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

Percentage Accurate: 90.2% → 94.5%

Time: 14.4s

Alternatives: 12

Speedup: 1.0×

• 47.6% 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: 90.2% 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: 94.5% 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 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. Step-by-step derivation

   1. associate--l+ 88.0%

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

   2. *-commutative 88.0%

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

   3. associate--l+ 88.0%

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

   4. associate--l+ 88.0%

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

   5. *-commutative 88.0%

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

   6. associate--l+ 88.0%

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

   7. fma-def 88.0%

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

   8. associate-*l* 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 2: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t_1\right)\\ t_3 := c \cdot \left(t_1 \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_3\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))) (t_3 (* c (* t_1 i))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* x y) t_3))
     (if (<= t_2 2e+294) (* 2.0 (- (+ (* x y) (* z t)) t_2)) (* t_3 -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 2e+294) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = t_3 * -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 2e+294) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = t_3 * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	t_3 = c * (t_1 * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) - t_3)
	elif t_2 <= 2e+294:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = t_3 * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	t_3 = Float64(c * Float64(t_1 * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_3));
	elseif (t_2 <= 2e+294)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(t_3 * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	t_3 = c * (t_1 * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) - t_3);
	elseif (t_2 <= 2e+294)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = t_3 * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+294], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$3 * -2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.1%

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

   2. Taylor expanded in z around 0 90.6%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.00000000000000013e294

   1. Initial program 98.6%

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

   if 2.00000000000000013e294 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 70.3%

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

   2. Taylor expanded in i around inf 89.3%

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

   3. Taylor expanded in i around 0 89.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 2 \cdot 10^{+294}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 3: 42.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -950000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+20} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+73}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= (* x y) -950000000000.0)
     t_1
     (if (<= (* x y) 1.9e-271)
       (* 2.0 (* z t))
       (if (<= (* x y) 3.6e-29)
         (* -2.0 (* a (* c i)))
         (if (or (<= (* x y) 1.2e+20) (not (<= (* x y) 4e+73)))
           t_1
           (* 2.0 (* (* a i) (- 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 tmp;
	if ((x * y) <= -950000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-271) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 3.6e-29) {
		tmp = -2.0 * (a * (c * i));
	} else if (((x * y) <= 1.2e+20) || !((x * y) <= 4e+73)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((a * i) * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if ((x * y) <= (-950000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 1.9d-271) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 3.6d-29) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (((x * y) <= 1.2d+20) .or. (.not. ((x * y) <= 4d+73))) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((a * i) * -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 tmp;
	if ((x * y) <= -950000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.9e-271) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 3.6e-29) {
		tmp = -2.0 * (a * (c * i));
	} else if (((x * y) <= 1.2e+20) || !((x * y) <= 4e+73)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((a * i) * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -950000000000.0:
		tmp = t_1
	elif (x * y) <= 1.9e-271:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 3.6e-29:
		tmp = -2.0 * (a * (c * i))
	elif ((x * y) <= 1.2e+20) or not ((x * y) <= 4e+73):
		tmp = t_1
	else:
		tmp = 2.0 * ((a * i) * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -950000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.9e-271)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 3.6e-29)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif ((Float64(x * y) <= 1.2e+20) || !(Float64(x * y) <= 4e+73))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(a * i) * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -950000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 1.9e-271)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 3.6e-29)
		tmp = -2.0 * (a * (c * i));
	elseif (((x * y) <= 1.2e+20) || ~(((x * y) <= 4e+73)))
		tmp = t_1;
	else
		tmp = 2.0 * ((a * i) * -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]}, If[LessEqual[N[(x * y), $MachinePrecision], -950000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-271], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e-29], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 1.2e+20], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+73]], $MachinePrecision]], t$95$1, N[(2.0 * N[(N[(a * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.5e11 or 3.59999999999999974e-29 < (*.f64 x y) < 1.2e20 or 3.99999999999999993e73 < (*.f64 x y)

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 60.8%

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

   if -9.5e11 < (*.f64 x y) < 1.90000000000000005e-271

   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 44.5%

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

   if 1.90000000000000005e-271 < (*.f64 x y) < 3.59999999999999974e-29

   1. Initial program 81.7%

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

   2. Taylor expanded in a around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. distribute-rgt-neg-in 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in c around 0 46.2%

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

   if 1.2e20 < (*.f64 x y) < 3.99999999999999993e73

   1. Initial program 80.4%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. associate-*l* 60.3%

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

   4. Simplified 60.3%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -950000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+20} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+73}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -2 \cdot 10^{+77} \lor \neg \left(a \leq 3.05 \cdot 10^{+29}\right):\\ \;\;\;\;2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= a -2e+77) (not (<= a 3.05e+29)))
     (* 2.0 (- t_1 (* a (* c i))))
     (* 2.0 (- t_1 (* (* b c) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -2e+77) || !(a <= 3.05e+29)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a <= (-2d+77)) .or. (.not. (a <= 3.05d+29))) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -2e+77) || !(a <= 3.05e+29)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a <= -2e+77) or not (a <= 3.05e+29):
		tmp = 2.0 * (t_1 - (a * (c * i)))
	else:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((a <= -2e+77) || !(a <= 3.05e+29))
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a <= -2e+77) || ~((a <= 3.05e+29)))
		tmp = 2.0 * (t_1 - (a * (c * i)));
	else
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -2e+77], N[Not[LessEqual[a, 3.05e+29]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.99999999999999997e77 or 3.0499999999999999e29 < a

