000000012e100

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 2.40000000000000012e100 < c < 3.1999999999999999e148

   1. Initial program 47.1%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*l* 62.0%

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

      4. *-commutative 62.0%

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

      5. distribute-rgt-neg-in 62.0%

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

      6. *-commutative 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in c around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 62.0%

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

      4. associate-*l* 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+77}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \end{array} \]

Alternative 9: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.25 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* (* b (* c (* c i))) -2.0)))
   (if (<= c -3.5e+61)
     t_2
     (if (<= c 3.9e+62)
       t_1
       (if (<= c 5.6e+76)
         t_2
         (if (<= c 4.25e+99)
           t_1
           (if (<= c 3.2e+148)
             (* c (* -2.0 (* a i)))
             (* c (* (* c i) (* b -2.0))))))))))

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)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -3.5e+61) {
		tmp = t_2;
	} else if (c <= 3.9e+62) {
		tmp = t_1;
	} else if (c <= 5.6e+76) {
		tmp = t_2;
	} else if (c <= 4.25e+99) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * ((c * i) * (b * -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (b * (c * (c * i))) * (-2.0d0)
    if (c <= (-3.5d+61)) then
        tmp = t_2
    else if (c <= 3.9d+62) then
        tmp = t_1
    else if (c <= 5.6d+76) then
        tmp = t_2
    else if (c <= 4.25d+99) then
        tmp = t_1
    else if (c <= 3.2d+148) then
        tmp = c * ((-2.0d0) * (a * i))
    else
        tmp = c * ((c * i) * (b * (-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 t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (b * (c * (c * i))) * -2.0;
	double tmp;
	if (c <= -3.5e+61) {
		tmp = t_2;
	} else if (c <= 3.9e+62) {
		tmp = t_1;
	} else if (c <= 5.6e+76) {
		tmp = t_2;
	} else if (c <= 4.25e+99) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * ((c * i) * (b * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = (b * (c * (c * i))) * -2.0
	tmp = 0
	if c <= -3.5e+61:
		tmp = t_2
	elif c <= 3.9e+62:
		tmp = t_1
	elif c <= 5.6e+76:
		tmp = t_2
	elif c <= 4.25e+99:
		tmp = t_1
	elif c <= 3.2e+148:
		tmp = c * (-2.0 * (a * i))
	else:
		tmp = c * ((c * i) * (b * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(Float64(b * Float64(c * Float64(c * i))) * -2.0)
	tmp = 0.0
	if (c <= -3.5e+61)
		tmp = t_2;
	elseif (c <= 3.9e+62)
		tmp = t_1;
	elseif (c <= 5.6e+76)
		tmp = t_2;
	elseif (c <= 4.25e+99)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	else
		tmp = Float64(c * Float64(Float64(c * i) * Float64(b * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = (b * (c * (c * i))) * -2.0;
	tmp = 0.0;
	if (c <= -3.5e+61)
		tmp = t_2;
	elseif (c <= 3.9e+62)
		tmp = t_1;
	elseif (c <= 5.6e+76)
		tmp = t_2;
	elseif (c <= 4.25e+99)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = c * (-2.0 * (a * i));
	else
		tmp = c * ((c * i) * (b * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -3.5e+61], t$95$2, If[LessEqual[c, 3.9e+62], t$95$1, If[LessEqual[c, 5.6e+76], t$95$2, If[LessEqual[c, 4.25e+99], t$95$1, If[LessEqual[c, 3.2e+148], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(c * i), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.50000000000000018e61 or 3.9e62 < c < 5.5999999999999997e76

   1. Initial program 87.1%

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

   2. Taylor expanded in b around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-*r* 74.5%

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

      3. unpow2 74.5%

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

      4. associate-*l* 76.3%

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

      5. *-commutative 76.3%

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

      6. associate-*r* 78.1%

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

      7. distribute-rgt-neg-in 78.1%

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

      8. associate-*r* 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in c around 0 78.1%

