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

Percentage Accurate: 89.5% → 96.1%

Time: 13.6s

Alternatives: 18

Speedup: 0.5×

• 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: 89.5% 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: 96.1% accurate, 0.1× speedup

Math

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

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 (* t_1 (- i)))))))

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 * (t_1 * -i));
	}
	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(t_1 * Float64(-i))));
	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[(t$95$1 * (-i)), $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 95.2%

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

      1. associate-*l* 99.5%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

   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 50.2%

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

4. Final simplification 96.8%

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

Alternative 2: 92.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2 \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (- (+ (* x y) (* z t)) (* (* c t_1) i))))
   (if (<= t_2 INFINITY) (* t_2 2.0) (* 2.0 (* c (* t_1 (- i)))))))

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 t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2 * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2 * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = ((x * y) + (z * t)) - ((c * t_1) * i)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2 * 2.0
	else:
		tmp = 2.0 * (c * (t_1 * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = Float64(t_2 * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2 * 2.0;
	else
		tmp = 2.0 * (c * (t_1 * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], N[(t$95$2 * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $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 95.2%

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

   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 50.2%

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

4. Final simplification 92.7%

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

Alternative 3: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= (* x y) -1.85e+105)
     t_1
     (if (<= (* x y) -1.05e-53)
       (* 2.0 (- (* x y) (* b (* i (* c c)))))
       (if (<= (* x y) 6.2e+49)
         (* 2.0 (- (* z t) (* a (* c i))))
         (if (<= (* x y) 1.02e+96)
           t_1
           (* 2.0 (- (* x y) (* c (* (* b c) i))))))))))

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 tmp;
	if ((x * y) <= -1.85e+105) {
		tmp = t_1;
	} else if ((x * y) <= -1.05e-53) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if ((x * y) <= 6.2e+49) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((x * y) <= 1.02e+96) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * ((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) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    if ((x * y) <= (-1.85d+105)) then
        tmp = t_1
    else if ((x * y) <= (-1.05d-53)) then
        tmp = 2.0d0 * ((x * y) - (b * (i * (c * c))))
    else if ((x * y) <= 6.2d+49) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if ((x * y) <= 1.02d+96) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) - (c * ((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 t_1 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if ((x * y) <= -1.85e+105) {
		tmp = t_1;
	} else if ((x * y) <= -1.05e-53) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if ((x * y) <= 6.2e+49) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((x * y) <= 1.02e+96) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if (x * y) <= -1.85e+105:
		tmp = t_1
	elif (x * y) <= -1.05e-53:
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))))
	elif (x * y) <= 6.2e+49:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif (x * y) <= 1.02e+96:
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)))
	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)
	tmp = 0.0
	if (Float64(x * y) <= -1.85e+105)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.05e-53)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(b * Float64(i * Float64(c * c)))));
	elseif (Float64(x * y) <= 6.2e+49)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (Float64(x * y) <= 1.02e+96)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(b * c) * i))));
	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;
	tmp = 0.0;
	if ((x * y) <= -1.85e+105)
		tmp = t_1;
	elseif ((x * y) <= -1.05e-53)
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	elseif ((x * y) <= 6.2e+49)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif ((x * y) <= 1.02e+96)
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e+105], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.05e-53], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.2e+49], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.02e+96], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.84999999999999992e105 or 6.19999999999999985e49 < (*.f64 x y) < 1.02000000000000001e96

   1. Initial program 86.5%

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

   2. Taylor expanded in c around 0 84.9%

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

   if -1.84999999999999992e105 < (*.f64 x y) < -1.04999999999999989e-53

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 90.5%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. unpow2 74.6%

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

   5. Simplified 74.6%

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

   if -1.04999999999999989e-53 < (*.f64 x y) < 6.19999999999999985e49

   1. Initial program 91.1%

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

   2. Taylor expanded in a around inf 73.3%

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

      1. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in x around 0 72.6%

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

   if 1.02000000000000001e96 < (*.f64 x y)

