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

Percentage Accurate: 90.0% → 92.8%

Time: 13.3s

Alternatives: 12

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% 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: 92.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (- (+ (* x y) (* z t)) (* (* c t_1) i))))
   (if (<= t_2 INFINITY) (* t_2 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 t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2 * 2.0;
	} else {
		tmp = -2.0 * (c * (t_1 * i));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2 * 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)
	t_2 = ((x * y) + (z * t)) - ((c * t_1) * i)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2 * 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))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = Float64(t_2 * 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);
	t_2 = ((x * y) + (z * t)) - ((c * t_1) * i);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2 * 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]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], N[(t$95$2 * 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 (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   1. Initial program 98.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 69.5%

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

   4. Taylor expanded in i around 0 69.5%

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

4. Final simplification 96.9%

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

Alternative 2: 41.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+143}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -2.75 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* i (* c (- a)))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -7e+143)
     t_3
     (if (<= (* x y) -2.75e-102)
       t_1
       (if (<= (* x y) 1.3e-183)
         t_2
         (if (<= (* x y) 4e-25) t_1 (if (<= (* x y) 1.05e+216) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (c * -a));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -7e+143) {
		tmp = t_3;
	} else if ((x * y) <= -2.75e-102) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e-183) {
		tmp = t_2;
	} else if ((x * y) <= 4e-25) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e+216) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (i * (c * -a))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-7d+143)) then
        tmp = t_3
    else if ((x * y) <= (-2.75d-102)) then
        tmp = t_1
    else if ((x * y) <= 1.3d-183) then
        tmp = t_2
    else if ((x * y) <= 4d-25) then
        tmp = t_1
    else if ((x * y) <= 1.05d+216) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (c * -a));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -7e+143) {
		tmp = t_3;
	} else if ((x * y) <= -2.75e-102) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e-183) {
		tmp = t_2;
	} else if ((x * y) <= 4e-25) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e+216) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (i * (c * -a))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -7e+143:
		tmp = t_3
	elif (x * y) <= -2.75e-102:
		tmp = t_1
	elif (x * y) <= 1.3e-183:
		tmp = t_2
	elif (x * y) <= 4e-25:
		tmp = t_1
	elif (x * y) <= 1.05e+216:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(i * Float64(c * Float64(-a))))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -7e+143)
		tmp = t_3;
	elseif (Float64(x * y) <= -2.75e-102)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.3e-183)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-25)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.05e+216)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (i * (c * -a));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -7e+143)
		tmp = t_3;
	elseif ((x * y) <= -2.75e-102)
		tmp = t_1;
	elseif ((x * y) <= 1.3e-183)
		tmp = t_2;
	elseif ((x * y) <= 4e-25)
		tmp = t_1;
	elseif ((x * y) <= 1.05e+216)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(i * N[(c * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7e+143], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2.75e-102], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.3e-183], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-25], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.05e+216], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.00000000000000017e143 or 1.05000000000000001e216 < (*.f64 x y)

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -7.00000000000000017e143 < (*.f64 x y) < -2.7499999999999999e-102 or 1.2999999999999999e-183 < (*.f64 x y) < 4.00000000000000015e-25

   1. Initial program 97.1%

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

   3. Taylor expanded in i around inf 91.5%

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

      1. associate--l+ 91.5%

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

      2. associate-/l* 90.1%

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

      3. associate-/l* 87.3%

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

      4. +-commutative 87.3%

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

      5. fma-undefine 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in a around inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. mul-1-neg 47.1%

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

   8. Simplified 47.1%

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

   if -2.7499999999999999e-102 < (*.f64 x y) < 1.2999999999999999e-183 or 4.00000000000000015e-25 < (*.f64 x y) < 1.05000000000000001e216

