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

Percentage Accurate: 89.8% → 95.8%

Time: 17.3s

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: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* y x) (* z t))))
   (if (<= (- t_2 (* i (* c t_1))) INFINITY)
     (* 2.0 (- t_2 (* (* c i) t_1)))
     (* 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 = (y * x) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	} 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 = (y * x) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	} 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 = (y * x) + (z * t)
	tmp = 0
	if (t_2 - (i * (c * t_1))) <= math.inf:
		tmp = 2.0 * (t_2 - ((c * i) * t_1))
	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(y * x) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(i * Float64(c * t_1))) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(Float64(c * i) * t_1)));
	else
		tmp = Float64(2.0 * Float64(-Float64(b * Float64(i * (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 = (y * x) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	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[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(N[(c * i), $MachinePrecision] * t$95$1), $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 92.7%

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

      1. fma-define 92.7%

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

      2. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

      1. fma-define 98.7%

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

      2. +-commutative 98.7%

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

   6. Applied egg-rr 98.7%

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

   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 78.0%

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

      1. associate-*r* 78.0%

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

      2. mul-1-neg 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 98.0%

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

Alternative 2: 97.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. associate--l+ 89.5%

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

   2. fma-neg 91.4%

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

   3. *-commutative 91.4%

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

   4. +-commutative 91.4%

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

   5. fma-undefine 91.4%

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

   6. associate-*r* 93.8%

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

   7. *-commutative 93.8%

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

   8. *-commutative 93.8%

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

   9. fma-define 94.6%

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

   10. *-commutative 94.6%

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

   11. associate-*r* 92.2%

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

   12. fma-undefine 92.2%

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

   13. +-commutative 92.2%

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

   14. *-commutative 92.2%

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

   15. associate-*r* 98.0%

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

   16. distribute-rgt-neg-in 98.0%

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

4. Applied egg-rr 98.0%

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

Alternative 3: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(a \cdot \left(i + \frac{c \cdot \left(b \cdot i\right)}{a}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (* c (* t_1 (- i))))
     (if (<= t_2 4e+291)
       (* 2.0 (- (+ (* y x) (* z t)) t_2))
       (* 2.0 (- (* y x) (* c (* a (+ i (/ (* c (* b i)) a))))))))))

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 = i * (c * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 4e+291) {
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((y * x) - (c * (a * (i + ((c * (b * i)) / a)))));
	}
	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 = i * (c * t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 4e+291) {
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((y * x) - (c * (a * (i + ((c * (b * i)) / a)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * (c * (t_1 * -i))
	elif t_2 <= 4e+291:
		tmp = 2.0 * (((y * x) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((y * x) - (c * (a * (i + ((c * (b * i)) / a)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	elseif (t_2 <= 4e+291)
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(c * Float64(a * Float64(i + Float64(Float64(c * Float64(b * i)) / a))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * (c * (t_1 * -i));
	elseif (t_2 <= 4e+291)
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((y * x) - (c * (a * (i + ((c * (b * i)) / a)))));
	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[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+291], N[(2.0 * N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(c * N[(a * N[(i + N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.3%