   1. Initial program 83.3%

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

   2. Taylor expanded in z around 0 82.2%

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

   3. Taylor expanded in a around 0 77.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+105}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+96}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 41.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 0.47:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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) -1.8e-24)
     t_2
     (if (<= (* x y) -2.3e-180)
       (* 2.0 (* i (* a (- c))))
       (if (<= (* x y) 2.2e-207)
         t_1
         (if (<= (* x y) 0.47)
           (* (* a (* c i)) -2.0)
           (if (<= (* x y) 8e+198) 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) <= -1.8e-24) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-180) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 2.2e-207) {
		tmp = t_1;
	} else if ((x * y) <= 0.47) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 8e+198) {
		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) <= (-1.8d-24)) then
        tmp = t_2
    else if ((x * y) <= (-2.3d-180)) then
        tmp = 2.0d0 * (i * (a * -c))
    else if ((x * y) <= 2.2d-207) then
        tmp = t_1
    else if ((x * y) <= 0.47d0) then
        tmp = (a * (c * i)) * (-2.0d0)
    else if ((x * y) <= 8d+198) 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) <= -1.8e-24) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-180) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 2.2e-207) {
		tmp = t_1;
	} else if ((x * y) <= 0.47) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 8e+198) {
		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) <= -1.8e-24:
		tmp = t_2
	elif (x * y) <= -2.3e-180:
		tmp = 2.0 * (i * (a * -c))
	elif (x * y) <= 2.2e-207:
		tmp = t_1
	elif (x * y) <= 0.47:
		tmp = (a * (c * i)) * -2.0
	elif (x * y) <= 8e+198:
		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) <= -1.8e-24)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.3e-180)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	elseif (Float64(x * y) <= 2.2e-207)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.47)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	elseif (Float64(x * y) <= 8e+198)
		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) <= -1.8e-24)
		tmp = t_2;
	elseif ((x * y) <= -2.3e-180)
		tmp = 2.0 * (i * (a * -c));
	elseif ((x * y) <= 2.2e-207)
		tmp = t_1;
	elseif ((x * y) <= 0.47)
		tmp = (a * (c * i)) * -2.0;
	elseif ((x * y) <= 8e+198)
		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], -1.8e-24], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e-180], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-207], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.47], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8e+198], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.8e-24 or 8.00000000000000014e198 < (*.f64 x y)

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 52.2%

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

   if -1.8e-24 < (*.f64 x y) < -2.29999999999999996e-180

   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 z around 0 73.1%

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

   3. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-*r* 46.2%

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

      3. *-commutative 46.2%

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

      4. distribute-lft-neg-in 46.2%

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

      5. *-commutative 46.2%

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

   5. Simplified 46.2%

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

   if -2.29999999999999996e-180 < (*.f64 x y) < 2.1999999999999999e-207 or 0.46999999999999997 < (*.f64 x y) < 8.00000000000000014e198

   1. Initial program 89.8%

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

   2. Taylor expanded in z around inf 49.1%

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

   if 2.1999999999999999e-207 < (*.f64 x y) < 0.46999999999999997

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 48.4%

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

   3. Taylor expanded in a around 0 48.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-207}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 0.47:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-83}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.55e+69)
     t_2
     (if (<= c -7e+29)
       t_1
       (if (<= c -2e-10)
         (* 2.0 (- (* x y) (* b (* i (* c c)))))
         (if (<= c -1.16e-83)
           (* 2.0 (- (* z t) (* a (* c i))))
           (if (<= c 4.5e+46) 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 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.55e+69) {
		tmp = t_2;
	} else if (c <= -7e+29) {
		tmp = t_1;
	} else if (c <= -2e-10) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if (c <= -1.16e-83) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 4.5e+46) {
		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 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.55d+69)) then
        tmp = t_2
    else if (c <= (-7d+29)) then
        tmp = t_1
    else if (c <= (-2d-10)) then
        tmp = 2.0d0 * ((x * y) - (b * (i * (c * c))))
    else if (c <= (-1.16d-83)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= 4.5d+46) 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 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.55e+69) {
		tmp = t_2;
	} else if (c <= -7e+29) {
		tmp = t_1;
	} else if (c <= -2e-10) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if (c <= -1.16e-83) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 4.5e+46) {
		tmp = t_1;
	} 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 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.55e+69:
		tmp = t_2
	elif c <= -7e+29:
		tmp = t_1
	elif c <= -2e-10:
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))))
	elif c <= -1.16e-83:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= 4.5e+46:
		tmp = t_1
	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(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.55e+69)
		tmp = t_2;
	elseif (c <= -7e+29)
		tmp = t_1;
	elseif (c <= -2e-10)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(b * Float64(i * Float64(c * c)))));
	elseif (c <= -1.16e-83)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= 4.5e+46)
		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 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.55e+69)
		tmp = t_2;
	elseif (c <= -7e+29)
		tmp = t_1;
	elseif (c <= -2e-10)
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	elseif (c <= -1.16e-83)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= 4.5e+46)
		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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+69], t$95$2, If[LessEqual[c, -7e+29], t$95$1, If[LessEqual[c, -2e-10], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.16e-83], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+46], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.5499999999999999e69 or 4.5000000000000001e46 < c

