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

Percentage Accurate: 90.0% → 96.1%

Time: 12.5s

Alternatives: 14

Speedup: 1.0×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 - \left(c \cdot t\_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t\_2 - t\_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(i \cdot \left(-{c}^{2}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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

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);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (b * (i * -pow(c, 2.0)));
	}
	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);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (b * (i * -Math.pow(c, 2.0)));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(b * Float64(i * Float64(-(c ^ 2.0)))));
	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);
	tmp = 0.0;
	if ((t_2 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * (b * (i * -(c ^ 2.0)));
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(b * N[(i * (-N[Power[c, 2.0], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.3%

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

      1. fma-define 95.3%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

      1. fma-define 99.2%

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

      2. +-commutative 99.2%

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

   6. Applied egg-rr 99.2%

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

   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. Add Preprocessing

   3. Taylor expanded in b around inf 63.6%

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

      1. associate-*r* 63.6%

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

      2. mul-1-neg 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 97.7%

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

Alternative 2: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := c \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 10^{+288}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* c t_1)))
   (if (<= t_3 (- INFINITY))
     (* 2.0 (- (* x y) t_2))
     (if (<= t_3 1e+288)
       (* (- (+ (* x y) (* z t)) (* t_3 i)) 2.0)
       (* 2.0 (- (* z t) t_2))))))

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 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (t_3 <= 1e+288) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	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 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (t_3 <= 1e+288) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = c * t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 2.0 * ((x * y) - t_2)
	elif t_3 <= 1e+288:
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(c * t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	elseif (t_3 <= 1e+288)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_3 * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	t_3 = c * t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 2.0 * ((x * y) - t_2);
	elseif (t_3 <= 1e+288)
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - t_2);
	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[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+288], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -inf.0

   1. Initial program 78.7%

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

   3. Taylor expanded in z around 0 92.6%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 1e288

   1. Initial program 98.7%

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

   if 1e288 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 74.6%

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

   3. Taylor expanded in x around 0 93.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 10^{+288}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+175}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-39} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -2e+242)
     t_1
     (if (<= (* x y) -2e+175)
       (* (* i (* a c)) -2.0)
       (if (or (<= (* x y) -5e-39) (not (<= (* x y) 5e+36)))
         t_1
         (* 2.0 (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+242) {
		tmp = t_1;
	} else if ((x * y) <= -2e+175) {
		tmp = (i * (a * c)) * -2.0;
	} else if (((x * y) <= -5e-39) || !((x * y) <= 5e+36)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) * 2.0d0
    if ((x * y) <= (-2d+242)) then
        tmp = t_1
    else if ((x * y) <= (-2d+175)) then
        tmp = (i * (a * c)) * (-2.0d0)
    else if (((x * y) <= (-5d-39)) .or. (.not. ((x * y) <= 5d+36))) then
        tmp = t_1
    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 t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+242) {
		tmp = t_1;
	} else if ((x * y) <= -2e+175) {
		tmp = (i * (a * c)) * -2.0;
	} else if (((x * y) <= -5e-39) || !((x * y) <= 5e+36)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2e+242:
		tmp = t_1
	elif (x * y) <= -2e+175:
		tmp = (i * (a * c)) * -2.0
	elif ((x * y) <= -5e-39) or not ((x * y) <= 5e+36):
		tmp = t_1
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2e+242)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e+175)
		tmp = Float64(Float64(i * Float64(a * c)) * -2.0);
	elseif ((Float64(x * y) <= -5e-39) || !(Float64(x * y) <= 5e+36))
		tmp = t_1;
	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)
	t_1 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2e+242)
		tmp = t_1;
	elseif ((x * y) <= -2e+175)
		tmp = (i * (a * c)) * -2.0;
	elseif (((x * y) <= -5e-39) || ~(((x * y) <= 5e+36)))
		tmp = t_1;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+242], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e+175], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e-39], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+36]], $MachinePrecision]], t$95$1, N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e242 or -1.9999999999999999e175 < (*.f64 x y) < -4.9999999999999998e-39 or 4.99999999999999977e36 < (*.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 56.9%

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

   if -2.0000000000000001e242 < (*.f64 x y) < -1.9999999999999999e175

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. associate-*r* 67.0%

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

      3. distribute-rgt-neg-in 67.0%

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

      4. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in c around 0 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*l* 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in c around 0 67.0%

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

       1. associate-*r* 67.0%

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

       2. *-commutative 67.0%

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

   11. Simplified 67.0%

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

   if -4.9999999999999998e-39 < (*.f64 x y) < 4.99999999999999977e36

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 47.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+242}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+175}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-39} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-36} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* x y) -4e-36) (not (<= (* x y) 5e+36)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -4e-36) || !((x * y) <= 5e+36)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (((x * y) <= (-4d-36)) .or. (.not. ((x * y) <= 5d+36))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -4e-36) || !((x * y) <= 5e+36)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if ((x * y) <= -4e-36) or not ((x * y) <= 5e+36):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if ((Float64(x * y) <= -4e-36) || !(Float64(x * y) <= 5e+36))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (((x * y) <= -4e-36) || ~(((x * y) <= 5e+36)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e-36], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+36]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.9999999999999998e-36 or 4.99999999999999977e36 < (*.f64 x y)

