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

Percentage Accurate: 90.0% → 96.4%

Time: 18.2s

Alternatives: 13

Speedup: 0.9×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.3%

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

      1. associate-*l* 98.0%

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

      2. fma-def 98.0%

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

   3. Simplified 98.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 63.8%

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

   3. Taylor expanded in i around 0 63.8%

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

4. Final simplification 96.6%

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

Alternative 2: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+231} \lor \neg \left(t_2 \leq 10^{+289}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 -5e+231) (not (<= t_2 1e+289)))
     (* -2.0 (* c (* t_1 i)))
     (* 2.0 (- (+ (* x y) (* z t)) (+ (* (* c i) (* b c)) (* a (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -5e+231) || !(t_2 <= 1e+289)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (((c * i) * (b * c)) + (a * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (c * t_1) * i
    if ((t_2 <= (-5d+231)) .or. (.not. (t_2 <= 1d+289))) then
        tmp = (-2.0d0) * (c * (t_1 * i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (((c * i) * (b * c)) + (a * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -5e+231) || !(t_2 <= 1e+289)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (((c * i) * (b * c)) + (a * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if (t_2 <= -5e+231) or not (t_2 <= 1e+289):
		tmp = -2.0 * (c * (t_1 * i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (((c * i) * (b * c)) + (a * (c * 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(c * t_1) * i)
	tmp = 0.0
	if ((t_2 <= -5e+231) || !(t_2 <= 1e+289))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(c * i) * Float64(b * c)) + Float64(a * Float64(c * 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 = (c * t_1) * i;
	tmp = 0.0;
	if ((t_2 <= -5e+231) || ~((t_2 <= 1e+289)))
		tmp = -2.0 * (c * (t_1 * i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (((c * i) * (b * c)) + (a * (c * 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[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+231], N[Not[LessEqual[t$95$2, 1e+289]], $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] - N[(N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.00000000000000028e231 or 1.0000000000000001e289 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.5%

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

   2. Taylor expanded in i around inf 90.4%

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

   3. Taylor expanded in i around 0 90.4%

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

   if -5.00000000000000028e231 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.0000000000000001e289