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

   3. Taylor expanded in i around inf 92.9%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 3.9999999999999998e291

   1. Initial program 99.3%

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

   if 3.9999999999999998e291 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 72.7%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in a around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*r* 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 4 \cdot 10^{+291}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(a \cdot \left(i + \frac{c \cdot \left(b \cdot i\right)}{a}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+55} \lor \neg \left(c \leq -6.2 \cdot 10^{+23} \lor \neg \left(c \leq -4 \cdot 10^{-41}\right) \land \left(c \leq 2.7 \cdot 10^{-106} \lor \neg \left(c \leq 2.1 \cdot 10^{-79}\right) \land c \leq 3.7 \cdot 10^{+79}\right)\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1e+55)
         (not
          (or (<= c -6.2e+23)
              (and (not (<= c -4e-41))
                   (or (<= c 2.7e-106)
                       (and (not (<= c 2.1e-79)) (<= c 3.7e+79)))))))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (+ (* y x) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1e+55) || !((c <= -6.2e+23) || (!(c <= -4e-41) && ((c <= 2.7e-106) || (!(c <= 2.1e-79) && (c <= 3.7e+79)))))) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1d+55)) .or. (.not. (c <= (-6.2d+23)) .or. (.not. (c <= (-4d-41))) .and. (c <= 2.7d-106) .or. (.not. (c <= 2.1d-79)) .and. (c <= 3.7d+79))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * ((y * x) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1e+55) || !((c <= -6.2e+23) || (!(c <= -4e-41) && ((c <= 2.7e-106) || (!(c <= 2.1e-79) && (c <= 3.7e+79)))))) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1e+55) or not ((c <= -6.2e+23) or (not (c <= -4e-41) and ((c <= 2.7e-106) or (not (c <= 2.1e-79) and (c <= 3.7e+79))))):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1e+55) || !((c <= -6.2e+23) || (!(c <= -4e-41) && ((c <= 2.7e-106) || (!(c <= 2.1e-79) && (c <= 3.7e+79))))))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1e+55) || ~(((c <= -6.2e+23) || (~((c <= -4e-41)) && ((c <= 2.7e-106) || (~((c <= 2.1e-79)) && (c <= 3.7e+79)))))))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1e+55], N[Not[Or[LessEqual[c, -6.2e+23], And[N[Not[LessEqual[c, -4e-41]], $MachinePrecision], Or[LessEqual[c, 2.7e-106], And[N[Not[LessEqual[c, 2.1e-79]], $MachinePrecision], LessEqual[c, 3.7e+79]]]]]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.00000000000000001e55 or -6.19999999999999941e23 < c < -4.00000000000000002e-41 or 2.70000000000000022e-106 < c < 2.0999999999999999e-79 or 3.70000000000000009e79 < 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. Add Preprocessing

   3. Taylor expanded in i around inf 78.8%

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

   if -1.00000000000000001e55 < c < -6.19999999999999941e23 or -4.00000000000000002e-41 < c < 2.70000000000000022e-106 or 2.0999999999999999e-79 < c < 3.70000000000000009e79

   1. Initial program 95.4%

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

   3. Taylor expanded in c around 0 79.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+55} \lor \neg \left(c \leq -6.2 \cdot 10^{+23} \lor \neg \left(c \leq -4 \cdot 10^{-41}\right) \land \left(c \leq 2.7 \cdot 10^{-106} \lor \neg \left(c \leq 2.1 \cdot 10^{-79}\right) \land c \leq 3.7 \cdot 10^{+79}\right)\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* y x) (* z t))))
   (if (<= (- t_2 (* i (* c t_1))) INFINITY)
     (* 2.0 (- t_2 (* (* c i) t_1)))
     (* 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 = (y * x) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	} 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 = (y * x) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	} 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 = (y * x) + (z * t)
	tmp = 0
	if (t_2 - (i * (c * t_1))) <= math.inf:
		tmp = 2.0 * (t_2 - ((c * i) * t_1))
	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(y * x) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(i * Float64(c * t_1))) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(Float64(c * i) * t_1)));
	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 = (y * x) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - ((c * i) * t_1));
	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[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(N[(c * i), $MachinePrecision] * t$95$1), $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 92.7%