   1. Initial program 84.4%

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

   2. Taylor expanded in a around inf 87.9%

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

   if -1.99999999999999997e77 < a < 3.0499999999999999e29

   1. Initial program 90.7%

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

      1. associate--l+ 90.7%

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

      2. *-commutative 90.7%

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

      3. associate--l+ 90.7%

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

      4. associate--l+ 90.7%

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

      5. *-commutative 90.7%

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

      6. associate--l+ 90.7%

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

      7. fma-def 90.7%

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

      8. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

      1. fma-def 96.5%

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

      2. +-commutative 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in a around 0 94.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+77} \lor \neg \left(a \leq 3.05 \cdot 10^{+29}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 42.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -29000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= (* x y) -29000000000.0)
     t_1
     (if (<= (* x y) 1.35e-273)
       (* 2.0 (* z t))
       (if (<= (* x y) 2.25e-29) (* -2.0 (* a (* c i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -29000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-273) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2.25e-29) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if ((x * y) <= (-29000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 1.35d-273) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 2.25d-29) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -29000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-273) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2.25e-29) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -29000000000.0:
		tmp = t_1
	elif (x * y) <= 1.35e-273:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 2.25e-29:
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -29000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.35e-273)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 2.25e-29)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -29000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 1.35e-273)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 2.25e-29)
		tmp = -2.0 * (a * (c * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -29000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.35e-273], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.25e-29], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.9e10 or 2.2499999999999999e-29 < (*.f64 x y)

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 57.2%

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

   if -2.9e10 < (*.f64 x y) < 1.34999999999999992e-273

   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 44.5%

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

   if 1.34999999999999992e-273 < (*.f64 x y) < 2.2499999999999999e-29

   1. Initial program 81.7%

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

   2. Taylor expanded in a around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. distribute-rgt-neg-in 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in c around 0 46.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -29000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 6: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-78} \lor \neg \left(c \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.9e-78) (not (<= c 1.25e-23)))
   (* 2.0 (- (* x y) (* 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 <= -1.9e-78) || !(c <= 1.25e-23)) {
		tmp = 2.0 * ((x * y) - (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 <= (-1.9d-78)) .or. (.not. (c <= 1.25d-23))) then
        tmp = 2.0d0 * ((x * y) - (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 <= -1.9e-78) || !(c <= 1.25e-23)) {
		tmp = 2.0 * ((x * y) - (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 <= -1.9e-78) or not (c <= 1.25e-23):
		tmp = 2.0 * ((x * y) - (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 <= -1.9e-78) || !(c <= 1.25e-23))
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 <= -1.9e-78) || ~((c <= 1.25e-23)))
		tmp = 2.0 * ((x * y) - (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, -1.9e-78], N[Not[LessEqual[c, 1.25e-23]], $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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8999999999999999e-78 or 1.2500000000000001e-23 < 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 83.4%

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

   if -1.8999999999999999e-78 < c < 1.2500000000000001e-23

   1. Initial program 97.9%

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

   2. Taylor expanded in c around 0 86.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-78} \lor \neg \left(c \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 7: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+56} \lor \neg \left(c \leq 5.1 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -5.8e+56) (not (<= c 5.1e+16)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.8e+56) || !(c <= 5.1e+16)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-5.8d+56)) .or. (.not. (c <= 5.1d+16))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.8e+56) || !(c <= 5.1e+16)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -5.8e+56) or not (c <= 5.1e+16):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -5.8e+56) || !(c <= 5.1e+16))
		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(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -5.8e+56) || ~((c <= 5.1e+16)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -5.8e+56], N[Not[LessEqual[c, 5.1e+16]], $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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.80000000000000014e56 or 5.1e16 < c

   1. Initial program 79.0%

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

   2. Taylor expanded in z around 0 86.3%

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

   if -5.80000000000000014e56 < c < 5.1e16

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 94.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+56} \lor \neg \left(c \leq 5.1 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Step-by-step derivation

   1. associate--l+ 88.0%

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

   2. *-commutative 88.0%

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

   3. associate--l+ 88.0%

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

   4. associate--l+ 88.0%

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

   5. *-commutative 88.0%

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

   6. associate--l+ 88.0%

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

   7. fma-def 88.0%

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

   8. associate-*l* 96.1%

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

3. Simplified 96.1%

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

   1. fma-def 96.1%

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

   2. +-commutative 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 9: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{+64} \lor \neg \left(c \leq 1.12 \cdot 10^{+60}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.3e+64) (not (<= c 1.12e+60)))
   (* (* c (* (+ a (* b c)) i)) -2.0)
   (* 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 <= -4.3e+64) || !(c <= 1.12e+60)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} 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 <= (-4.3d+64)) .or. (.not. (c <= 1.12d+60))) then
        tmp = (c * ((a + (b * c)) * i)) * (-2.0d0)
    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 <= -4.3e+64) || !(c <= 1.12e+60)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} 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 <= -4.3e+64) or not (c <= 1.12e+60):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	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 <= -4.3e+64) || !(c <= 1.12e+60))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0);
	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 <= -4.3e+64) || ~((c <= 1.12e+60)))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	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, -4.3e+64], N[Not[LessEqual[c, 1.12e+60]], $MachinePrecision]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $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 < -4.2999999999999998e64 or 1.1199999999999999e60 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in i around inf 77.1%