   1. Initial program 80.4%

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

   2. Taylor expanded in i around inf 77.2%

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

   if -1.5499999999999999e69 < c < -6.99999999999999958e29 or -1.16000000000000008e-83 < c < 4.5000000000000001e46

   1. Initial program 96.8%

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

   2. Taylor expanded in c around 0 78.8%

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

   if -6.99999999999999958e29 < c < -2.00000000000000007e-10

   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 0 87.1%

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

   3. Taylor expanded in z around 0 73.3%

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

      1. unpow2 73.3%

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

   5. Simplified 73.3%

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

   if -2.00000000000000007e-10 < c < -1.16000000000000008e-83

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 92.9%

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

      1. *-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 70.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{+29}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-83}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 6: 40.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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) -2.9e+264)
     t_2
     (if (<= (* x y) 4.6e-210)
       t_1
       (if (<= (* x y) 1.0)
         (* (* a (* c i)) -2.0)
         (if (<= (* x y) 9.5e+198) 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) <= -2.9e+264) {
		tmp = t_2;
	} else if ((x * y) <= 4.6e-210) {
		tmp = t_1;
	} else if ((x * y) <= 1.0) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 9.5e+198) {
		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) <= (-2.9d+264)) then
        tmp = t_2
    else if ((x * y) <= 4.6d-210) then
        tmp = t_1
    else if ((x * y) <= 1.0d0) then
        tmp = (a * (c * i)) * (-2.0d0)
    else if ((x * y) <= 9.5d+198) 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) <= -2.9e+264) {
		tmp = t_2;
	} else if ((x * y) <= 4.6e-210) {
		tmp = t_1;
	} else if ((x * y) <= 1.0) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 9.5e+198) {
		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) <= -2.9e+264:
		tmp = t_2
	elif (x * y) <= 4.6e-210:
		tmp = t_1
	elif (x * y) <= 1.0:
		tmp = (a * (c * i)) * -2.0
	elif (x * y) <= 9.5e+198:
		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) <= -2.9e+264)
		tmp = t_2;
	elseif (Float64(x * y) <= 4.6e-210)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.0)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	elseif (Float64(x * y) <= 9.5e+198)
		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) <= -2.9e+264)
		tmp = t_2;
	elseif ((x * y) <= 4.6e-210)
		tmp = t_1;
	elseif ((x * y) <= 1.0)
		tmp = (a * (c * i)) * -2.0;
	elseif ((x * y) <= 9.5e+198)
		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], -2.9e+264], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4.6e-210], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.0], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.5e+198], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.8999999999999998e264 or 9.5e198 < (*.f64 x y)