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

      1. fma-define 92.7%

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

      2. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

      1. fma-define 98.7%

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

      2. +-commutative 98.7%

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

   6. Applied egg-rr 98.7%

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

   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 i around inf 67.3%

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

4. Final simplification 97.6%

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

Alternative 6: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-125}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + \frac{y \cdot x}{t}\right)\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* y x) (* c (* a i))))))
   (if (<= (* z t) -1e+181)
     (* 2.0 (* z t))
     (if (<= (* z t) -5e+133)
       t_1
       (if (<= (* z t) -1e-125)
         (* 2.0 (* t (+ z (/ (* y x) t))))
         (if (<= (* z t) 2e-20) t_1 (* 2.0 (+ (* y x) (* z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((y * x) - (c * (a * i)));
	double tmp;
	if ((z * t) <= -1e+181) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= -5e+133) {
		tmp = t_1;
	} else if ((z * t) <= -1e-125) {
		tmp = 2.0 * (t * (z + ((y * x) / t)));
	} else if ((z * t) <= 2e-20) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((y * x) + (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 = 2.0d0 * ((y * x) - (c * (a * i)))
    if ((z * t) <= (-1d+181)) then
        tmp = 2.0d0 * (z * t)
    else if ((z * t) <= (-5d+133)) then
        tmp = t_1
    else if ((z * t) <= (-1d-125)) then
        tmp = 2.0d0 * (t * (z + ((y * x) / t)))
    else if ((z * t) <= 2d-20) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((y * x) + (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 = 2.0 * ((y * x) - (c * (a * i)));
	double tmp;
	if ((z * t) <= -1e+181) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= -5e+133) {
		tmp = t_1;
	} else if ((z * t) <= -1e-125) {
		tmp = 2.0 * (t * (z + ((y * x) / t)));
	} else if ((z * t) <= 2e-20) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((y * x) - (c * (a * i)))
	tmp = 0
	if (z * t) <= -1e+181:
		tmp = 2.0 * (z * t)
	elif (z * t) <= -5e+133:
		tmp = t_1
	elif (z * t) <= -1e-125:
		tmp = 2.0 * (t * (z + ((y * x) / t)))
	elif (z * t) <= 2e-20:
		tmp = t_1
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(y * x) - Float64(c * Float64(a * i))))
	tmp = 0.0
	if (Float64(z * t) <= -1e+181)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(z * t) <= -5e+133)
		tmp = t_1;
	elseif (Float64(z * t) <= -1e-125)
		tmp = Float64(2.0 * Float64(t * Float64(z + Float64(Float64(y * x) / t))));
	elseif (Float64(z * t) <= 2e-20)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((y * x) - (c * (a * i)));
	tmp = 0.0;
	if ((z * t) <= -1e+181)
		tmp = 2.0 * (z * t);
	elseif ((z * t) <= -5e+133)
		tmp = t_1;
	elseif ((z * t) <= -1e-125)
		tmp = 2.0 * (t * (z + ((y * x) / t)));
	elseif ((z * t) <= 2e-20)
		tmp = t_1;
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+181], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e+133], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -1e-125], N[(2.0 * N[(t * N[(z + N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-20], t$95$1, N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -9.9999999999999992e180

   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 z around inf 77.5%

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

   if -9.9999999999999992e180 < (*.f64 z t) < -4.99999999999999961e133 or -1.00000000000000001e-125 < (*.f64 z t) < 1.99999999999999989e-20

   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 a around inf 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around 0 71.3%

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

      1. associate-*r* 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-*r* 67.0%

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

   8. Simplified 67.0%

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

   if -4.99999999999999961e133 < (*.f64 z t) < -1.00000000000000001e-125

   1. Initial program 93.3%

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

   3. Taylor expanded in c around 0 53.5%

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

   4. Taylor expanded in t around inf 58.1%

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

   if 1.99999999999999989e-20 < (*.f64 z t)

   1. Initial program 84.1%

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

   3. Taylor expanded in c around 0 70.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+133}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-125}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + \frac{y \cdot x}{t}\right)\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-20}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1.65 \cdot 10^{+38} \lor \neg \left(y \cdot x \leq 10^{+61} \lor \neg \left(y \cdot x \leq 6.2 \cdot 10^{+125}\right) \land y \cdot x \leq 8 \cdot 10^{+246}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* y x) -1.65e+38)
         (not
          (or (<= (* y x) 1e+61)
              (and (not (<= (* y x) 6.2e+125)) (<= (* y x) 8e+246)))))
   (* 2.0 (* y x))
   (* 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 (((y * x) <= -1.65e+38) || !(((y * x) <= 1e+61) || (!((y * x) <= 6.2e+125) && ((y * x) <= 8e+246)))) {
		tmp = 2.0 * (y * x);
	} 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 (((y * x) <= (-1.65d+38)) .or. (.not. ((y * x) <= 1d+61) .or. (.not. ((y * x) <= 6.2d+125)) .and. ((y * x) <= 8d+246))) then
        tmp = 2.0d0 * (y * x)
    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 (((y * x) <= -1.65e+38) || !(((y * x) <= 1e+61) || (!((y * x) <= 6.2e+125) && ((y * x) <= 8e+246)))) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((y * x) <= -1.65e+38) or not (((y * x) <= 1e+61) or (not ((y * x) <= 6.2e+125) and ((y * x) <= 8e+246))):
		tmp = 2.0 * (y * x)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(y * x) <= -1.65e+38) || !((Float64(y * x) <= 1e+61) || (!(Float64(y * x) <= 6.2e+125) && (Float64(y * x) <= 8e+246))))
		tmp = Float64(2.0 * Float64(y * x));
	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 (((y * x) <= -1.65e+38) || ~((((y * x) <= 1e+61) || (~(((y * x) <= 6.2e+125)) && ((y * x) <= 8e+246)))))
		tmp = 2.0 * (y * x);
	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[(y * x), $MachinePrecision], -1.65e+38], N[Not[Or[LessEqual[N[(y * x), $MachinePrecision], 1e+61], And[N[Not[LessEqual[N[(y * x), $MachinePrecision], 6.2e+125]], $MachinePrecision], LessEqual[N[(y * x), $MachinePrecision], 8e+246]]]], $MachinePrecision]], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.65e38 or 9.99999999999999949e60 < (*.f64 x y) < 6.2e125 or 8.00000000000000055e246 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 59.9%