   1. Initial program 98.8%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

      3. +-commutative 99.3%

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

      4. distribute-lft-in 99.3%

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

   3. Applied egg-rr 99.3%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+231} \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+289}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 3: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+128} \lor \neg \left(c \leq 3.2 \cdot 10^{+148}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* b (* c (* c i)))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -2.75e+48)
     t_2
     (if (<= c -2.1e-147)
       t_1
       (if (<= c 1.9e-289)
         t_3
         (if (<= c 4.5e-261)
           t_1
           (if (<= c 2.55e-26)
             t_3
             (if (<= c 2.8e+42)
               t_1
               (if (or (<= c 8.5e+128) (not (<= c 3.2e+148)))
                 t_2
                 (* c (* -2.0 (* a i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (b * (c * (c * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.75e+48) {
		tmp = t_2;
	} else if (c <= -2.1e-147) {
		tmp = t_1;
	} else if (c <= 1.9e-289) {
		tmp = t_3;
	} else if (c <= 4.5e-261) {
		tmp = t_1;
	} else if (c <= 2.55e-26) {
		tmp = t_3;
	} else if (c <= 2.8e+42) {
		tmp = t_1;
	} else if ((c <= 8.5e+128) || !(c <= 3.2e+148)) {
		tmp = t_2;
	} else {
		tmp = c * (-2.0 * (a * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (b * (c * (c * i)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-2.75d+48)) then
        tmp = t_2
    else if (c <= (-2.1d-147)) then
        tmp = t_1
    else if (c <= 1.9d-289) then
        tmp = t_3
    else if (c <= 4.5d-261) then
        tmp = t_1
    else if (c <= 2.55d-26) then
        tmp = t_3
    else if (c <= 2.8d+42) then
        tmp = t_1
    else if ((c <= 8.5d+128) .or. (.not. (c <= 3.2d+148))) then
        tmp = t_2
    else
        tmp = c * ((-2.0d0) * (a * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (b * (c * (c * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.75e+48) {
		tmp = t_2;
	} else if (c <= -2.1e-147) {
		tmp = t_1;
	} else if (c <= 1.9e-289) {
		tmp = t_3;
	} else if (c <= 4.5e-261) {
		tmp = t_1;
	} else if (c <= 2.55e-26) {
		tmp = t_3;
	} else if (c <= 2.8e+42) {
		tmp = t_1;
	} else if ((c <= 8.5e+128) || !(c <= 3.2e+148)) {
		tmp = t_2;
	} else {
		tmp = c * (-2.0 * (a * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (b * (c * (c * i)))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -2.75e+48:
		tmp = t_2
	elif c <= -2.1e-147:
		tmp = t_1
	elif c <= 1.9e-289:
		tmp = t_3
	elif c <= 4.5e-261:
		tmp = t_1
	elif c <= 2.55e-26:
		tmp = t_3
	elif c <= 2.8e+42:
		tmp = t_1
	elif (c <= 8.5e+128) or not (c <= 3.2e+148):
		tmp = t_2
	else:
		tmp = c * (-2.0 * (a * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(b * Float64(c * Float64(c * i))))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -2.75e+48)
		tmp = t_2;
	elseif (c <= -2.1e-147)
		tmp = t_1;
	elseif (c <= 1.9e-289)
		tmp = t_3;
	elseif (c <= 4.5e-261)
		tmp = t_1;
	elseif (c <= 2.55e-26)
		tmp = t_3;
	elseif (c <= 2.8e+42)
		tmp = t_1;
	elseif ((c <= 8.5e+128) || !(c <= 3.2e+148))
		tmp = t_2;
	else
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (b * (c * (c * i)));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -2.75e+48)
		tmp = t_2;
	elseif (c <= -2.1e-147)
		tmp = t_1;
	elseif (c <= 1.9e-289)
		tmp = t_3;
	elseif (c <= 4.5e-261)
		tmp = t_1;
	elseif (c <= 2.55e-26)
		tmp = t_3;
	elseif (c <= 2.8e+42)
		tmp = t_1;
	elseif ((c <= 8.5e+128) || ~((c <= 3.2e+148)))
		tmp = t_2;
	else
		tmp = c * (-2.0 * (a * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.75e+48], t$95$2, If[LessEqual[c, -2.1e-147], t$95$1, If[LessEqual[c, 1.9e-289], t$95$3, If[LessEqual[c, 4.5e-261], t$95$1, If[LessEqual[c, 2.55e-26], t$95$3, If[LessEqual[c, 2.8e+42], t$95$1, If[Or[LessEqual[c, 8.5e+128], N[Not[LessEqual[c, 3.2e+148]], $MachinePrecision]], t$95$2, N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.7500000000000001e48 or 2.7999999999999999e42 < c < 8.50000000000000045e128 or 3.1999999999999999e148 < c

   1. Initial program 82.6%

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

   2. Taylor expanded in i around inf 79.7%

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

   3. Taylor expanded in c around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. unpow2 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in c around 0 73.3%

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

      1. unpow2 73.3%

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

      2. associate-*r* 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l* 77.4%

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

   8. Simplified 77.4%

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

   if -2.7500000000000001e48 < c < -2.1e-147 or 1.90000000000000005e-289 < c < 4.5000000000000001e-261 or 2.54999999999999995e-26 < c < 2.7999999999999999e42

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -2.1e-147 < c < 1.90000000000000005e-289 or 4.5000000000000001e-261 < c < 2.54999999999999995e-26

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf 51.4%

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

   if 8.50000000000000045e128 < c < 3.1999999999999999e148

   1. Initial program 67.2%

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

   2. Taylor expanded in a around inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. associate-*r* 83.7%

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

      3. *-commutative 83.7%

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

      4. distribute-rgt-neg-in 83.7%

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

      5. *-commutative 83.7%

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

      6. distribute-rgt-neg-in 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in a around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*l* 83.8%