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 77.6%

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

   if -2.8999999999999998e264 < (*.f64 x y) < 4.6e-210 or 1 < (*.f64 x y) < 9.5e198

   1. Initial program 90.7%

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

   2. Taylor expanded in z around inf 41.6%

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

   if 4.6e-210 < (*.f64 x y) < 1

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 48.4%

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

   3. Taylor expanded in a 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 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+264}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{-210}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 7: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+92} \lor \neg \left(a \leq 1.95 \cdot 10^{-89}\right):\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= a -7.6e+92) (not (<= a 1.95e-89)))
     (* 2.0 (- t_1 (* i (* a c))))
     (* 2.0 (- t_1 (* i (* c (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -7.6e+92) || !(a <= 1.95e-89)) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - (i * (c * (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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a <= (-7.6d+92)) .or. (.not. (a <= 1.95d-89))) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * (t_1 - (i * (c * (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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -7.6e+92) || !(a <= 1.95e-89)) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a <= -7.6e+92) or not (a <= 1.95e-89):
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * (t_1 - (i * (c * (b * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((a <= -7.6e+92) || !(a <= 1.95e-89))
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(b * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a <= -7.6e+92) || ~((a <= 1.95e-89)))
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -7.6e+92], N[Not[LessEqual[a, 1.95e-89]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.6000000000000001e92 or 1.94999999999999989e-89 < a

   1. Initial program 85.8%

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

   2. Taylor expanded in a around inf 80.7%

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

      1. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -7.6000000000000001e92 < a < 1.94999999999999989e-89

   1. Initial program 94.9%

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

   2. Taylor expanded in a around 0 94.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+92} \lor \neg \left(a \leq 1.95 \cdot 10^{-89}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 8: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* a (* c i)))))
        (t_2 (* 2.0 (* i (* c (* b (- c)))))))
   (if (<= c -1.65e+201)
     t_2
     (if (<= c -1.8e+69)
       t_1
       (if (<= c 5.3e-17)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= c 4.9e+136) 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) - (a * (c * i)));
	double t_2 = 2.0 * (i * (c * (b * -c)));
	double tmp;
	if (c <= -1.65e+201) {
		tmp = t_2;
	} else if (c <= -1.8e+69) {
		tmp = t_1;
	} else if (c <= 5.3e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 4.9e+136) {
		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) - (a * (c * i)))
    t_2 = 2.0d0 * (i * (c * (b * -c)))
    if (c <= (-1.65d+201)) then
        tmp = t_2
    else if (c <= (-1.8d+69)) then
        tmp = t_1
    else if (c <= 5.3d-17) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 4.9d+136) 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) - (a * (c * i)));
	double t_2 = 2.0 * (i * (c * (b * -c)));
	double tmp;
	if (c <= -1.65e+201) {
		tmp = t_2;
	} else if (c <= -1.8e+69) {
		tmp = t_1;
	} else if (c <= 5.3e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 4.9e+136) {
		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) - (a * (c * i)))
	t_2 = 2.0 * (i * (c * (b * -c)))
	tmp = 0
	if c <= -1.65e+201:
		tmp = t_2
	elif c <= -1.8e+69:
		tmp = t_1
	elif c <= 5.3e-17:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 4.9e+136:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))))
	t_2 = Float64(2.0 * Float64(i * Float64(c * Float64(b * Float64(-c)))))
	tmp = 0.0
	if (c <= -1.65e+201)
		tmp = t_2;
	elseif (c <= -1.8e+69)
		tmp = t_1;
	elseif (c <= 5.3e-17)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 4.9e+136)
		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) - (a * (c * i)));
	t_2 = 2.0 * (i * (c * (b * -c)));
	tmp = 0.0;
	if (c <= -1.65e+201)
		tmp = t_2;
	elseif (c <= -1.8e+69)
		tmp = t_1;
	elseif (c <= 5.3e-17)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 4.9e+136)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(i * N[(c * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+201], t$95$2, If[LessEqual[c, -1.8e+69], t$95$1, If[LessEqual[c, 5.3e-17], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 4.9e+136], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.65e201 or 4.90000000000000012e136 < c