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 42.8%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2.75 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-183}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-25}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 9.7 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+213}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* a (* c i))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1.22e+145)
     t_3
     (if (<= (* x y) -5.5e-102)
       t_1
       (if (<= (* x y) 2.6e-179)
         t_2
         (if (<= (* x y) 9.7e-26) t_1 (if (<= (* x y) 5.8e+213) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.22e+145) {
		tmp = t_3;
	} else if ((x * y) <= -5.5e-102) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e-179) {
		tmp = t_2;
	} else if ((x * y) <= 9.7e-26) {
		tmp = t_1;
	} else if ((x * y) <= 5.8e+213) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-2.0d0) * (a * (c * i))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1.22d+145)) then
        tmp = t_3
    else if ((x * y) <= (-5.5d-102)) then
        tmp = t_1
    else if ((x * y) <= 2.6d-179) then
        tmp = t_2
    else if ((x * y) <= 9.7d-26) then
        tmp = t_1
    else if ((x * y) <= 5.8d+213) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.22e+145) {
		tmp = t_3;
	} else if ((x * y) <= -5.5e-102) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e-179) {
		tmp = t_2;
	} else if ((x * y) <= 9.7e-26) {
		tmp = t_1;
	} else if ((x * y) <= 5.8e+213) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (a * (c * i))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.22e+145:
		tmp = t_3
	elif (x * y) <= -5.5e-102:
		tmp = t_1
	elif (x * y) <= 2.6e-179:
		tmp = t_2
	elif (x * y) <= 9.7e-26:
		tmp = t_1
	elif (x * y) <= 5.8e+213:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(a * Float64(c * i)))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.22e+145)
		tmp = t_3;
	elseif (Float64(x * y) <= -5.5e-102)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.6e-179)
		tmp = t_2;
	elseif (Float64(x * y) <= 9.7e-26)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.8e+213)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (a * (c * i));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.22e+145)
		tmp = t_3;
	elseif ((x * y) <= -5.5e-102)
		tmp = t_1;
	elseif ((x * y) <= 2.6e-179)
		tmp = t_2;
	elseif ((x * y) <= 9.7e-26)
		tmp = t_1;
	elseif ((x * y) <= 5.8e+213)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.22e+145], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-102], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.6e-179], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9.7e-26], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.8e+213], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.21999999999999994e145 or 5.8000000000000006e213 < (*.f64 x y)

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -1.21999999999999994e145 < (*.f64 x y) < -5.4999999999999997e-102 or 2.60000000000000005e-179 < (*.f64 x y) < 9.7000000000000001e-26

   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. Add Preprocessing

   3. Taylor expanded in i around inf 60.2%

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

   4. Taylor expanded in c around 0 46.8%

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

      1. *-commutative 46.8%

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

   6. Simplified 46.8%

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

   if -5.4999999999999997e-102 < (*.f64 x y) < 2.60000000000000005e-179 or 9.7000000000000001e-26 < (*.f64 x y) < 5.8000000000000006e213