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

      3. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+128} \lor \neg \left(c \leq 3.2 \cdot 10^{+148}\right):\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c 2.4e+100)
     (* (- (+ (* x y) (* z t)) (* (* c t_1) i)) 2.0)
     (* -2.0 (* c (* t_1 i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= 2.4e+100) {
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	} else {
		tmp = -2.0 * (c * (t_1 * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (b * c)
    if (c <= 2.4d+100) then
        tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0d0
    else
        tmp = (-2.0d0) * (c * (t_1 * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= 2.4e+100) {
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	} else {
		tmp = -2.0 * (c * (t_1 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= 2.4e+100:
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0
	else:
		tmp = -2.0 * (c * (t_1 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (c <= 2.4e+100)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) * 2.0);
	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);
	tmp = 0.0;
	if (c <= 2.4e+100)
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	else
		tmp = -2.0 * (c * (t_1 * i));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if c < 2.40000000000000012e100

   1. Initial program 94.6%

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

   if 2.40000000000000012e100 < c

   1. Initial program 71.2%

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

   2. Taylor expanded in i around inf 92.2%

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

   3. Taylor expanded in i around 0 92.2%

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

4. Final simplification 94.3%

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

Alternative 5: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* -2.0 (* b (* c (* c i))))))
   (if (<= c -6.8e+59)
     t_2
     (if (<= c 5.6e+59)
       t_1
       (if (<= c 3.6e+76)
         t_2
         (if (<= c 2.5e+100)
           t_1
           (if (<= c 3.2e+148) (* c (* -2.0 (* a i))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -6.8e+59) {
		tmp = t_2;
	} else if (c <= 5.6e+59) {
		tmp = t_1;
	} else if (c <= 3.6e+76) {
		tmp = t_2;
	} else if (c <= 2.5e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (b * (c * (c * i)))
    if (c <= (-6.8d+59)) then
        tmp = t_2
    else if (c <= 5.6d+59) then
        tmp = t_1
    else if (c <= 3.6d+76) then
        tmp = t_2
    else if (c <= 2.5d+100) then
        tmp = t_1
    else if (c <= 3.2d+148) then
        tmp = c * ((-2.0d0) * (a * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -6.8e+59) {
		tmp = t_2;
	} else if (c <= 5.6e+59) {
		tmp = t_1;
	} else if (c <= 3.6e+76) {
		tmp = t_2;
	} else if (c <= 2.5e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (b * (c * (c * i)))
	tmp = 0
	if c <= -6.8e+59:
		tmp = t_2
	elif c <= 5.6e+59:
		tmp = t_1
	elif c <= 3.6e+76:
		tmp = t_2
	elif c <= 2.5e+100:
		tmp = t_1
	elif c <= 3.2e+148:
		tmp = c * (-2.0 * (a * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(b * Float64(c * Float64(c * i))))
	tmp = 0.0
	if (c <= -6.8e+59)
		tmp = t_2;
	elseif (c <= 5.6e+59)
		tmp = t_1;
	elseif (c <= 3.6e+76)
		tmp = t_2;
	elseif (c <= 2.5e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (b * (c * (c * i)));
	tmp = 0.0;
	if (c <= -6.8e+59)
		tmp = t_2;
	elseif (c <= 5.6e+59)
		tmp = t_1;
	elseif (c <= 3.6e+76)
		tmp = t_2;
	elseif (c <= 2.5e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = c * (-2.0 * (a * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+59], t$95$2, If[LessEqual[c, 5.6e+59], t$95$1, If[LessEqual[c, 3.6e+76], t$95$2, If[LessEqual[c, 2.5e+100], t$95$1, If[LessEqual[c, 3.2e+148], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.80000000000000012e59 or 5.5999999999999996e59 < c < 3.6000000000000003e76 or 3.1999999999999999e148 < c

   1. Initial program 85.2%

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

   2. Taylor expanded in i around inf 84.2%

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

   3. Taylor expanded in c around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. unpow2 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in c around 0 80.3%

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

      1. unpow2 80.3%

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

      2. associate-*r* 80.5%

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

      3. *-commutative 80.5%

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

      4. associate-*l* 85.3%

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

   8. Simplified 85.3%

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

   if -6.80000000000000012e59 < c < 5.5999999999999996e59 or 3.6000000000000003e76 < c < 2.4999999999999999e100