   1. Initial program 79.8%

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

   2. Taylor expanded in a around 0 81.2%

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

   3. Taylor expanded in b around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unpow2 76.8%

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

      3. associate-*r* 72.4%

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

      4. associate-*l* 76.9%

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

      5. distribute-rgt-neg-in 76.9%

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

      6. distribute-rgt-neg-in 76.9%

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

   5. Simplified 76.9%

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

      1. associate-*r* 81.2%

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

      2. distribute-rgt-neg-out 81.2%

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

      3. add-sqr-sqrt 38.2%

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

      4. sqrt-unprod 25.8%

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

      5. sqr-neg 25.8%

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

      6. sqrt-unprod 2.1%

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

      7. add-sqr-sqrt 2.2%

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

      8. associate-*r* 0.8%

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

      9. *-commutative 0.8%

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

      10. *-commutative 0.8%

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

      11. associate-*l* 2.2%

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

      12. add-sqr-sqrt 2.1%

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

      13. sqrt-unprod 25.8%

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

      14. sqr-neg 25.8%

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

      15. sqrt-unprod 38.2%

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

      16. add-sqr-sqrt 81.2%

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

   7. Applied egg-rr 81.2%

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

   if -1.65e201 < c < -1.8000000000000001e69 or 5.2999999999999998e-17 < c < 4.90000000000000012e136

   1. Initial program 84.8%

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

   2. Taylor expanded in a around inf 73.3%

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

      1. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in x around 0 64.8%

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

   if -1.8000000000000001e69 < c < 5.2999999999999998e-17

   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 76.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+201}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+136}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-81} \lor \neg \left(c \leq 4 \cdot 10^{-69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4e-81) (not (<= c 4e-69)))
   (* 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 <= -4e-81) || !(c <= 4e-69)) {
		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 <= (-4d-81)) .or. (.not. (c <= 4d-69))) 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 <= -4e-81) || !(c <= 4e-69)) {
		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 <= -4e-81) or not (c <= 4e-69):
		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 <= -4e-81) || !(c <= 4e-69))
		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 <= -4e-81) || ~((c <= 4e-69)))
		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, -4e-81], N[Not[LessEqual[c, 4e-69]], $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 < -3.9999999999999998e-81 or 3.9999999999999999e-69 < c

   1. Initial program 85.6%

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

   2. Taylor expanded in z around 0 78.3%

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

   if -3.9999999999999998e-81 < c < 3.9999999999999999e-69

   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 c around 0 83.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-81} \lor \neg \left(c \leq 4 \cdot 10^{-69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 10: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+201}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -7.2e+201)
   (* 2.0 (* i (* c (* b (- c)))))
   (if (<= c 8e+124)
     (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
     (* 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 (c <= -7.2e+201) {
		tmp = 2.0 * (i * (c * (b * -c)));
	} else if (c <= 8e+124) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} 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 (c <= (-7.2d+201)) then
        tmp = 2.0d0 * (i * (c * (b * -c)))
    else if (c <= 8d+124) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    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 (c <= -7.2e+201) {
		tmp = 2.0 * (i * (c * (b * -c)));
	} else if (c <= 8e+124) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} 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 c <= -7.2e+201:
		tmp = 2.0 * (i * (c * (b * -c)))
	elif c <= 8e+124:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	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 (c <= -7.2e+201)
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(b * Float64(-c)))));
	elseif (c <= 8e+124)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	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 (c <= -7.2e+201)
		tmp = 2.0 * (i * (c * (b * -c)));
	elseif (c <= 8e+124)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	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[LessEqual[c, -7.2e+201], N[(2.0 * N[(i * N[(c * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+124], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $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 3 regimes

