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

Percentage Accurate: 90.3% → 94.2%

Time: 17.8s

Alternatives: 16

Speedup: 0.5×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t_1\right)\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+250}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+250)))
     (* -2.0 (* c (* t_1 i)))
     (* 2.0 (- (+ (* x y) (* z t)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+250)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+250)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	}
	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) or not (t_2 <= 5e+250):
		tmp = -2.0 * (c * (t_1 * i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+250))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+250)))
		tmp = -2.0 * (c * (t_1 * i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+250]], $MachinePrecision]], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5.0000000000000002e250 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 90.8%

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

   4. Taylor expanded in t around 0 93.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000002e250

   1. Initial program 97.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty \lor \neg \left(i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 5 \cdot 10^{+250}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.1%

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

   1. fma-def 92.3%

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

   2. associate-*l* 94.7%

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

3. Simplified 94.7%

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

5. Final simplification 94.7%

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

Alternative 3: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -3.75 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-274}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* c (* b (* c i)))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -3.75e+49)
     t_2
     (if (<= c -5.3e-17)
       (* (* c i) (* a -2.0))
       (if (<= c -3.3e-59)
         t_2
         (if (<= c -2.95e-229)
           t_3
           (if (<= c 9.5e-302)
             t_1
             (if (<= c 8.8e-274) t_3 (if (<= c 1.6e+26) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * (b * (c * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -3.75e+49) {
		tmp = t_2;
	} else if (c <= -5.3e-17) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= -3.3e-59) {
		tmp = t_2;
	} else if (c <= -2.95e-229) {
		tmp = t_3;
	} else if (c <= 9.5e-302) {
		tmp = t_1;
	} else if (c <= 8.8e-274) {
		tmp = t_3;
	} else if (c <= 1.6e+26) {
		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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (c * (b * (c * i)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-3.75d+49)) then
        tmp = t_2
    else if (c <= (-5.3d-17)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= (-3.3d-59)) then
        tmp = t_2
    else if (c <= (-2.95d-229)) then
        tmp = t_3
    else if (c <= 9.5d-302) then
        tmp = t_1
    else if (c <= 8.8d-274) then
        tmp = t_3
    else if (c <= 1.6d+26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * (b * (c * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -3.75e+49) {
		tmp = t_2;
	} else if (c <= -5.3e-17) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= -3.3e-59) {
		tmp = t_2;
	} else if (c <= -2.95e-229) {
		tmp = t_3;
	} else if (c <= 9.5e-302) {
		tmp = t_1;
	} else if (c <= 8.8e-274) {
		tmp = t_3;
	} else if (c <= 1.6e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (c * (b * (c * i)))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -3.75e+49:
		tmp = t_2
	elif c <= -5.3e-17:
		tmp = (c * i) * (a * -2.0)
	elif c <= -3.3e-59:
		tmp = t_2
	elif c <= -2.95e-229:
		tmp = t_3
	elif c <= 9.5e-302:
		tmp = t_1
	elif c <= 8.8e-274:
		tmp = t_3
	elif c <= 1.6e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -3.75e+49)
		tmp = t_2;
	elseif (c <= -5.3e-17)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= -3.3e-59)
		tmp = t_2;
	elseif (c <= -2.95e-229)
		tmp = t_3;
	elseif (c <= 9.5e-302)
		tmp = t_1;
	elseif (c <= 8.8e-274)
		tmp = t_3;
	elseif (c <= 1.6e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (c * (b * (c * i)));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -3.75e+49)
		tmp = t_2;
	elseif (c <= -5.3e-17)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= -3.3e-59)
		tmp = t_2;
	elseif (c <= -2.95e-229)
		tmp = t_3;
	elseif (c <= 9.5e-302)
		tmp = t_1;
	elseif (c <= 8.8e-274)
		tmp = t_3;
	elseif (c <= 1.6e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.75e+49], t$95$2, If[LessEqual[c, -5.3e-17], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e-59], t$95$2, If[LessEqual[c, -2.95e-229], t$95$3, If[LessEqual[c, 9.5e-302], t$95$1, If[LessEqual[c, 8.8e-274], t$95$3, If[LessEqual[c, 1.6e+26], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.7499999999999998e49 or -5.2999999999999998e-17 < c < -3.29999999999999982e-59 or 1.60000000000000014e26 < c