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 2.4999999999999999e100 < c < 3.1999999999999999e148

   1. Initial program 47.1%

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

   2. Taylor expanded in a around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. *-commutative 61.9%

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

      6. distribute-rgt-neg-in 61.9%

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

   4. Simplified 61.9%

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

   5. Taylor expanded in a around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*l* 62.0%

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

      3. *-commutative 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+59}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+59}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+100}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 6: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.58 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(c \cdot \left(i \cdot \left(b \cdot -2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* -2.0 (* b (* c (* c i))))))
   (if (<= c -1.8e+59)
     t_2
     (if (<= c 2.2e+63)
       t_1
       (if (<= c 2.2e+76)
         t_2
         (if (<= c 1.58e+100)
           t_1
           (if (<= c 3.2e+148)
             (* c (* -2.0 (* a i)))
             (* c (* c (* i (* b -2.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -1.8e+59) {
		tmp = t_2;
	} else if (c <= 2.2e+63) {
		tmp = t_1;
	} else if (c <= 2.2e+76) {
		tmp = t_2;
	} else if (c <= 1.58e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * (c * (i * (b * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (b * (c * (c * i)))
    if (c <= (-1.8d+59)) then
        tmp = t_2
    else if (c <= 2.2d+63) then
        tmp = t_1
    else if (c <= 2.2d+76) then
        tmp = t_2
    else if (c <= 1.58d+100) then
        tmp = t_1
    else if (c <= 3.2d+148) then
        tmp = c * ((-2.0d0) * (a * i))
    else
        tmp = c * (c * (i * (b * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -1.8e+59) {
		tmp = t_2;
	} else if (c <= 2.2e+63) {
		tmp = t_1;
	} else if (c <= 2.2e+76) {
		tmp = t_2;
	} else if (c <= 1.58e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * (c * (i * (b * -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (b * (c * (c * i)))
	tmp = 0
	if c <= -1.8e+59:
		tmp = t_2
	elif c <= 2.2e+63:
		tmp = t_1
	elif c <= 2.2e+76:
		tmp = t_2
	elif c <= 1.58e+100:
		tmp = t_1
	elif c <= 3.2e+148:
		tmp = c * (-2.0 * (a * i))
	else:
		tmp = c * (c * (i * (b * -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(b * Float64(c * Float64(c * i))))
	tmp = 0.0
	if (c <= -1.8e+59)
		tmp = t_2;
	elseif (c <= 2.2e+63)
		tmp = t_1;
	elseif (c <= 2.2e+76)
		tmp = t_2;
	elseif (c <= 1.58e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	else
		tmp = Float64(c * Float64(c * Float64(i * Float64(b * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (b * (c * (c * i)));
	tmp = 0.0;
	if (c <= -1.8e+59)
		tmp = t_2;
	elseif (c <= 2.2e+63)
		tmp = t_1;
	elseif (c <= 2.2e+76)
		tmp = t_2;
	elseif (c <= 1.58e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = c * (-2.0 * (a * i));
	else
		tmp = c * (c * (i * (b * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+59], t$95$2, If[LessEqual[c, 2.2e+63], t$95$1, If[LessEqual[c, 2.2e+76], t$95$2, If[LessEqual[c, 1.58e+100], t$95$1, If[LessEqual[c, 3.2e+148], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(c * N[(i * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.7999999999999999e59 or 2.1999999999999999e63 < c < 2.2e76

   1. Initial program 87.1%

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

   2. Taylor expanded in i around inf 81.9%

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

   3. Taylor expanded in c around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. unpow2 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in c around 0 77.8%

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

      1. unpow2 77.8%

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

      2. associate-*r* 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*l* 83.5%

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

   8. Simplified 83.5%

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

   if -1.7999999999999999e59 < c < 2.1999999999999999e63 or 2.2e76 < c < 1.5800000000000001e100

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 1.5800000000000001e100 < c < 3.1999999999999999e148

   1. Initial program 47.1%

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

   2. Taylor expanded in a around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. *-commutative 61.9%

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

      6. distribute-rgt-neg-in 61.9%

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

   4. Simplified 61.9%

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

   5. Taylor expanded in a around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*l* 62.0%

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

      3. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if 3.1999999999999999e148 < c