2. if c < -7.19999999999999951e201

   1. Initial program 75.2%

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

   2. Taylor expanded in a around 0 80.0%

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

   3. Taylor expanded in b around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unpow2 85.4%

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

      3. associate-*r* 80.8%

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

      4. associate-*l* 85.3%

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

      5. distribute-rgt-neg-in 85.3%

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

      6. distribute-rgt-neg-in 85.3%

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

   5. Simplified 85.3%

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

      1. associate-*r* 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

      3. add-sqr-sqrt 60.1%

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

      4. sqrt-unprod 40.1%

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

      5. sqr-neg 40.1%

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

      6. sqrt-unprod 0.3%

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

      7. add-sqr-sqrt 0.5%

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

      8. associate-*r* 0.6%

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

      9. *-commutative 0.6%

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

      10. *-commutative 0.6%

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

      11. associate-*l* 0.5%

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

      12. add-sqr-sqrt 0.3%

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

      13. sqrt-unprod 40.1%

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

      14. sqr-neg 40.1%

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

      15. sqrt-unprod 60.1%

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

      16. add-sqr-sqrt 90.1%

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

   7. Applied egg-rr 90.1%

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

   if -7.19999999999999951e201 < c < 7.99999999999999959e124

   1. Initial program 93.2%

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

   2. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

   4. Simplified 85.9%

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

   if 7.99999999999999959e124 < c

   1. Initial program 83.0%

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

   2. Taylor expanded in z around 0 89.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+201}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 74.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+69} \lor \neg \left(c \leq 4 \cdot 10^{+43}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.55e+69) (not (<= c 4e+43)))
   (* 2.0 (* 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 <= -1.55e+69) || !(c <= 4e+43)) {
		tmp = 2.0 * (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 <= (-1.55d+69)) .or. (.not. (c <= 4d+43))) then
        tmp = 2.0d0 * (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 <= -1.55e+69) || !(c <= 4e+43)) {
		tmp = 2.0 * (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 <= -1.55e+69) or not (c <= 4e+43):
		tmp = 2.0 * (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 <= -1.55e+69) || !(c <= 4e+43))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-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 <= -1.55e+69) || ~((c <= 4e+43)))
		tmp = 2.0 * (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, -1.55e+69], N[Not[LessEqual[c, 4e+43]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $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 < -1.5499999999999999e69 or 4.00000000000000006e43 < c

   1. Initial program 80.4%

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

   2. Taylor expanded in i around inf 77.2%

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

   if -1.5499999999999999e69 < c < 4.00000000000000006e43

   1. Initial program 97.2%

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

   2. Taylor expanded in c around 0 74.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+69} \lor \neg \left(c \leq 4 \cdot 10^{+43}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 12: 68.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+121} \lor \neg \left(c \leq 1.3 \cdot 10^{+130}\right):\\ \;\;\;\;2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4e+121) (not (<= c 1.3e+130)))
   (* 2.0 (* b (* i (* c (- 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 <= -4e+121) || !(c <= 1.3e+130)) {
		tmp = 2.0 * (b * (i * (c * -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 <= (-4d+121)) .or. (.not. (c <= 1.3d+130))) then
        tmp = 2.0d0 * (b * (i * (c * -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 <= -4e+121) || !(c <= 1.3e+130)) {
		tmp = 2.0 * (b * (i * (c * -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 <= -4e+121) or not (c <= 1.3e+130):
		tmp = 2.0 * (b * (i * (c * -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 <= -4e+121) || !(c <= 1.3e+130))
		tmp = Float64(2.0 * Float64(b * Float64(i * Float64(c * Float64(-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 <= -4e+121) || ~((c <= 1.3e+130)))
		tmp = 2.0 * (b * (i * (c * -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, -4e+121], N[Not[LessEqual[c, 1.3e+130]], $MachinePrecision]], N[(2.0 * N[(b * N[(i * N[(c * (-c)), $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 < -4.00000000000000015e121 or 1.2999999999999999e130 < c

   1. Initial program 83.4%

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

   2. Taylor expanded in b around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-rgt-neg-in 70.6%

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

      3. unpow2 70.6%

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

      4. associate-*r* 65.1%

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

      5. distribute-rgt-neg-in 65.1%

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

      6. associate-*r* 70.6%

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

   4. Simplified 70.6%

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

   if -4.00000000000000015e121 < c < 1.2999999999999999e130

   1. Initial program 93.1%

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

   2. Taylor expanded in c around 0 69.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+121} \lor \neg \left(c \leq 1.3 \cdot 10^{+130}\right):\\ \;\;\;\;2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 13: 68.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+121} \lor \neg \left(c \leq 5 \cdot 10^{+126}\right):\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.5e+121) (not (<= c 5e+126)))
   (* 2.0 (* i (* c (* 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 <= -3.5e+121) || !(c <= 5e+126)) {
		tmp = 2.0 * (i * (c * (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 <= (-3.5d+121)) .or. (.not. (c <= 5d+126))) then
        tmp = 2.0d0 * (i * (c * (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 <= -3.5e+121) || !(c <= 5e+126)) {
		tmp = 2.0 * (i * (c * (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 <= -3.5e+121) or not (c <= 5e+126):
		tmp = 2.0 * (i * (c * (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 <= -3.5e+121) || !(c <= 5e+126))
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(b * Float64(-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 <= -3.5e+121) || ~((c <= 5e+126)))
		tmp = 2.0 * (i * (c * (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, -3.5e+121], N[Not[LessEqual[c, 5e+126]], $MachinePrecision]], N[(2.0 * N[(i * N[(c * N[(b * (-c)), $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 < -3.5e121 or 4.99999999999999977e126 < c