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

      1. unpow2 78.1%

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

      2. associate-*r* 83.5%

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

   7. Simplified 83.5%

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

   if -3.50000000000000018e61 < c < 3.9e62 or 5.5999999999999997e76 < c < 4.24999999999999992e99

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 4.24999999999999992e99 < c < 3.1999999999999999e148

   1. Initial program 47.1%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*l* 62.0%

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

      4. *-commutative 62.0%

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

      5. distribute-rgt-neg-in 62.0%

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

      6. *-commutative 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in c around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 62.0%

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

      4. associate-*l* 62.0%

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

   7. Simplified 62.0%

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

   if 3.1999999999999999e148 < c

   1. Initial program 81.4%

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

   2. Taylor expanded in b around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-*r* 81.8%

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

      3. unpow2 81.8%

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

      4. associate-*l* 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-*r* 85.4%

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

      7. distribute-rgt-neg-in 85.4%

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

      8. associate-*r* 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in c around 0 85.2%

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

      1. unpow2 85.2%

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

      2. associate-*r* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in b around 0 85.2%

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

      1. unpow2 85.2%

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

      2. associate-*r* 88.8%

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

      3. associate-*r* 88.8%

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

      4. *-commutative 88.8%

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

      5. associate-*l* 89.0%

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

   10. Simplified 89.0%

       \[\leadsto \color{blue}{c \cdot \left(\left(c \cdot i\right) \cdot \left(-2 \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+76}:\\ \;\;\;\;\left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 4.25 \cdot 10^{+99}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]

Alternative 10: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+33} \lor \neg \left(c \leq 7.5 \cdot 10^{+40}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.15e+33) (not (<= c 7.5e+40)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.15e+33) || !(c <= 7.5e+40)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((c <= (-2.15d+33)) .or. (.not. (c <= 7.5d+40))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 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 ((c <= -2.15e+33) || !(c <= 7.5e+40)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.15e+33) or not (c <= 7.5e+40):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.15e+33) || !(c <= 7.5e+40))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.15e+33) || ~((c <= 7.5e+40)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.15e+33], N[Not[LessEqual[c, 7.5e+40]], $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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.15000000000000014e33 or 7.4999999999999996e40 < c

   1. Initial program 82.4%

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

   2. Taylor expanded in z around 0 87.1%

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

   if -2.15000000000000014e33 < c < 7.4999999999999996e40

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 81.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+33} \lor \neg \left(c \leq 7.5 \cdot 10^{+40}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 11: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+36} \lor \neg \left(c \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.7e+36) (not (<= c 6.2e+41)))
   (* 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 <= -1.7e+36) || !(c <= 6.2e+41)) {
		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 <= (-1.7d+36)) .or. (.not. (c <= 6.2d+41))) 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 <= -1.7e+36) || !(c <= 6.2e+41)) {
		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 <= -1.7e+36) or not (c <= 6.2e+41):
		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 <= -1.7e+36) || !(c <= 6.2e+41))
		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 <= -1.7e+36) || ~((c <= 6.2e+41)))
		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, -1.7e+36], N[Not[LessEqual[c, 6.2e+41]], $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 < -1.6999999999999999e36 or 6.2e41 < c

   1. Initial program 82.4%

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

   2. Taylor expanded in z around 0 87.1%

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

   if -1.6999999999999999e36 < c < 6.2e41

   1. Initial program 97.4%

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

   2. Taylor expanded in a around inf 92.1%

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

      1. *-commutative 92.1%

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

   4. Simplified 92.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+36} \lor \neg \left(c \leq 6.2 \cdot 10^{+41}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 12: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+103} \lor \neg \left(c \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.6e+103) (not (<= c 5.2e+42)))
   (* 2.0 (* c (* i (- (- a) (* b c)))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.6e+103) || !(c <= 5.2e+42)) {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((c <= (-8.6d+103)) .or. (.not. (c <= 5.2d+42))) then
        tmp = 2.0d0 * (c * (i * (-a - (b * c))))
    else
        tmp = ((x * y) + (z * t)) * 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 ((c <= -8.6e+103) || !(c <= 5.2e+42)) {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.6e+103) or not (c <= 5.2e+42):
		tmp = 2.0 * (c * (i * (-a - (b * c))))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.6e+103) || !(c <= 5.2e+42))
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8.6e+103) || ~((c <= 5.2e+42)))
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.6e+103], N[Not[LessEqual[c, 5.2e+42]], $MachinePrecision]], N[(2.0 * N[(c * N[(i * N[((-a) - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.59999999999999938e103 or 5.1999999999999998e42 < c