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 88.4%

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

   if -3.9999999999999998e-36 < (*.f64 x y) < 4.99999999999999977e36

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 89.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-36} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+291}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+291)
   (* (* x y) 2.0)
   (if (<= (* x y) 5e+36)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* 2.0 (- (* x y) (* a (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+291) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e+36) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - (a * (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 ((x * y) <= (-1d+291)) then
        tmp = (x * y) * 2.0d0
    else if ((x * y) <= 5d+36) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) - (a * (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 ((x * y) <= -1e+291) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e+36) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+291:
		tmp = (x * y) * 2.0
	elif (x * y) <= 5e+36:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+291)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (Float64(x * y) <= 5e+36)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+291)
		tmp = (x * y) * 2.0;
	elseif ((x * y) <= 5e+36)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+291], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+36], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999996e290

   1. Initial program 88.0%

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

   3. Taylor expanded in x around inf 92.6%

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

   if -9.9999999999999996e290 < (*.f64 x y) < 4.99999999999999977e36

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 83.5%

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

   if 4.99999999999999977e36 < (*.f64 x y)

   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. Add Preprocessing

   3. Taylor expanded in a around inf 73.1%

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

      1. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in z around 0 75.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+291}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= a -4.5e+45)
     (* 2.0 (- t_1 (* i (* a c))))
     (if (<= a 8.2e+176)
       (* 2.0 (- t_1 (* (* b c) (* c i))))
       (* 2.0 (- (* x y) (* a (* 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);
	double tmp;
	if (a <= -4.5e+45) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 8.2e+176) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - (a * (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)
    if (a <= (-4.5d+45)) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (a <= 8.2d+176) then
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) - (a * (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);
	double tmp;
	if (a <= -4.5e+45) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 8.2e+176) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if a <= -4.5e+45:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif a <= 8.2e+176:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	else:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	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 <= -4.5e+45)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (a <= 8.2e+176)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(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);
	tmp = 0.0;
	if (a <= -4.5e+45)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (a <= 8.2e+176)
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	else
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	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[LessEqual[a, -4.5e+45], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+176], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999998e45

   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. Add Preprocessing

   3. Taylor expanded in a around inf 85.3%

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

      1. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   if -4.4999999999999998e45 < a < 8.1999999999999998e176

   1. Initial program 92.8%

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

      1. fma-define 92.8%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

      1. fma-define 95.8%

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

      2. +-commutative 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in a around 0 92.8%

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

   if 8.1999999999999998e176 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 88.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+131}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (* b (* c i)) (- c)))))
   (if (<= c -6.2e+114)
     t_1
     (if (<= c 4.3e+57)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 2.75e+131) (* 2.0 (- (* z t) (* c (* a i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((b * (c * i)) * -c);
	double tmp;
	if (c <= -6.2e+114) {
		tmp = t_1;
	} else if (c <= 4.3e+57) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.75e+131) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((b * (c * i)) * -c)
    if (c <= (-6.2d+114)) then
        tmp = t_1
    else if (c <= 4.3d+57) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 2.75d+131) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((b * (c * i)) * -c);
	double tmp;
	if (c <= -6.2e+114) {
		tmp = t_1;
	} else if (c <= 4.3e+57) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.75e+131) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((b * (c * i)) * -c)
	tmp = 0
	if c <= -6.2e+114:
		tmp = t_1
	elif c <= 4.3e+57:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 2.75e+131:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(b * Float64(c * i)) * Float64(-c)))
	tmp = 0.0
	if (c <= -6.2e+114)
		tmp = t_1;
	elseif (c <= 4.3e+57)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 2.75e+131)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((b * (c * i)) * -c);
	tmp = 0.0;
	if (c <= -6.2e+114)
		tmp = t_1;
	elseif (c <= 4.3e+57)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 2.75e+131)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+114], t$95$1, If[LessEqual[c, 4.3e+57], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 2.75e+131], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.2000000000000001e114 or 2.74999999999999986e131 < c

   1. Initial program 81.5%

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

   3. Taylor expanded in i around inf 82.0%

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

   4. Taylor expanded in a around 0 72.2%

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

   if -6.2000000000000001e114 < c < 4.30000000000000033e57

   1. Initial program 97.9%

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

   3. Taylor expanded in c around 0 73.8%

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

   if 4.30000000000000033e57 < c < 2.74999999999999986e131

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in x around 0 67.4%

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

      1. *-commutative 67.4%

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

      2. associate-*r* 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+131}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-85} \lor \neg \left(c \leq 2 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.8e-85) (not (<= c 2e-29)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e-85) || !(c <= 2e-29)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.8d-85)) .or. (.not. (c <= 2d-29))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e-85) || !(c <= 2e-29)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.8e-85) or not (c <= 2e-29):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.8e-85) || !(c <= 2e-29))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.8e-85) || ~((c <= 2e-29)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.8e-85], N[Not[LessEqual[c, 2e-29]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.7999999999999999e-85 or 1.99999999999999989e-29 < c