   1. Initial program 83.4%

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

   2. Taylor expanded in a around 0 77.4%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. unpow2 70.6%

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

      3. associate-*r* 65.1%

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

      4. associate-*l* 69.8%

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

      5. distribute-rgt-neg-in 69.8%

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

      6. distribute-rgt-neg-in 69.8%

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

   5. Simplified 69.8%

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

      1. associate-*r* 74.1%

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

      2. distribute-rgt-neg-out 74.1%

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

      3. add-sqr-sqrt 35.1%

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

      4. sqrt-unprod 29.4%

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

      5. sqr-neg 29.4%

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

      6. sqrt-unprod 4.2%

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

      7. add-sqr-sqrt 4.5%

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

      8. associate-*r* 3.4%

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

      9. *-commutative 3.4%

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

      10. *-commutative 3.4%

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

      11. associate-*l* 4.5%

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

      12. add-sqr-sqrt 4.2%

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

      13. sqrt-unprod 29.4%

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

      14. sqr-neg 29.4%

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

      15. sqrt-unprod 35.1%

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

      16. add-sqr-sqrt 74.1%

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

   7. Applied egg-rr 74.1%

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

   if -3.5e121 < c < 4.99999999999999977e126

   1. Initial program 93.1%

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

   2. Taylor expanded in c around 0 69.6%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+121} \lor \neg \left(c \leq 5 \cdot 10^{+126}\right):\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 14: 41.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+264} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+200}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.9e+264) (not (<= (* x y) 2.9e+200)))
   (* (* 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) <= -2.9e+264) || !((x * y) <= 2.9e+200)) {
		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) <= (-2.9d+264)) .or. (.not. ((x * y) <= 2.9d+200))) 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) <= -2.9e+264) || !((x * y) <= 2.9e+200)) {
		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) <= -2.9e+264) or not ((x * y) <= 2.9e+200):
		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) <= -2.9e+264) || !(Float64(x * y) <= 2.9e+200))
		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) <= -2.9e+264) || ~(((x * y) <= 2.9e+200)))
		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], -2.9e+264], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+200]], $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) < -2.8999999999999998e264 or 2.8999999999999999e200 < (*.f64 x y)

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 77.6%

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

   if -2.8999999999999998e264 < (*.f64 x y) < 2.8999999999999999e200

   1. Initial program 91.4%

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

   2. Taylor expanded in z around inf 39.2%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+264} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+200}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 69.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+121} \lor \neg \left(c \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;\left(c \cdot \left(c \cdot i\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.5e+121) (not (<= c 1.65e+125)))
   (* (* c (* c i)) (* b -2.0))
   (* (+ (* 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 <= -4.5e+121) || !(c <= 1.65e+125)) {
		tmp = (c * (c * i)) * (b * -2.0);
	} 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 <= (-4.5d+121)) .or. (.not. (c <= 1.65d+125))) then
        tmp = (c * (c * i)) * (b * (-2.0d0))
    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 <= -4.5e+121) || !(c <= 1.65e+125)) {
		tmp = (c * (c * i)) * (b * -2.0);
	} 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 <= -4.5e+121) or not (c <= 1.65e+125):
		tmp = (c * (c * i)) * (b * -2.0)
	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 <= -4.5e+121) || !(c <= 1.65e+125))
		tmp = Float64(Float64(c * Float64(c * i)) * Float64(b * -2.0));
	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 <= -4.5e+121) || ~((c <= 1.65e+125)))
		tmp = (c * (c * i)) * (b * -2.0);
	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, -4.5e+121], N[Not[LessEqual[c, 1.65e+125]], $MachinePrecision]], N[(N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(b * -2.0), $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 < -4.5000000000000003e121 or 1.65000000000000003e125 < c