   1. Initial program 81.4%

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

   2. Taylor expanded in i around inf 88.9%

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

   3. Taylor expanded in c around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in c around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*r* 85.3%

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

      5. associate-*l* 88.9%

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

      6. *-commutative 88.9%

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

      7. associate-*r* 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+76}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.58 \cdot 10^{+100}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(c \cdot \left(i \cdot \left(b \cdot -2\right)\right)\right)\\ \end{array} \]

Alternative 7: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* -2.0 (* b (* c (* c i))))))
   (if (<= c -9.2e+61)
     t_2
     (if (<= c 1.95e+62)
       t_1
       (if (<= c 1.55e+76)
         t_2
         (if (<= c 2.2e+100)
           t_1
           (if (<= c 3.2e+148)
             (* c (* -2.0 (* a i)))
             (* c (* (* c i) (* b -2.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -9.2e+61) {
		tmp = t_2;
	} else if (c <= 1.95e+62) {
		tmp = t_1;
	} else if (c <= 1.55e+76) {
		tmp = t_2;
	} else if (c <= 2.2e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * ((c * i) * (b * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (b * (c * (c * i)))
    if (c <= (-9.2d+61)) then
        tmp = t_2
    else if (c <= 1.95d+62) then
        tmp = t_1
    else if (c <= 1.55d+76) then
        tmp = t_2
    else if (c <= 2.2d+100) then
        tmp = t_1
    else if (c <= 3.2d+148) then
        tmp = c * ((-2.0d0) * (a * i))
    else
        tmp = c * ((c * i) * (b * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (b * (c * (c * i)));
	double tmp;
	if (c <= -9.2e+61) {
		tmp = t_2;
	} else if (c <= 1.95e+62) {
		tmp = t_1;
	} else if (c <= 1.55e+76) {
		tmp = t_2;
	} else if (c <= 2.2e+100) {
		tmp = t_1;
	} else if (c <= 3.2e+148) {
		tmp = c * (-2.0 * (a * i));
	} else {
		tmp = c * ((c * i) * (b * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (b * (c * (c * i)))
	tmp = 0
	if c <= -9.2e+61:
		tmp = t_2
	elif c <= 1.95e+62:
		tmp = t_1
	elif c <= 1.55e+76:
		tmp = t_2
	elif c <= 2.2e+100:
		tmp = t_1
	elif c <= 3.2e+148:
		tmp = c * (-2.0 * (a * i))
	else:
		tmp = c * ((c * i) * (b * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(b * Float64(c * Float64(c * i))))
	tmp = 0.0
	if (c <= -9.2e+61)
		tmp = t_2;
	elseif (c <= 1.95e+62)
		tmp = t_1;
	elseif (c <= 1.55e+76)
		tmp = t_2;
	elseif (c <= 2.2e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	else
		tmp = Float64(c * Float64(Float64(c * i) * Float64(b * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (b * (c * (c * i)));
	tmp = 0.0;
	if (c <= -9.2e+61)
		tmp = t_2;
	elseif (c <= 1.95e+62)
		tmp = t_1;
	elseif (c <= 1.55e+76)
		tmp = t_2;
	elseif (c <= 2.2e+100)
		tmp = t_1;
	elseif (c <= 3.2e+148)
		tmp = c * (-2.0 * (a * i));
	else
		tmp = c * ((c * i) * (b * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.2e+61], t$95$2, If[LessEqual[c, 1.95e+62], t$95$1, If[LessEqual[c, 1.55e+76], t$95$2, If[LessEqual[c, 2.2e+100], t$95$1, If[LessEqual[c, 3.2e+148], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(c * i), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 87.1%

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

   2. Taylor expanded in i around inf 81.9%

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

   3. Taylor expanded in c around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. unpow2 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in c around 0 77.8%

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

      1. unpow2 77.8%

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

      2. associate-*r* 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*l* 83.5%

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

   8. Simplified 83.5%

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

   if -9.1999999999999998e61 < c < 1.95e62 or 1.55000000000000006e76 < c < 2.2000000000000001e100