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in t around 0 80.9%

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

   5. Taylor expanded in a around 0 68.0%

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

   if -3.7499999999999998e49 < c < -5.2999999999999998e-17

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf 81.5%

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

      1. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in x around 0 75.1%

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

   7. Taylor expanded in t around 0 51.0%

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

      1. associate-*r* 51.0%

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

      2. *-commutative 51.0%

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

      3. *-commutative 51.0%

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

   9. Simplified 51.0%

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

   if -3.29999999999999982e-59 < c < -2.9500000000000002e-229 or 9.49999999999999991e-302 < c < 8.7999999999999998e-274

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 53.6%

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

   if -2.9500000000000002e-229 < c < 9.49999999999999991e-302 or 8.7999999999999998e-274 < c < 1.60000000000000014e26

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 52.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.75 \cdot 10^{+49}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-59}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-274}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_3 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -0.0001:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* 2.0 (- (* z t) (* a (* c i)))))
        (t_3 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -1.8e+71)
     t_3
     (if (<= c -0.0001)
       t_2
       (if (<= c -4.2e-61)
         t_3
         (if (<= c 4.5e-30)
           t_1
           (if (<= c 7.4e+52) t_2 (if (<= c 2.1e+91) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.8e+71) {
		tmp = t_3;
	} else if (c <= -0.0001) {
		tmp = t_2;
	} else if (c <= -4.2e-61) {
		tmp = t_3;
	} else if (c <= 4.5e-30) {
		tmp = t_1;
	} else if (c <= 7.4e+52) {
		tmp = t_2;
	} else if (c <= 2.1e+91) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = 2.0d0 * ((z * t) - (a * (c * i)))
    t_3 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-1.8d+71)) then
        tmp = t_3
    else if (c <= (-0.0001d0)) then
        tmp = t_2
    else if (c <= (-4.2d-61)) then
        tmp = t_3
    else if (c <= 4.5d-30) then
        tmp = t_1
    else if (c <= 7.4d+52) then
        tmp = t_2
    else if (c <= 2.1d+91) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.8e+71) {
		tmp = t_3;
	} else if (c <= -0.0001) {
		tmp = t_2;
	} else if (c <= -4.2e-61) {
		tmp = t_3;
	} else if (c <= 4.5e-30) {
		tmp = t_1;
	} else if (c <= 7.4e+52) {
		tmp = t_2;
	} else if (c <= 2.1e+91) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = 2.0 * ((z * t) - (a * (c * i)))
	t_3 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.8e+71:
		tmp = t_3
	elif c <= -0.0001:
		tmp = t_2
	elif c <= -4.2e-61:
		tmp = t_3
	elif c <= 4.5e-30:
		tmp = t_1
	elif c <= 7.4e+52:
		tmp = t_2
	elif c <= 2.1e+91:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))))
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.8e+71)
		tmp = t_3;
	elseif (c <= -0.0001)
		tmp = t_2;
	elseif (c <= -4.2e-61)
		tmp = t_3;
	elseif (c <= 4.5e-30)
		tmp = t_1;
	elseif (c <= 7.4e+52)
		tmp = t_2;
	elseif (c <= 2.1e+91)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = 2.0 * ((z * t) - (a * (c * i)));
	t_3 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.8e+71)
		tmp = t_3;
	elseif (c <= -0.0001)
		tmp = t_2;
	elseif (c <= -4.2e-61)
		tmp = t_3;
	elseif (c <= 4.5e-30)
		tmp = t_1;
	elseif (c <= 7.4e+52)
		tmp = t_2;
	elseif (c <= 2.1e+91)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+71], t$95$3, If[LessEqual[c, -0.0001], t$95$2, If[LessEqual[c, -4.2e-61], t$95$3, If[LessEqual[c, 4.5e-30], t$95$1, If[LessEqual[c, 7.4e+52], t$95$2, If[LessEqual[c, 2.1e+91], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.8e71 or -1.00000000000000005e-4 < c < -4.1999999999999998e-61 or 2.10000000000000008e91 < c

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in t around 0 88.0%

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

   if -1.8e71 < c < -1.00000000000000005e-4 or 4.49999999999999967e-30 < c < 7.3999999999999999e52

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 83.1%

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

      1. *-commutative 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in x around 0 73.2%