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

   if -1.65e38 < (*.f64 x y) < 9.99999999999999949e60 or 6.2e125 < (*.f64 x y) < 8.00000000000000055e246

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 42.6%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1.65 \cdot 10^{+38} \lor \neg \left(y \cdot x \leq 10^{+61} \lor \neg \left(y \cdot x \leq 6.2 \cdot 10^{+125}\right) \land y \cdot x \leq 8 \cdot 10^{+246}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-106}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-27} \lor \neg \left(c \leq 1.5 \cdot 10^{+145}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* y x) (* c (* c (* b i)))))))
   (if (<= c -2e+54)
     t_1
     (if (<= c 2.7e-106)
       (* 2.0 (+ (* y x) (* z t)))
       (if (or (<= c 1.7e-27) (not (<= c 1.5e+145)))
         (* 2.0 (* c (* (+ a (* b c)) (- 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 * ((y * x) - (c * (c * (b * i))));
	double tmp;
	if (c <= -2e+54) {
		tmp = t_1;
	} else if (c <= 2.7e-106) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if ((c <= 1.7e-27) || !(c <= 1.5e+145)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -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 * ((y * x) - (c * (c * (b * i))))
    if (c <= (-2d+54)) then
        tmp = t_1
    else if (c <= 2.7d-106) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if ((c <= 1.7d-27) .or. (.not. (c <= 1.5d+145))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -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 * ((y * x) - (c * (c * (b * i))));
	double tmp;
	if (c <= -2e+54) {
		tmp = t_1;
	} else if (c <= 2.7e-106) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if ((c <= 1.7e-27) || !(c <= 1.5e+145)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((y * x) - (c * (c * (b * i))))
	tmp = 0
	if c <= -2e+54:
		tmp = t_1
	elif c <= 2.7e-106:
		tmp = 2.0 * ((y * x) + (z * t))
	elif (c <= 1.7e-27) or not (c <= 1.5e+145):
		tmp = 2.0 * (c * ((a + (b * c)) * -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(y * x) - Float64(c * Float64(c * Float64(b * i)))))
	tmp = 0.0
	if (c <= -2e+54)
		tmp = t_1;
	elseif (c <= 2.7e-106)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif ((c <= 1.7e-27) || !(c <= 1.5e+145))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-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 * ((y * x) - (c * (c * (b * i))));
	tmp = 0.0;
	if (c <= -2e+54)
		tmp = t_1;
	elseif (c <= 2.7e-106)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif ((c <= 1.7e-27) || ~((c <= 1.5e+145)))
		tmp = 2.0 * (c * ((a + (b * c)) * -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[(y * x), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+54], t$95$1, If[LessEqual[c, 2.7e-106], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 1.7e-27], N[Not[LessEqual[c, 1.5e+145]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.0000000000000002e54 or 1.69999999999999985e-27 < c < 1.5000000000000001e145

   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. Add Preprocessing

   3. Taylor expanded in z around 0 83.3%

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

   4. Taylor expanded in a around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*r* 76.4%

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

   6. Simplified 76.4%

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

   if -2.0000000000000002e54 < c < 2.70000000000000022e-106

   1. Initial program 97.1%

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

   3. Taylor expanded in c around 0 80.7%

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

   if 2.70000000000000022e-106 < c < 1.69999999999999985e-27 or 1.5000000000000001e145 < c