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 79.4%

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

   if 2.2000000000000001e100 < c < 3.1999999999999999e148

   1. Initial program 47.1%

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

   2. Taylor expanded in a around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. *-commutative 61.9%

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

      6. distribute-rgt-neg-in 61.9%

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

   4. Simplified 61.9%

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

   5. Taylor expanded in a around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*l* 62.0%

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

      3. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if 3.1999999999999999e148 < c

   1. Initial program 81.4%

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

   2. Taylor expanded in i around inf 88.9%

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

   3. Taylor expanded in c around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in c around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*r* 85.3%

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

      5. associate-*l* 88.9%

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

      6. *-commutative 88.9%

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

      7. associate-*r* 88.9%

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

   8. Simplified 88.9%

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

   9. Taylor expanded in c around 0 88.9%

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

       1. *-commutative 88.9%

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

       2. associate-*r* 89.0%

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

       3. associate-*l* 89.0%

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

       4. *-commutative 89.0%

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

   11. Simplified 89.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+100}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]

Alternative 8: 78.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.15d+33)) .or. (.not. (c <= 7.5d+40))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.15e+33) || !(c <= 7.5e+40)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 82.4%

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

   2. Taylor expanded in z around 0 87.1%

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

   if -2.15000000000000014e33 < c < 7.4999999999999996e40

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 81.2%

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

4. Final simplification 83.6%

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

Alternative 9: 87.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.7e+36) (not (<= c 6.2e+41)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.7e+36) || !(c <= 6.2e+41)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.7d+36)) .or. (.not. (c <= 6.2d+41))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.7e+36) || !(c <= 6.2e+41)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.7e+36) or not (c <= 6.2e+41):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.7e+36) || !(c <= 6.2e+41))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.7e+36) || ~((c <= 6.2e+41)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.7e+36], N[Not[LessEqual[c, 6.2e+41]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6999999999999999e36 or 6.2e41 < c

   1. Initial program 82.4%

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

   2. Taylor expanded in z around 0 87.1%

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

   if -1.6999999999999999e36 < c < 6.2e41

   1. Initial program 97.4%

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

   2. Taylor expanded in a around inf 92.1%

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

4. Final simplification 90.0%

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

Alternative 10: 74.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-8.6d+103)) .or. (.not. (c <= 5.2d+42))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.6e+103) || !(c <= 5.2e+42)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 80.3%

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

   2. Taylor expanded in i around inf 85.9%

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

   3. Taylor expanded in i around 0 85.9%

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

   if -8.59999999999999938e103 < c < 5.1999999999999998e42

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 78.9%

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

4. Final simplification 81.4%

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

Alternative 11: 74.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2.55d+48)) then
        tmp = 2.0d0 * ((x * y) - (c * (i * (b * c))))
    else if (c <= 1.7d+40) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if c < -2.5499999999999999e48

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0 88.5%

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

   3. Taylor expanded in c around inf 84.5%

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

   if -2.5499999999999999e48 < c < 1.69999999999999994e40

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 80.5%

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

   if 1.69999999999999994e40 < c

   1. Initial program 77.1%

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

   2. Taylor expanded in i around inf 82.9%

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

   3. Taylor expanded in i around 0 82.9%

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

4. Final simplification 81.7%

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

Alternative 12: 40.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+27} \lor \neg \left(z \leq 4.2 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -7.4e+27) (not (<= z 4.2e-16)))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -7.4e+27) || !(z <= 4.2e-16)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-7.4d+27)) .or. (.not. (z <= 4.2d-16))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -7.4e+27) || !(z <= 4.2e-16)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -7.4e+27) or not (z <= 4.2e-16):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -7.4e+27) || !(z <= 4.2e-16))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -7.4e+27) || ~((z <= 4.2e-16)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -7.4e+27], N[Not[LessEqual[z, 4.2e-16]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.40000000000000004e27 or 4.2000000000000002e-16 < z

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -7.40000000000000004e27 < z < 4.2000000000000002e-16

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 39.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+27} \lor \neg \left(z \leq 4.2 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 30.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

2. Taylor expanded in z around inf 31.4%

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

3. Final simplification 31.4%

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

Developer target: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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