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

   if -4.1999999999999998e-61 < c < 4.49999999999999967e-30 or 7.3999999999999999e52 < c < 2.10000000000000008e91

   1. Initial program 94.7%

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

   3. Taylor expanded in c around 0 79.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -0.0001:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-61}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.06 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -1.06e+72)
     t_2
     (if (<= c -8e-5)
       (* 2.0 (- (* z t) (* a (* c i))))
       (if (<= c -1.6e-58)
         t_2
         (if (<= c 4.2e-26)
           t_1
           (if (<= c 1.45e+85)
             (* 2.0 (- (* z t) (* c (* b (* c i)))))
             (if (<= c 2.2e+91) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.06e+72) {
		tmp = t_2;
	} else if (c <= -8e-5) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -1.6e-58) {
		tmp = t_2;
	} else if (c <= 4.2e-26) {
		tmp = t_1;
	} else if (c <= 1.45e+85) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 2.2e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-1.06d+72)) then
        tmp = t_2
    else if (c <= (-8d-5)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= (-1.6d-58)) then
        tmp = t_2
    else if (c <= 4.2d-26) then
        tmp = t_1
    else if (c <= 1.45d+85) then
        tmp = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    else if (c <= 2.2d+91) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.06e+72) {
		tmp = t_2;
	} else if (c <= -8e-5) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -1.6e-58) {
		tmp = t_2;
	} else if (c <= 4.2e-26) {
		tmp = t_1;
	} else if (c <= 1.45e+85) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 2.2e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.06e+72:
		tmp = t_2
	elif c <= -8e-5:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= -1.6e-58:
		tmp = t_2
	elif c <= 4.2e-26:
		tmp = t_1
	elif c <= 1.45e+85:
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))))
	elif c <= 2.2e+91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.06e+72)
		tmp = t_2;
	elseif (c <= -8e-5)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= -1.6e-58)
		tmp = t_2;
	elseif (c <= 4.2e-26)
		tmp = t_1;
	elseif (c <= 1.45e+85)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 2.2e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.06e+72)
		tmp = t_2;
	elseif (c <= -8e-5)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= -1.6e-58)
		tmp = t_2;
	elseif (c <= 4.2e-26)
		tmp = t_1;
	elseif (c <= 1.45e+85)
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	elseif (c <= 2.2e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.06e+72], t$95$2, If[LessEqual[c, -8e-5], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.6e-58], t$95$2, If[LessEqual[c, 4.2e-26], t$95$1, If[LessEqual[c, 1.45e+85], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+91], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.06e72 or -8.00000000000000065e-5 < c < -1.6e-58 or 2.19999999999999999e91 < c

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in t around 0 88.0%

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

   if -1.06e72 < c < -8.00000000000000065e-5

   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 a around inf 86.3%

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

      1. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around 0 76.9%

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

   if -1.6e-58 < c < 4.20000000000000016e-26 or 1.44999999999999999e85 < c < 2.19999999999999999e91

   1. Initial program 97.2%

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

   3. Taylor expanded in c around 0 80.0%

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

   if 4.20000000000000016e-26 < c < 1.44999999999999999e85

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 77.0%

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

   4. Taylor expanded in a around 0 72.3%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.06 \cdot 10^{+72}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-58}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-26}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	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[(x * y), $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[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.8%