   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 i around inf 77.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-106}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-27} \lor \neg \left(c \leq 1.5 \cdot 10^{+145}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-106}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-28} \lor \neg \left(c \leq 8.6 \cdot 10^{+144}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* y x) (* c (* b (* c i)))))))
   (if (<= c -1.5e+55)
     t_1
     (if (<= c 2.7e-106)
       (* 2.0 (+ (* y x) (* z t)))
       (if (or (<= c 5.6e-28) (not (<= c 8.6e+144)))
         (* 2.0 (* c (* (+ a (* b c)) (- 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 * ((y * x) - (c * (b * (c * i))));
	double tmp;
	if (c <= -1.5e+55) {
		tmp = t_1;
	} else if (c <= 2.7e-106) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if ((c <= 5.6e-28) || !(c <= 8.6e+144)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -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 * ((y * x) - (c * (b * (c * i))))
    if (c <= (-1.5d+55)) then
        tmp = t_1
    else if (c <= 2.7d-106) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if ((c <= 5.6d-28) .or. (.not. (c <= 8.6d+144))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -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 * ((y * x) - (c * (b * (c * i))));
	double tmp;
	if (c <= -1.5e+55) {
		tmp = t_1;
	} else if (c <= 2.7e-106) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if ((c <= 5.6e-28) || !(c <= 8.6e+144)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((y * x) - (c * (b * (c * i))))
	tmp = 0
	if c <= -1.5e+55:
		tmp = t_1
	elif c <= 2.7e-106:
		tmp = 2.0 * ((y * x) + (z * t))
	elif (c <= 5.6e-28) or not (c <= 8.6e+144):
		tmp = 2.0 * (c * ((a + (b * c)) * -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(y * x) - Float64(c * Float64(b * Float64(c * i)))))
	tmp = 0.0
	if (c <= -1.5e+55)
		tmp = t_1;
	elseif (c <= 2.7e-106)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif ((c <= 5.6e-28) || !(c <= 8.6e+144))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-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 * ((y * x) - (c * (b * (c * i))));
	tmp = 0.0;
	if (c <= -1.5e+55)
		tmp = t_1;
	elseif (c <= 2.7e-106)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif ((c <= 5.6e-28) || ~((c <= 8.6e+144)))
		tmp = 2.0 * (c * ((a + (b * c)) * -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[(y * x), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+55], t$95$1, If[LessEqual[c, 2.7e-106], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 5.6e-28], N[Not[LessEqual[c, 8.6e+144]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.50000000000000008e55 or 5.5999999999999996e-28 < c < 8.59999999999999968e144

   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. Add Preprocessing

   3. Taylor expanded in z around 0 83.3%

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

   4. Taylor expanded in a around 0 75.4%

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

   if -1.50000000000000008e55 < c < 2.70000000000000022e-106

   1. Initial program 97.1%

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

   3. Taylor expanded in c around 0 80.7%

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

   if 2.70000000000000022e-106 < c < 5.5999999999999996e-28 or 8.59999999999999968e144 < c

   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 i around inf 77.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-106}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-28} \lor \neg \left(c \leq 8.6 \cdot 10^{+144}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-114} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -5e-114) (not (<= (* z t) 2e-20)))
   (* 2.0 (- (+ (* y x) (* z t)) (* c (* b (* c i)))))
   (* 2.0 (- (* y x) (* c (* i (+ a (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -5e-114) || !((z * t) <= 2e-20)) {
		tmp = 2.0 * (((y * x) + (z * t)) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((y * x) - (c * (i * (a + (b * c)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((z * t) <= (-5d-114)) .or. (.not. ((z * t) <= 2d-20))) then
        tmp = 2.0d0 * (((y * x) + (z * t)) - (c * (b * (c * i))))
    else
        tmp = 2.0d0 * ((y * x) - (c * (i * (a + (b * c)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -5e-114) || !((z * t) <= 2e-20)) {
		tmp = 2.0 * (((y * x) + (z * t)) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((y * x) - (c * (i * (a + (b * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -5e-114) or not ((z * t) <= 2e-20):
		tmp = 2.0 * (((y * x) + (z * t)) - (c * (b * (c * i))))
	else:
		tmp = 2.0 * ((y * x) - (c * (i * (a + (b * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -5e-114) || !(Float64(z * t) <= 2e-20))
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + Float64(z * t)) - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(c * Float64(i * Float64(a + Float64(b * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((z * t) <= -5e-114) || ~(((z * t) <= 2e-20)))
		tmp = 2.0 * (((y * x) + (z * t)) - (c * (b * (c * i))));
	else
		tmp = 2.0 * ((y * x) - (c * (i * (a + (b * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-114], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(2.0 * N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999989e-114 or 1.99999999999999989e-20 < (*.f64 z t)