   1. Initial program 80.3%

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

   2. Taylor expanded in i around inf 85.9%

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

   if -8.59999999999999938e103 < c < 5.1999999999999998e42

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 78.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+103} \lor \neg \left(c \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 13: 72.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+40}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.55e+48)
   (* 2.0 (- (* x y) (* (* c c) (* b i))))
   (if (<= c 1.7e+40)
     (* (+ (* x y) (* z t)) 2.0)
     (* 2.0 (* c (* i (- (- a) (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.55e+48) {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	} else if (c <= 1.7e+40) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * 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 <= (-2.55d+48)) then
        tmp = 2.0d0 * ((x * y) - ((c * c) * (b * i)))
    else if (c <= 1.7d+40) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * (c * (i * (-a - (b * 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 <= -2.55e+48) {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	} else if (c <= 1.7e+40) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.55e+48:
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)))
	elif c <= 1.7e+40:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * (c * (i * (-a - (b * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.55e+48)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * c) * Float64(b * i))));
	elseif (c <= 1.7e+40)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.55e+48)
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	elseif (c <= 1.7e+40)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.55e+48], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+40], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(i * N[((-a) - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.5499999999999999e48

   1. Initial program 86.4%

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

   2. Taylor expanded in a around 0 84.6%

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

      1. unpow2 84.6%

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

      2. associate-*r* 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 82.7%

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

      1. unpow2 82.7%

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

      2. associate-*r* 88.5%

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

      3. *-commutative 88.5%

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

      4. associate-*r* 82.7%

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

      5. unpow2 82.7%

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

      6. associate-*l* 84.4%

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

      7. unpow2 84.4%

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

   7. Simplified 84.4%

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

   if -2.5499999999999999e48 < c < 1.69999999999999994e40

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 80.5%

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

   if 1.69999999999999994e40 < c

   1. Initial program 77.1%

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

   2. Taylor expanded in i around inf 82.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+40}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 14: 45.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+81} \lor \neg \left(x \cdot y \leq 8.4 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.35e+81) (not (<= (* x y) 8.4e+111)))
   (* (* x y) 2.0)
   (* 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) <= -1.35e+81) || !((x * y) <= 8.4e+111)) {
		tmp = (x * y) * 2.0;
	} 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) <= (-1.35d+81)) .or. (.not. ((x * y) <= 8.4d+111))) then
        tmp = (x * y) * 2.0d0
    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) <= -1.35e+81) || !((x * y) <= 8.4e+111)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.35e+81) or not ((x * y) <= 8.4e+111):
		tmp = (x * y) * 2.0
	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) <= -1.35e+81) || !(Float64(x * y) <= 8.4e+111))
		tmp = Float64(Float64(x * y) * 2.0);
	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) <= -1.35e+81) || ~(((x * y) <= 8.4e+111)))
		tmp = (x * y) * 2.0;
	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], -1.35e+81], N[Not[LessEqual[N[(x * y), $MachinePrecision], 8.4e+111]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.35e81 or 8.3999999999999998e111 < (*.f64 x y)

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 62.3%

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

   if -1.35e81 < (*.f64 x y) < 8.3999999999999998e111

   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. Taylor expanded in z around inf 41.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+81} \lor \neg \left(x \cdot y \leq 8.4 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 30.1% 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 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. Taylor expanded in z around inf 31.4%

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

3. Final simplification 31.4%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]

Developer target: 94.3% 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 2023279 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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