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

      1. fma-def 96.8%

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

      2. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

      1. fma-def 98.1%

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

      2. +-commutative 98.1%

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

   6. Applied egg-rr 98.1%

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

   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 x around 0 47.1%

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

   4. Taylor expanded in t around 0 53.8%

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

4. Final simplification 95.5%

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

Alternative 7: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;-2 \cdot t_1\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-6} \lor \neg \left(c \leq -2.4 \cdot 10^{-65}\right) \land c \leq 7.6 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -3.5e+87)
     (* -2.0 t_1)
     (if (or (<= c -1.6e-6) (and (not (<= c -2.4e-65)) (<= c 7.6e+96)))
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -3.5e+87) {
		tmp = -2.0 * t_1;
	} else if ((c <= -1.6e-6) || (!(c <= -2.4e-65) && (c <= 7.6e+96))) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-3.5d+87)) then
        tmp = (-2.0d0) * t_1
    else if ((c <= (-1.6d-6)) .or. (.not. (c <= (-2.4d-65))) .and. (c <= 7.6d+96)) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -3.5e+87) {
		tmp = -2.0 * t_1;
	} else if ((c <= -1.6e-6) || (!(c <= -2.4e-65) && (c <= 7.6e+96))) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -3.5e+87:
		tmp = -2.0 * t_1
	elif (c <= -1.6e-6) or (not (c <= -2.4e-65) and (c <= 7.6e+96)):
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -3.5e+87)
		tmp = Float64(-2.0 * t_1);
	elseif ((c <= -1.6e-6) || (!(c <= -2.4e-65) && (c <= 7.6e+96)))
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -3.5e+87)
		tmp = -2.0 * t_1;
	elseif ((c <= -1.6e-6) || (~((c <= -2.4e-65)) && (c <= 7.6e+96)))
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+87], N[(-2.0 * t$95$1), $MachinePrecision], If[Or[LessEqual[c, -1.6e-6], And[N[Not[LessEqual[c, -2.4e-65]], $MachinePrecision], LessEqual[c, 7.6e+96]]], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.49999999999999986e87

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in t around 0 94.8%

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

   if -3.49999999999999986e87 < c < -1.5999999999999999e-6 or -2.4000000000000002e-65 < c < 7.6000000000000003e96

   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 88.5%

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

      1. *-commutative 88.5%

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

   5. Simplified 88.5%

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

   if -1.5999999999999999e-6 < c < -2.4000000000000002e-65 or 7.6000000000000003e96 < c

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 91.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-6} \lor \neg \left(c \leq -2.4 \cdot 10^{-65}\right) \land c \leq 7.6 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* (* c i) (* a -2.0)))
        (t_3 (* 2.0 (* z t))))
   (if (<= c -5.5e-51)
     t_2
     (if (<= c -5.2e-230)
       t_1
       (if (<= c 6.2e-303)
         t_3
         (if (<= c 1.3e-274) t_1 (if (<= c 1.2e+132) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (c * i) * (a * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -5.5e-51) {
		tmp = t_2;
	} else if (c <= -5.2e-230) {
		tmp = t_1;
	} else if (c <= 6.2e-303) {
		tmp = t_3;
	} else if (c <= 1.3e-274) {
		tmp = t_1;
	} else if (c <= 1.2e+132) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = (c * i) * (a * (-2.0d0))
    t_3 = 2.0d0 * (z * t)
    if (c <= (-5.5d-51)) then
        tmp = t_2
    else if (c <= (-5.2d-230)) then
        tmp = t_1
    else if (c <= 6.2d-303) then
        tmp = t_3
    else if (c <= 1.3d-274) then
        tmp = t_1
    else if (c <= 1.2d+132) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (c * i) * (a * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -5.5e-51) {
		tmp = t_2;
	} else if (c <= -5.2e-230) {
		tmp = t_1;
	} else if (c <= 6.2e-303) {
		tmp = t_3;
	} else if (c <= 1.3e-274) {
		tmp = t_1;
	} else if (c <= 1.2e+132) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = (c * i) * (a * -2.0)
	t_3 = 2.0 * (z * t)
	tmp = 0
	if c <= -5.5e-51:
		tmp = t_2
	elif c <= -5.2e-230:
		tmp = t_1
	elif c <= 6.2e-303:
		tmp = t_3
	elif c <= 1.3e-274:
		tmp = t_1
	elif c <= 1.2e+132:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -5.5e-51)
		tmp = t_2;
	elseif (c <= -5.2e-230)
		tmp = t_1;
	elseif (c <= 6.2e-303)
		tmp = t_3;
	elseif (c <= 1.3e-274)
		tmp = t_1;
	elseif (c <= 1.2e+132)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = (c * i) * (a * -2.0);
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -5.5e-51)
		tmp = t_2;
	elseif (c <= -5.2e-230)
		tmp = t_1;
	elseif (c <= 6.2e-303)
		tmp = t_3;
	elseif (c <= 1.3e-274)
		tmp = t_1;
	elseif (c <= 1.2e+132)
		tmp = t_3;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e-51], t$95$2, If[LessEqual[c, -5.2e-230], t$95$1, If[LessEqual[c, 6.2e-303], t$95$3, If[LessEqual[c, 1.3e-274], t$95$1, If[LessEqual[c, 1.2e+132], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.4999999999999997e-51 or 1.2000000000000001e132 < c