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 42.5%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-102}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 9.7 \cdot 10^{-26}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+213}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot \left(-2\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 48000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* b (* c i))))))
        (t_2 (* (* (* c (+ a (* b c))) i) (- 2.0))))
   (if (<= i -1.5e+47)
     t_2
     (if (<= i -6.8e-63)
       t_1
       (if (<= i -5.2e-103)
         t_2
         (if (<= i 3.6e-56)
           (* (+ (* x y) (* z t)) 2.0)
           (if (<= i 48000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	double t_2 = ((c * (a + (b * c))) * i) * -2.0;
	double tmp;
	if (i <= -1.5e+47) {
		tmp = t_2;
	} else if (i <= -6.8e-63) {
		tmp = t_1;
	} else if (i <= -5.2e-103) {
		tmp = t_2;
	} else if (i <= 3.6e-56) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 48000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    t_2 = ((c * (a + (b * c))) * i) * -2.0d0
    if (i <= (-1.5d+47)) then
        tmp = t_2
    else if (i <= (-6.8d-63)) then
        tmp = t_1
    else if (i <= (-5.2d-103)) then
        tmp = t_2
    else if (i <= 3.6d-56) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (i <= 48000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	double t_2 = ((c * (a + (b * c))) * i) * -2.0;
	double tmp;
	if (i <= -1.5e+47) {
		tmp = t_2;
	} else if (i <= -6.8e-63) {
		tmp = t_1;
	} else if (i <= -5.2e-103) {
		tmp = t_2;
	} else if (i <= 3.6e-56) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 48000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (b * (c * i))))
	t_2 = ((c * (a + (b * c))) * i) * -2.0
	tmp = 0
	if i <= -1.5e+47:
		tmp = t_2
	elif i <= -6.8e-63:
		tmp = t_1
	elif i <= -5.2e-103:
		tmp = t_2
	elif i <= 3.6e-56:
		tmp = ((x * y) + (z * t)) * 2.0
	elif i <= 48000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))))
	t_2 = Float64(Float64(Float64(c * Float64(a + Float64(b * c))) * i) * Float64(-2.0))
	tmp = 0.0
	if (i <= -1.5e+47)
		tmp = t_2;
	elseif (i <= -6.8e-63)
		tmp = t_1;
	elseif (i <= -5.2e-103)
		tmp = t_2;
	elseif (i <= 3.6e-56)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (i <= 48000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	t_2 = ((c * (a + (b * c))) * i) * -2.0;
	tmp = 0.0;
	if (i <= -1.5e+47)
		tmp = t_2;
	elseif (i <= -6.8e-63)
		tmp = t_1;
	elseif (i <= -5.2e-103)
		tmp = t_2;
	elseif (i <= 3.6e-56)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (i <= 48000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-2.0)), $MachinePrecision]}, If[LessEqual[i, -1.5e+47], t$95$2, If[LessEqual[i, -6.8e-63], t$95$1, If[LessEqual[i, -5.2e-103], t$95$2, If[LessEqual[i, 3.6e-56], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[i, 48000000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.5000000000000001e47 or -6.79999999999999997e-63 < i < -5.19999999999999993e-103 or 4.8e7 < i

   1. Initial program 93.2%

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

   3. Taylor expanded in i around inf 93.2%

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

      1. associate--l+ 93.2%

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

      2. associate-/l* 94.0%

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

      3. associate-/l* 96.5%

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

      4. +-commutative 96.5%

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

      5. fma-undefine 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in i around inf 82.1%

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

   if -1.5000000000000001e47 < i < -6.79999999999999997e-63 or 3.59999999999999978e-56 < i < 4.8e7

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 86.1%

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

   4. Taylor expanded in a around 0 75.5%

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

   if -5.19999999999999993e-103 < i < 3.59999999999999978e-56

   1. Initial program 93.2%

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

   3. Taylor expanded in c around 0 80.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;\left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot \left(-2\right)\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-63}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-103}:\\ \;\;\;\;\left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot \left(-2\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 48000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot \left(-2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+262}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.25e+85)
   (* 2.0 (- (* x y) (* a (* c i))))
   (if (<= (* x y) 3.9e+262)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* (* x y) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.25e+85) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if ((x * y) <= 3.9e+262) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = (x * y) * 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 ((x * y) <= (-2.25d+85)) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if ((x * y) <= 3.9d+262) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = (x * y) * 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 ((x * y) <= -2.25e+85) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if ((x * y) <= 3.9e+262) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2.25e+85:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif (x * y) <= 3.9e+262:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.25e+85)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (Float64(x * y) <= 3.9e+262)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2.25e+85)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif ((x * y) <= 3.9e+262)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.25e+85], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.9e+262], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.25000000000000003e85

   1. Initial program 89.5%

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

      1. fma-define 89.5%

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

      2. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

      1. fma-define 93.6%

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

      2. +-commutative 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around inf 77.3%

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

   8. Taylor expanded in z around 0 87.5%

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

   9. Taylor expanded in b around 0 83.2%

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

   if -2.25000000000000003e85 < (*.f64 x y) < 3.89999999999999985e262

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 80.3%

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

   if 3.89999999999999985e262 < (*.f64 x y)