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 85.5%

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

   if -1.7999999999999999e-85 < c < 1.99999999999999989e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 98.1%

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

      1. *-commutative 98.1%

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

   5. Simplified 98.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-85} \lor \neg \left(c \leq 2 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+23} \lor \neg \left(c \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.35e+23) (not (<= c 9e+60)))
   (* 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 <= -1.35e+23) || !(c <= 9e+60)) {
		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 <= (-1.35d+23)) .or. (.not. (c <= 9d+60))) 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 <= -1.35e+23) || !(c <= 9e+60)) {
		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 <= -1.35e+23) or not (c <= 9e+60):
		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 <= -1.35e+23) || !(c <= 9e+60))
		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 <= -1.35e+23) || ~((c <= 9e+60)))
		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, -1.35e+23], N[Not[LessEqual[c, 9e+60]], $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 < -1.3499999999999999e23 or 9.00000000000000026e60 < c

   1. Initial program 83.5%

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

   3. Taylor expanded in i around inf 78.4%

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

   if -1.3499999999999999e23 < c < 9.00000000000000026e60

   1. Initial program 98.4%

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

   3. Taylor expanded in c around 0 76.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+23} \lor \neg \left(c \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+115} \lor \neg \left(c \leq 1.2 \cdot 10^{+71}\right):\\ \;\;\;\;2 \cdot \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.15e+115) (not (<= c 1.2e+71)))
   (* 2.0 (* (* b (* c i)) (- 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 <= -1.15e+115) || !(c <= 1.2e+71)) {
		tmp = 2.0 * ((b * (c * i)) * -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 <= (-1.15d+115)) .or. (.not. (c <= 1.2d+71))) then
        tmp = 2.0d0 * ((b * (c * i)) * -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 <= -1.15e+115) || !(c <= 1.2e+71)) {
		tmp = 2.0 * ((b * (c * i)) * -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 <= -1.15e+115) or not (c <= 1.2e+71):
		tmp = 2.0 * ((b * (c * i)) * -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 <= -1.15e+115) || !(c <= 1.2e+71))
		tmp = Float64(2.0 * Float64(Float64(b * Float64(c * i)) * 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 <= -1.15e+115) || ~((c <= 1.2e+71)))
		tmp = 2.0 * ((b * (c * i)) * -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, -1.15e+115], N[Not[LessEqual[c, 1.2e+71]], $MachinePrecision]], N[(2.0 * N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-c)), $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 < -1.15000000000000002e115 or 1.1999999999999999e71 < c

   1. Initial program 82.7%

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

   3. Taylor expanded in i around inf 81.3%

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

   4. Taylor expanded in a around 0 66.9%

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

   if -1.15000000000000002e115 < c < 1.1999999999999999e71

   1. Initial program 97.3%

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

   3. Taylor expanded in c around 0 73.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+115} \lor \neg \left(c \leq 1.2 \cdot 10^{+71}\right):\\ \;\;\;\;2 \cdot \left(\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-39} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e-39) (not (<= (* x y) 5e+36)))
   (* (* 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) <= -5e-39) || !((x * y) <= 5e+36)) {
		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) <= (-5d-39)) .or. (.not. ((x * y) <= 5d+36))) 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) <= -5e-39) || !((x * y) <= 5e+36)) {
		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) <= -5e-39) or not ((x * y) <= 5e+36):
		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) <= -5e-39) || !(Float64(x * y) <= 5e+36))
		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) <= -5e-39) || ~(((x * y) <= 5e+36)))
		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], -5e-39], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+36]], $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) < -4.9999999999999998e-39 or 4.99999999999999977e36 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf 54.1%

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

   if -4.9999999999999998e-39 < (*.f64 x y) < 4.99999999999999977e36

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 47.0%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-39} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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]

Derivation

1. Initial program 91.3%

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

   1. fma-define 91.6%

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

   2. associate-*l* 96.1%

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

3. Simplified 96.1%

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

   1. fma-define 95.7%

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

   2. +-commutative 95.7%

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

6. Applied egg-rr 95.7%

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

7. Final simplification 95.7%

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

Alternative 13: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+176}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 8.5e+176) (* (+ (* x y) (* z t)) 2.0) (* (* c i) (* a -2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.5e+176) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 8.5d+176) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (c * i) * (a * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.5e+176) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8.5e+176:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (c * i) * (a * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8.5e+176)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 8.5e+176)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (c * i) * (a * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8.5e+176], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 8.4999999999999995e176

   1. Initial program 92.4%

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

   3. Taylor expanded in c around 0 57.7%

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

   if 8.4999999999999995e176 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-*r* 70.1%

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

      3. distribute-rgt-neg-in 70.1%

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

      4. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in c around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l* 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+176}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

3. Taylor expanded in z around inf 26.1%

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

4. Final simplification 26.1%

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

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 2024098 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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