   1. Initial program 87.1%

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

   3. Taylor expanded in c around 0 89.8%

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

   4. Taylor expanded in a around 0 87.9%

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

   if -4.99999999999999989e-114 < (*.f64 z t) < 1.99999999999999989e-20

   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. Add Preprocessing

   3. Taylor expanded in z around 0 93.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-114} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (+ a (* b c))))))
   (if (<= (* z t) -1e+59)
     (* 2.0 (- (* z t) t_1))
     (if (<= (* z t) 5e+121)
       (* 2.0 (- (* y x) t_1))
       (* 2.0 (+ (* y x) (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * (a + (b * c)));
	double tmp;
	if ((z * t) <= -1e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((z * t) <= 5e+121) {
		tmp = 2.0 * ((y * x) - t_1);
	} else {
		tmp = 2.0 * ((y * x) + (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 = c * (i * (a + (b * c)))
    if ((z * t) <= (-1d+59)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if ((z * t) <= 5d+121) then
        tmp = 2.0d0 * ((y * x) - t_1)
    else
        tmp = 2.0d0 * ((y * x) + (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 = c * (i * (a + (b * c)));
	double tmp;
	if ((z * t) <= -1e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((z * t) <= 5e+121) {
		tmp = 2.0 * ((y * x) - t_1);
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * (a + (b * c)))
	tmp = 0
	if (z * t) <= -1e+59:
		tmp = 2.0 * ((z * t) - t_1)
	elif (z * t) <= 5e+121:
		tmp = 2.0 * ((y * x) - t_1)
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(a + Float64(b * c))))
	tmp = 0.0
	if (Float64(z * t) <= -1e+59)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (Float64(z * t) <= 5e+121)
		tmp = Float64(2.0 * Float64(Float64(y * x) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * (a + (b * c)));
	tmp = 0.0;
	if ((z * t) <= -1e+59)
		tmp = 2.0 * ((z * t) - t_1);
	elseif ((z * t) <= 5e+121)
		tmp = 2.0 * ((y * x) - t_1);
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+59], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+121], N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.99999999999999972e58

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 86.1%

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

   if -9.99999999999999972e58 < (*.f64 z t) < 5.00000000000000007e121

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 85.2%

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

   if 5.00000000000000007e121 < (*.f64 z t)

   1. Initial program 81.6%

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

   3. Taylor expanded in c around 0 81.5%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-164}:\\ \;\;\;\;\left(c \cdot a\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* y x))) (t_2 (* 2.0 (* z t))))
   (if (<= t -8.5e-19)
     t_2
     (if (<= t -6.8e-185)
       t_1
       (if (<= t 1.65e-164)
         (* (* c a) (* i -2.0))
         (if (<= t 2.5e+23) 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 * (y * x);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -8.5e-19) {
		tmp = t_2;
	} else if (t <= -6.8e-185) {
		tmp = t_1;
	} else if (t <= 1.65e-164) {
		tmp = (c * a) * (i * -2.0);
	} else if (t <= 2.5e+23) {
		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 * (y * x)
    t_2 = 2.0d0 * (z * t)
    if (t <= (-8.5d-19)) then
        tmp = t_2
    else if (t <= (-6.8d-185)) then
        tmp = t_1
    else if (t <= 1.65d-164) then
        tmp = (c * a) * (i * (-2.0d0))
    else if (t <= 2.5d+23) 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 * (y * x);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -8.5e-19) {
		tmp = t_2;
	} else if (t <= -6.8e-185) {
		tmp = t_1;
	} else if (t <= 1.65e-164) {
		tmp = (c * a) * (i * -2.0);
	} else if (t <= 2.5e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (y * x)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -8.5e-19:
		tmp = t_2
	elif t <= -6.8e-185:
		tmp = t_1
	elif t <= 1.65e-164:
		tmp = (c * a) * (i * -2.0)
	elif t <= 2.5e+23:
		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(y * x))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -8.5e-19)
		tmp = t_2;
	elseif (t <= -6.8e-185)
		tmp = t_1;
	elseif (t <= 1.65e-164)
		tmp = Float64(Float64(c * a) * Float64(i * -2.0));
	elseif (t <= 2.5e+23)
		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 * (y * x);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -8.5e-19)
		tmp = t_2;
	elseif (t <= -6.8e-185)
		tmp = t_1;
	elseif (t <= 1.65e-164)
		tmp = (c * a) * (i * -2.0);
	elseif (t <= 2.5e+23)
		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[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e-19], t$95$2, If[LessEqual[t, -6.8e-185], t$95$1, If[LessEqual[t, 1.65e-164], N[(N[(c * a), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000003e-19 or 2.5e23 < t