   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 a around inf 53.9%

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

      1. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in x around 0 48.2%

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

   7. Taylor expanded in t around 0 41.1%

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

      1. associate-*r* 41.1%

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

      2. *-commutative 41.1%

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

      3. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -5.4999999999999997e-51 < c < -5.2000000000000003e-230 or 6.2000000000000002e-303 < c < 1.3e-274

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -5.2000000000000003e-230 < c < 6.2000000000000002e-303 or 1.3e-274 < c < 1.2000000000000001e132

   1. Initial program 90.3%

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

   3. Taylor expanded in z around inf 46.9%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= c -7.5e-48)
     (* (* c i) (* a -2.0))
     (if (<= c -4.8e-231)
       t_1
       (if (<= c 2.25e-302)
         t_2
         (if (<= c 9e-274)
           t_1
           (if (<= c 6e+134) t_2 (* -2.0 (* i (* a c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (c <= -7.5e-48) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= -4.8e-231) {
		tmp = t_1;
	} else if (c <= 2.25e-302) {
		tmp = t_2;
	} else if (c <= 9e-274) {
		tmp = t_1;
	} else if (c <= 6e+134) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (i * (a * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (c <= (-7.5d-48)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= (-4.8d-231)) then
        tmp = t_1
    else if (c <= 2.25d-302) then
        tmp = t_2
    else if (c <= 9d-274) then
        tmp = t_1
    else if (c <= 6d+134) then
        tmp = t_2
    else
        tmp = (-2.0d0) * (i * (a * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (c <= -7.5e-48) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= -4.8e-231) {
		tmp = t_1;
	} else if (c <= 2.25e-302) {
		tmp = t_2;
	} else if (c <= 9e-274) {
		tmp = t_1;
	} else if (c <= 6e+134) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (i * (a * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if c <= -7.5e-48:
		tmp = (c * i) * (a * -2.0)
	elif c <= -4.8e-231:
		tmp = t_1
	elif c <= 2.25e-302:
		tmp = t_2
	elif c <= 9e-274:
		tmp = t_1
	elif c <= 6e+134:
		tmp = t_2
	else:
		tmp = -2.0 * (i * (a * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -7.5e-48)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= -4.8e-231)
		tmp = t_1;
	elseif (c <= 2.25e-302)
		tmp = t_2;
	elseif (c <= 9e-274)
		tmp = t_1;
	elseif (c <= 6e+134)
		tmp = t_2;
	else
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -7.5e-48)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= -4.8e-231)
		tmp = t_1;
	elseif (c <= 2.25e-302)
		tmp = t_2;
	elseif (c <= 9e-274)
		tmp = t_1;
	elseif (c <= 6e+134)
		tmp = t_2;
	else
		tmp = -2.0 * (i * (a * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e-48], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.8e-231], t$95$1, If[LessEqual[c, 2.25e-302], t$95$2, If[LessEqual[c, 9e-274], t$95$1, If[LessEqual[c, 6e+134], t$95$2, N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.50000000000000042e-48

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 59.5%

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

      1. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in x around 0 52.6%

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

   7. Taylor expanded in t around 0 43.1%

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

      1. associate-*r* 43.1%

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

      2. *-commutative 43.1%

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

      3. *-commutative 43.1%

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

   9. Simplified 43.1%

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

   if -7.50000000000000042e-48 < c < -4.79999999999999983e-231 or 2.25000000000000005e-302 < c < 8.99999999999999982e-274

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -4.79999999999999983e-231 < c < 2.25000000000000005e-302 or 8.99999999999999982e-274 < c < 5.99999999999999993e134

   1. Initial program 90.3%

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

   3. Taylor expanded in z around inf 46.9%

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

   if 5.99999999999999993e134 < c

   1. Initial program 89.7%

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

      1. fma-def 89.7%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

      1. fma-def 95.0%

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

      2. +-commutative 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in x around 0 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*r* 92.5%