   1. Initial program 72.7%

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

   3. Taylor expanded in x around inf 86.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+262}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+18} \lor \neg \left(c \leq 32000\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.2e+18) (not (<= c 32000.0)))
   (* 2.0 (- (* z t) (* 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 <= -2.2e+18) || !(c <= 32000.0)) {
		tmp = 2.0 * ((z * t) - (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 <= (-2.2d+18)) .or. (.not. (c <= 32000.0d0))) then
        tmp = 2.0d0 * ((z * t) - (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 <= -2.2e+18) || !(c <= 32000.0)) {
		tmp = 2.0 * ((z * t) - (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 <= -2.2e+18) or not (c <= 32000.0):
		tmp = 2.0 * ((z * t) - (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 <= -2.2e+18) || !(c <= 32000.0))
		tmp = Float64(2.0 * Float64(Float64(z * t) - 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 <= -2.2e+18) || ~((c <= 32000.0)))
		tmp = 2.0 * ((z * t) - (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, -2.2e+18], N[Not[LessEqual[c, 32000.0]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(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 < -2.2e18 or 32000 < c

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 87.7%

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

   if -2.2e18 < c < 32000

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 96.2%

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

      1. *-commutative 96.2%

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

   5. Simplified 96.2%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+18} \lor \neg \left(c \leq 32000\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;y \leq -100000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1 \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= y -100000.0)
     (* (+ (* x y) (* z t)) 2.0)
     (if (<= y 6.5e+50)
       (* 2.0 (- (* z t) (* c (* t_1 i))))
       (* 2.0 (- (* x y) (* t_1 (* 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 tmp;
	if (y <= -100000.0) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (y <= 6.5e+50) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else {
		tmp = 2.0 * ((x * y) - (t_1 * (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 = a + (b * c)
    if (y <= (-100000.0d0)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (y <= 6.5d+50) then
        tmp = 2.0d0 * ((z * t) - (c * (t_1 * i)))
    else
        tmp = 2.0d0 * ((x * y) - (t_1 * (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 tmp;
	if (y <= -100000.0) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (y <= 6.5e+50) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else {
		tmp = 2.0 * ((x * y) - (t_1 * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if y <= -100000.0:
		tmp = ((x * y) + (z * t)) * 2.0
	elif y <= 6.5e+50:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	else:
		tmp = 2.0 * ((x * y) - (t_1 * (c * 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 (y <= -100000.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (y <= 6.5e+50)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(t_1 * 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);
	tmp = 0.0;
	if (y <= -100000.0)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (y <= 6.5e+50)
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	else
		tmp = 2.0 * ((x * y) - (t_1 * (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]}, If[LessEqual[y, -100000.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[y, 6.5e+50], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e5

   1. Initial program 86.9%

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

   3. Taylor expanded in c around 0 67.9%

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

   if -1e5 < y < 6.5000000000000003e50

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 80.0%

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

   if 6.5000000000000003e50 < y

   1. Initial program 89.6%

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

      1. fma-define 89.7%

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

      2. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

      1. fma-define 93.6%

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

      2. +-commutative 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around inf 89.6%

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

   8. Taylor expanded in z around 0 92.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -100000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{+30} \lor \neg \left(c \leq 13500000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.85e+30) (not (<= c 13500000000.0)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.85e+30) || !(c <= 13500000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.85d+30)) .or. (.not. (c <= 13500000000.0d0))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.85e+30) || !(c <= 13500000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.85e+30) or not (c <= 13500000000.0):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.85e+30) || !(c <= 13500000000.0))
		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 <= -1.85e+30) || ~((c <= 13500000000.0)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.85e+30], N[Not[LessEqual[c, 13500000000.0]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.85000000000000008e30 or 1.35e10 < c