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

   3. Taylor expanded in i around 0 77.1%

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

   if -4.2999999999999998e64 < c < 1.1199999999999999e60

   1. Initial program 95.9%

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

   2. Taylor expanded in c around 0 77.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{+64} \lor \neg \left(c \leq 1.12 \cdot 10^{+60}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 10: 56.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+254}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(2 \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* a (* c i)))))
   (if (<= c -5.2e+224)
     t_1
     (if (<= c 2.3e+163)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 1.75e+254) t_1 (* i (* 2.0 (* 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 * (a * (c * i));
	double tmp;
	if (c <= -5.2e+224) {
		tmp = t_1;
	} else if (c <= 2.3e+163) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.75e+254) {
		tmp = t_1;
	} else {
		tmp = i * (2.0 * (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) :: tmp
    t_1 = (-2.0d0) * (a * (c * i))
    if (c <= (-5.2d+224)) then
        tmp = t_1
    else if (c <= 2.3d+163) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 1.75d+254) then
        tmp = t_1
    else
        tmp = i * (2.0d0 * (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 * (a * (c * i));
	double tmp;
	if (c <= -5.2e+224) {
		tmp = t_1;
	} else if (c <= 2.3e+163) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.75e+254) {
		tmp = t_1;
	} else {
		tmp = i * (2.0 * (a * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (a * (c * i))
	tmp = 0
	if c <= -5.2e+224:
		tmp = t_1
	elif c <= 2.3e+163:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 1.75e+254:
		tmp = t_1
	else:
		tmp = i * (2.0 * (a * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(a * Float64(c * i)))
	tmp = 0.0
	if (c <= -5.2e+224)
		tmp = t_1;
	elseif (c <= 2.3e+163)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 1.75e+254)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(2.0 * Float64(a * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (a * (c * i));
	tmp = 0.0;
	if (c <= -5.2e+224)
		tmp = t_1;
	elseif (c <= 2.3e+163)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 1.75e+254)
		tmp = t_1;
	else
		tmp = i * (2.0 * (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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+224], t$95$1, If[LessEqual[c, 2.3e+163], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e+254], t$95$1, N[(i * N[(2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.2000000000000001e224 or 2.30000000000000002e163 < c < 1.75000000000000008e254

   1. Initial program 77.6%

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

   2. Taylor expanded in a around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in c around 0 66.7%

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

   if -5.2000000000000001e224 < c < 2.30000000000000002e163

   1. Initial program 90.7%

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

   2. Taylor expanded in c around 0 66.8%

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

   if 1.75000000000000008e254 < c

   1. Initial program 67.4%

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

   2. Taylor expanded in a around inf 22.4%

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

      1. mul-1-neg 22.4%

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

      2. *-commutative 22.4%

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

      3. distribute-rgt-neg-in 22.4%

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

   4. Simplified 22.4%

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

   5. Taylor expanded in c around 0 22.4%

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

   7. Applied egg-rr 67.0%

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

      1. distribute-lft-neg-in 67.0%

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

      2. metadata-eval 67.0%

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

      3. count-2 67.0%

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

      4. distribute-lft-out 67.0%

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

      5. count-2 67.0%

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

      6. *-commutative 67.0%

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

   9. Simplified 67.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+224}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+254}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(2 \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 11: 43.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9000000000000 \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -9000000000000.0) (not (<= (* x y) 4.2e-29)))
   (* 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 * y) <= -9000000000000.0) || !((x * y) <= 4.2e-29)) {
		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 * y) <= (-9000000000000.0d0)) .or. (.not. ((x * y) <= 4.2d-29))) 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 * y) <= -9000000000000.0) || !((x * y) <= 4.2e-29)) {
		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 * y) <= -9000000000000.0) or not ((x * y) <= 4.2e-29):
		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 ((Float64(x * y) <= -9000000000000.0) || !(Float64(x * y) <= 4.2e-29))
		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 * y) <= -9000000000000.0) || ~(((x * y) <= 4.2e-29)))
		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[N[(x * y), $MachinePrecision], -9000000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.2e-29]], $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 (*.f64 x y) < -9e12 or 4.19999999999999979e-29 < (*.f64 x y)

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 57.2%

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

   if -9e12 < (*.f64 x y) < 4.19999999999999979e-29

   1. Initial program 86.8%

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

   2. Taylor expanded in z around inf 38.9%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9000000000000 \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 12: 29.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Taylor expanded in z around inf 27.4%

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

3. Final simplification 27.4%

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

Developer target: 94.2% 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 2023335 
(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))))