   1. Initial program 88.6%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -8.50000000000000003e-19 < t < -6.7999999999999996e-185 or 1.65e-164 < t < 2.5e23

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf 38.9%

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

   if -6.7999999999999996e-185 < t < 1.65e-164

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 36.8%

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

      1. mul-1-neg 36.8%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in a around 0 36.8%

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

      1. *-commutative 36.8%

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

      2. associate-*r* 34.8%

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

      3. associate-*l* 34.8%

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

      4. *-commutative 34.8%

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

   8. Simplified 34.8%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-185}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-164}:\\ \;\;\;\;\left(c \cdot a\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-164}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* y x))) (t_2 (* 2.0 (* z t))))
   (if (<= t -9.5e-24)
     t_2
     (if (<= t -3.25e-186)
       t_1
       (if (<= t 4.8e-164)
         (* (* c i) (* a -2.0))
         (if (<= t 9e+22) 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 * (y * x);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.5e-24) {
		tmp = t_2;
	} else if (t <= -3.25e-186) {
		tmp = t_1;
	} else if (t <= 4.8e-164) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 9e+22) {
		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 * (y * x)
    t_2 = 2.0d0 * (z * t)
    if (t <= (-9.5d-24)) then
        tmp = t_2
    else if (t <= (-3.25d-186)) then
        tmp = t_1
    else if (t <= 4.8d-164) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (t <= 9d+22) 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 * (y * x);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.5e-24) {
		tmp = t_2;
	} else if (t <= -3.25e-186) {
		tmp = t_1;
	} else if (t <= 4.8e-164) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 9e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (y * x)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -9.5e-24:
		tmp = t_2
	elif t <= -3.25e-186:
		tmp = t_1
	elif t <= 4.8e-164:
		tmp = (c * i) * (a * -2.0)
	elif t <= 9e+22:
		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(y * x))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -9.5e-24)
		tmp = t_2;
	elseif (t <= -3.25e-186)
		tmp = t_1;
	elseif (t <= 4.8e-164)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (t <= 9e+22)
		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 * (y * x);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -9.5e-24)
		tmp = t_2;
	elseif (t <= -3.25e-186)
		tmp = t_1;
	elseif (t <= 4.8e-164)
		tmp = (c * i) * (a * -2.0);
	elseif (t <= 9e+22)
		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[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-24], t$95$2, If[LessEqual[t, -3.25e-186], t$95$1, If[LessEqual[t, 4.8e-164], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000029e-24 or 8.9999999999999996e22 < t

   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 z around inf 49.7%

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

   if -9.50000000000000029e-24 < t < -3.24999999999999981e-186 or 4.79999999999999966e-164 < t < 8.9999999999999996e22

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf 39.4%

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

   if -3.24999999999999981e-186 < t < 4.79999999999999966e-164

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 36.8%

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

      1. mul-1-neg 36.8%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in a around 0 36.8%

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

      1. associate-*r* 36.8%

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

   8. Simplified 36.8%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-186}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-164}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-69} \lor \neg \left(c \leq 8.6 \cdot 10^{-107}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.1e-69) (not (<= c 8.6e-107)))
   (* 2.0 (- (* z t) (* c (* i (+ a (* b c))))))
   (* 2.0 (+ (* y x) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.1e-69) || !(c <= 8.6e-107)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.1d-69)) .or. (.not. (c <= 8.6d-107))) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (b * c)))))
    else
        tmp = 2.0d0 * ((y * x) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.1e-69) || !(c <= 8.6e-107)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.1e-69) or not (c <= 8.6e-107):
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))))
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.1e-69) || !(c <= 8.6e-107))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(b * c))))));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.1e-69) || ~((c <= 8.6e-107)))
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.1e-69], N[Not[LessEqual[c, 8.6e-107]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.1e-69 or 8.5999999999999995e-107 < c