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

      3. +-commutative 92.5%

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

      4. fma-udef 92.5%

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

      5. cancel-sign-sub-inv 92.5%

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

      6. *-commutative 92.5%

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

      7. +-commutative 92.5%

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

      8. fma-def 92.5%

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

      9. distribute-rgt-neg-in 92.5%

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

      10. *-commutative 92.5%

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

   9. Simplified 92.5%

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

   10. Taylor expanded in a around inf 37.3%

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

       1. *-commutative 37.3%

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

       2. associate-*r* 41.9%

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

   12. Simplified 41.9%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-48}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-302}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-274}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+134}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+87} \lor \neg \left(c \leq -3 \cdot 10^{-7}\right) \land \left(c \leq -3.6 \cdot 10^{-58} \lor \neg \left(c \leq 3.7 \cdot 10^{+28}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.8e+87)
         (and (not (<= c -3e-7)) (or (<= c -3.6e-58) (not (<= c 3.7e+28)))))
   (* -2.0 (* c (* b (* c i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.8e+87) || (!(c <= -3e-7) && ((c <= -3.6e-58) || !(c <= 3.7e+28)))) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.8d+87)) .or. (.not. (c <= (-3d-7))) .and. (c <= (-3.6d-58)) .or. (.not. (c <= 3.7d+28))) then
        tmp = (-2.0d0) * (c * (b * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.8e+87) || (!(c <= -3e-7) && ((c <= -3.6e-58) || !(c <= 3.7e+28)))) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.8e+87) or (not (c <= -3e-7) and ((c <= -3.6e-58) or not (c <= 3.7e+28))):
		tmp = -2.0 * (c * (b * (c * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.8e+87) || (!(c <= -3e-7) && ((c <= -3.6e-58) || !(c <= 3.7e+28))))
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.8e+87) || (~((c <= -3e-7)) && ((c <= -3.6e-58) || ~((c <= 3.7e+28)))))
		tmp = -2.0 * (c * (b * (c * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.8e+87], And[N[Not[LessEqual[c, -3e-7]], $MachinePrecision], Or[LessEqual[c, -3.6e-58], N[Not[LessEqual[c, 3.7e+28]], $MachinePrecision]]]], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.80000000000000011e87 or -2.9999999999999999e-7 < c < -3.60000000000000009e-58 or 3.6999999999999999e28 < c

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 87.1%

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

   4. Taylor expanded in t around 0 85.5%

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

   5. Taylor expanded in a around 0 71.0%

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

   if -3.80000000000000011e87 < c < -2.9999999999999999e-7 or -3.60000000000000009e-58 < c < 3.6999999999999999e28

   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 72.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+87} \lor \neg \left(c \leq -3 \cdot 10^{-7}\right) \land \left(c \leq -3.6 \cdot 10^{-58} \lor \neg \left(c \leq 3.7 \cdot 10^{+28}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+101} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* x y) -2e+101) (not (<= (* x y) 2e+129)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -2e+101) || !((x * y) <= 2e+129)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (((x * y) <= (-2d+101)) .or. (.not. ((x * y) <= 2d+129))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -2e+101) || !((x * y) <= 2e+129)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if ((x * y) <= -2e+101) or not ((x * y) <= 2e+129):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if ((Float64(x * y) <= -2e+101) || !(Float64(x * y) <= 2e+129))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (((x * y) <= -2e+101) || ~(((x * y) <= 2e+129)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+101], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+129]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e101 or 2e129 < (*.f64 x y)

   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 z around 0 79.3%

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

   if -2e101 < (*.f64 x y) < 2e129

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 83.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+101} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{-60} \lor \neg \left(c \leq 1.5 \cdot 10^{-81}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.1e-60) (not (<= c 1.5e-81)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.1e-60) || !(c <= 1.5e-81)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.1d-60)) .or. (.not. (c <= 1.5d-81))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.1e-60) || !(c <= 1.5e-81)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.1e-60) or not (c <= 1.5e-81):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.1e-60) || !(c <= 1.5e-81))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.1e-60) || ~((c <= 1.5e-81)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.1e-60], N[Not[LessEqual[c, 1.5e-81]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.10000000000000013e-60 or 1.4999999999999999e-81 < c