   1. Initial program 83.4%

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

   2. Taylor expanded in i around inf 81.6%

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

   3. Taylor expanded in c around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. *-commutative 70.6%

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

      3. *-commutative 70.6%

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

      4. unpow2 70.6%

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

      5. associate-*l* 65.1%

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

   5. Simplified 65.1%

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

   if -4.5000000000000003e121 < c < 1.65000000000000003e125

   1. Initial program 93.1%

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

   2. Taylor expanded in c around 0 69.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+121} \lor \neg \left(c \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;\left(c \cdot \left(c \cdot i\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 16: 68.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+121} \lor \neg \left(c \leq 4.5 \cdot 10^{+129}\right):\\ \;\;\;\;\left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6.5e+121) (not (<= c 4.5e+129)))
   (* (* i (* b (* c c))) -2.0)
   (* (+ (* 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 <= -6.5e+121) || !(c <= 4.5e+129)) {
		tmp = (i * (b * (c * c))) * -2.0;
	} 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 <= (-6.5d+121)) .or. (.not. (c <= 4.5d+129))) then
        tmp = (i * (b * (c * c))) * (-2.0d0)
    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 <= -6.5e+121) || !(c <= 4.5e+129)) {
		tmp = (i * (b * (c * c))) * -2.0;
	} 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 <= -6.5e+121) or not (c <= 4.5e+129):
		tmp = (i * (b * (c * c))) * -2.0
	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 <= -6.5e+121) || !(c <= 4.5e+129))
		tmp = Float64(Float64(i * Float64(b * Float64(c * c))) * -2.0);
	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 <= -6.5e+121) || ~((c <= 4.5e+129)))
		tmp = (i * (b * (c * c))) * -2.0;
	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, -6.5e+121], N[Not[LessEqual[c, 4.5e+129]], $MachinePrecision]], N[(N[(i * N[(b * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $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 < -6.50000000000000019e121 or 4.5000000000000001e129 < c

   1. Initial program 83.4%

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

   2. Taylor expanded in i around inf 81.6%

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

   3. Taylor expanded in c around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*r* 70.5%

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

      3. unpow2 70.5%

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

   5. Simplified 70.5%

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

   if -6.50000000000000019e121 < c < 4.5000000000000001e129

   1. Initial program 93.1%

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

   2. Taylor expanded in c around 0 69.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+121} \lor \neg \left(c \leq 4.5 \cdot 10^{+129}\right):\\ \;\;\;\;\left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 17: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+222}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -2.7e+222)
   (* (* a (* c i)) -2.0)
   (if (<= a 9e+148) (* (+ (* x y) (* z t)) 2.0) (* 2.0 (* 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 (a <= -2.7e+222) {
		tmp = (a * (c * i)) * -2.0;
	} else if (a <= 9e+148) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (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 (a <= (-2.7d+222)) then
        tmp = (a * (c * i)) * (-2.0d0)
    else if (a <= 9d+148) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * (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 (a <= -2.7e+222) {
		tmp = (a * (c * i)) * -2.0;
	} else if (a <= 9e+148) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (i * (a * -c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -2.7e+222:
		tmp = (a * (c * i)) * -2.0
	elif a <= 9e+148:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * (i * (a * -c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -2.7e+222)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	elseif (a <= 9e+148)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -2.7e+222)
		tmp = (a * (c * i)) * -2.0;
	elseif (a <= 9e+148)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * (i * (a * -c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -2.7e+222], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[a, 9e+148], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.70000000000000013e222

   1. Initial program 73.4%

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

   2. Taylor expanded in a around inf 67.6%

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

   3. Taylor expanded in a around 0 67.6%

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

   if -2.70000000000000013e222 < a < 8.99999999999999987e148

   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 c around 0 61.8%

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

   if 8.99999999999999987e148 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 70.4%

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

   3. Taylor expanded in a around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. associate-*r* 61.5%

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

      3. *-commutative 61.5%

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

      4. distribute-lft-neg-in 61.5%

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

      5. *-commutative 61.5%

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

   5. Simplified 61.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+222}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+148}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 18: 29.1% 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 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 z around inf 35.9%

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

3. Final simplification 35.9%

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

Developer target: 93.9% 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 2023293 
(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))))