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 81.8%

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

   if -1.1e-69 < c < 8.5999999999999995e-107

   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. Add Preprocessing

   3. Taylor expanded in c around 0 86.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-69} \lor \neg \left(c \leq 8.6 \cdot 10^{-107}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (+ a (* b c))))))
   (if (<= c -1e-68)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 7.5e-66)
       (* 2.0 (- (+ (* y x) (* z t)) (* i (* c a))))
       (* 2.0 (- (* y x) 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 * (i * (a + (b * c)));
	double tmp;
	if (c <= -1e-68) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7.5e-66) {
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((y * x) - 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 * (i * (a + (b * c)))
    if (c <= (-1d-68)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 7.5d-66) then
        tmp = 2.0d0 * (((y * x) + (z * t)) - (i * (c * a)))
    else
        tmp = 2.0d0 * ((y * x) - 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 * (i * (a + (b * c)));
	double tmp;
	if (c <= -1e-68) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7.5e-66) {
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((y * x) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * (a + (b * c)))
	tmp = 0
	if c <= -1e-68:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 7.5e-66:
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)))
	else:
		tmp = 2.0 * ((y * x) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(a + Float64(b * c))))
	tmp = 0.0
	if (c <= -1e-68)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 7.5e-66)
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + Float64(z * t)) - Float64(i * Float64(c * a))));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * (a + (b * c)));
	tmp = 0.0;
	if (c <= -1e-68)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 7.5e-66)
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)));
	else
		tmp = 2.0 * ((y * x) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e-68], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e-66], N[(2.0 * N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.00000000000000007e-68

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 86.5%

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

   if -1.00000000000000007e-68 < c < 7.49999999999999995e-66

   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 a around inf 94.9%

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

      1. *-commutative 94.9%

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

   5. Simplified 94.9%

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

   if 7.49999999999999995e-66 < c

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 83.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-182} \lor \neg \left(t \leq 2.1 \cdot 10^{-23}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -5e-182) (not (<= t 2.1e-23)))
   (* 2.0 (+ (* y x) (* z t)))
   (* 2.0 (- (* y x) (* i (* c a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -5e-182) || !(t <= 2.1e-23)) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-5d-182)) .or. (.not. (t <= 2.1d-23))) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else
        tmp = 2.0d0 * ((y * x) - (i * (c * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -5e-182) || !(t <= 2.1e-23)) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -5e-182) or not (t <= 2.1e-23):
		tmp = 2.0 * ((y * x) + (z * t))
	else:
		tmp = 2.0 * ((y * x) - (i * (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -5e-182) || !(t <= 2.1e-23))
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(i * Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -5e-182) || ~((t <= 2.1e-23)))
		tmp = 2.0 * ((y * x) + (z * t));
	else
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -5e-182], N[Not[LessEqual[t, 2.1e-23]], $MachinePrecision]], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000024e-182 or 2.1000000000000001e-23 < t

   1. Initial program 87.9%

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

   3. Taylor expanded in c around 0 57.3%

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

   if -5.00000000000000024e-182 < t < 2.1000000000000001e-23

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around 0 72.7%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in x around 0 72.7%

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

       1. associate-*r* 68.3%

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

       2. *-commutative 68.3%

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

       3. *-commutative 68.3%

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

   11. Simplified 68.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-182} \lor \neg \left(t \leq 2.1 \cdot 10^{-23}\right):\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+163}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -4.2e+163) (* (* c i) (* a -2.0)) (* 2.0 (+ (* y x) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -4.2e+163) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((y * x) + (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 (a <= (-4.2d+163)) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = 2.0d0 * ((y * x) + (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 (a <= -4.2e+163) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -4.2e+163:
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -4.2e+163)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -4.2e+163)
		tmp = (c * i) * (a * -2.0);
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -4.2e+163], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2000000000000001e163

   1. Initial program 90.1%

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

   3. Taylor expanded in a around inf 57.5%

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

      1. mul-1-neg 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in a around 0 57.5%

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

      1. associate-*r* 57.5%

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

   8. Simplified 57.5%

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

   if -4.2000000000000001e163 < a

   1. Initial program 89.4%

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

   3. Taylor expanded in c around 0 58.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+163}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% 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 89.5%

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

3. Taylor expanded in z around inf 31.3%

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

4. Final simplification 31.3%

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

Developer target: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024086 
(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))))