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 84.3%

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

   if -4.10000000000000013e-60 < c < 1.4999999999999999e-81

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0 81.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{-60} \lor \neg \left(c \leq 1.5 \cdot 10^{-81}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -2.8e+85)
     t_1
     (if (<= z -6e-273)
       (* 2.0 (* x y))
       (if (<= z 1.85e-128) (* c (* i (* a -2.0))) 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 * (z * t);
	double tmp;
	if (z <= -2.8e+85) {
		tmp = t_1;
	} else if (z <= -6e-273) {
		tmp = 2.0 * (x * y);
	} else if (z <= 1.85e-128) {
		tmp = c * (i * (a * -2.0));
	} 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 * (z * t)
    if (z <= (-2.8d+85)) then
        tmp = t_1
    else if (z <= (-6d-273)) then
        tmp = 2.0d0 * (x * y)
    else if (z <= 1.85d-128) then
        tmp = c * (i * (a * (-2.0d0)))
    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 * (z * t);
	double tmp;
	if (z <= -2.8e+85) {
		tmp = t_1;
	} else if (z <= -6e-273) {
		tmp = 2.0 * (x * y);
	} else if (z <= 1.85e-128) {
		tmp = c * (i * (a * -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -2.8e+85:
		tmp = t_1
	elif z <= -6e-273:
		tmp = 2.0 * (x * y)
	elif z <= 1.85e-128:
		tmp = c * (i * (a * -2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -2.8e+85)
		tmp = t_1;
	elseif (z <= -6e-273)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (z <= 1.85e-128)
		tmp = Float64(c * Float64(i * Float64(a * -2.0)));
	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 * (z * t);
	tmp = 0.0;
	if (z <= -2.8e+85)
		tmp = t_1;
	elseif (z <= -6e-273)
		tmp = 2.0 * (x * y);
	elseif (z <= 1.85e-128)
		tmp = c * (i * (a * -2.0));
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+85], t$95$1, If[LessEqual[z, -6e-273], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-128], N[(c * N[(i * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e85 or 1.85e-128 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 42.2%

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

   if -2.7999999999999999e85 < z < -5.99999999999999975e-273

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 32.0%

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

   if -5.99999999999999975e-273 < z < 1.85e-128

   1. Initial program 91.7%

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

      1. fma-def 91.7%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

      1. fma-def 97.2%

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

      2. +-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in x around 0 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*r* 75.9%

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

      3. +-commutative 75.9%

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

      4. fma-udef 75.9%

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

      5. cancel-sign-sub-inv 75.9%

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

      6. *-commutative 75.9%

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

      7. +-commutative 75.9%

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

      8. fma-def 76.0%

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

      9. distribute-rgt-neg-in 76.0%

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

      10. *-commutative 76.0%

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

   9. Simplified 76.0%

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

   10. Taylor expanded in a around inf 37.7%

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

       1. *-commutative 37.7%

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

       2. *-commutative 37.7%

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

       3. associate-*r* 37.7%

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

       4. associate-*r* 37.7%

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

   12. Simplified 37.7%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{-58} \lor \neg \left(c \leq 2.1 \cdot 10^{+91}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.6e-58) (not (<= c 2.1e+91)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e-58) || !(c <= 2.1e+91)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.6d-58)) .or. (.not. (c <= 2.1d+91))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e-58) || !(c <= 2.1e+91)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.6e-58) or not (c <= 2.1e+91):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.6e-58) || !(c <= 2.1e+91))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.6e-58) || ~((c <= 2.1e+91)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.6e-58], N[Not[LessEqual[c, 2.1e+91]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.60000000000000009e-58 or 2.10000000000000008e91 < c

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in t around 0 82.2%

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

   if -3.60000000000000009e-58 < c < 2.10000000000000008e91

   1. Initial program 94.7%

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

   3. Taylor expanded in c around 0 74.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{-58} \lor \neg \left(c \leq 2.1 \cdot 10^{+91}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+170} \lor \neg \left(x \leq 1.2 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+170) (not (<= x 1.2e+19)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.8e+170) || !(x <= 1.2e+19)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.8d+170)) .or. (.not. (x <= 1.2d+19))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.8e+170) || !(x <= 1.2e+19)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+170) or not (x <= 1.2e+19):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.8e+170) || !(x <= 1.2e+19))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.8e+170) || ~((x <= 1.2e+19)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.8e+170], N[Not[LessEqual[x, 1.2e+19]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e170 or 1.2e19 < x

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf 42.7%

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

   if -4.8e170 < x < 1.2e19

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 33.6%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+170} \lor \neg \left(x \leq 1.2 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.1%

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

3. Taylor expanded in z around inf 28.5%

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

4. Final simplification 28.5%

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

Developer target: 94.4% 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 2024011 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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