   1. Initial program 85.3%

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

   3. Taylor expanded in i around inf 83.6%

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

   4. Taylor expanded in i around 0 83.6%

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

   if -1.85000000000000008e30 < c < 1.35e10

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0 69.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{+30} \lor \neg \left(c \leq 13500000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+30}:\\ \;\;\;\;\left(\left(c \cdot t\_1\right) \cdot i\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq 15000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t\_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -4.2e+30)
     (* (* (* c t_1) i) (- 2.0))
     (if (<= c 15000000000.0)
       (* (+ (* x y) (* z t)) 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 <= -4.2e+30) {
		tmp = ((c * t_1) * i) * -2.0;
	} else if (c <= 15000000000.0) {
		tmp = ((x * y) + (z * t)) * 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 <= (-4.2d+30)) then
        tmp = ((c * t_1) * i) * -2.0d0
    else if (c <= 15000000000.0d0) then
        tmp = ((x * y) + (z * t)) * 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 <= -4.2e+30) {
		tmp = ((c * t_1) * i) * -2.0;
	} else if (c <= 15000000000.0) {
		tmp = ((x * y) + (z * t)) * 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 <= -4.2e+30:
		tmp = ((c * t_1) * i) * -2.0
	elif c <= 15000000000.0:
		tmp = ((x * y) + (z * t)) * 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 <= -4.2e+30)
		tmp = Float64(Float64(Float64(c * t_1) * i) * Float64(-2.0));
	elseif (c <= 15000000000.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 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 <= -4.2e+30)
		tmp = ((c * t_1) * i) * -2.0;
	elseif (c <= 15000000000.0)
		tmp = ((x * y) + (z * t)) * 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, -4.2e+30], N[(N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, 15000000000.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.2e30

   1. Initial program 91.1%

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

   3. Taylor expanded in i around inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 84.3%

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

      4. +-commutative 84.3%

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

      5. fma-undefine 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in i around inf 86.1%

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

   if -4.2e30 < c < 1.5e10

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0 69.6%

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

   if 1.5e10 < c

   1. Initial program 78.9%

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

   3. Taylor expanded in i around inf 82.9%

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

   4. Taylor expanded in i around 0 82.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+30}:\\ \;\;\;\;\left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq 15000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+52} \lor \neg \left(i \leq 5.5 \cdot 10^{+134}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1e+52) (not (<= i 5.5e+134)))
   (* -2.0 (* a (* 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 ((i <= -1e+52) || !(i <= 5.5e+134)) {
		tmp = -2.0 * (a * (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 ((i <= (-1d+52)) .or. (.not. (i <= 5.5d+134))) then
        tmp = (-2.0d0) * (a * (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 ((i <= -1e+52) || !(i <= 5.5e+134)) {
		tmp = -2.0 * (a * (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 (i <= -1e+52) or not (i <= 5.5e+134):
		tmp = -2.0 * (a * (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 ((i <= -1e+52) || !(i <= 5.5e+134))
		tmp = Float64(-2.0 * Float64(a * Float64(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 ((i <= -1e+52) || ~((i <= 5.5e+134)))
		tmp = -2.0 * (a * (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[i, -1e+52], N[Not[LessEqual[i, 5.5e+134]], $MachinePrecision]], N[(-2.0 * N[(a * N[(c * 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 i < -9.9999999999999999e51 or 5.4999999999999999e134 < i

   1. Initial program 92.8%

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

   3. Taylor expanded in i around inf 72.1%

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

   4. Taylor expanded in c around 0 62.4%

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

      1. *-commutative 62.4%

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

   6. Simplified 62.4%

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

   if -9.9999999999999999e51 < i < 5.4999999999999999e134

   1. Initial program 93.6%

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

   3. Taylor expanded in c around 0 67.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+52} \lor \neg \left(i \leq 5.5 \cdot 10^{+134}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{-12} \lor \neg \left(x \cdot y \leq 1.05 \cdot 10^{+213}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -6.8e-12) (not (<= (* x y) 1.05e+213)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -6.8e-12) || !((x * y) <= 1.05e+213)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-6.8d-12)) .or. (.not. ((x * y) <= 1.05d+213))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -6.8e-12) || !((x * y) <= 1.05e+213)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -6.8e-12) or not ((x * y) <= 1.05e+213):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -6.8e-12) || !(Float64(x * y) <= 1.05e+213))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -6.8e-12) || ~(((x * y) <= 1.05e+213)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -6.8e-12], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.05e+213]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.8000000000000001e-12 or 1.05e213 < (*.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf 57.9%

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

   if -6.8000000000000001e-12 < (*.f64 x y) < 1.05e213

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 37.5%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{-12} \lor \neg \left(x \cdot y \leq 1.05 \cdot 10^{+213}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

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 93.3%

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

3. Taylor expanded in z around inf 27.4%

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

4. Final simplification 27.4%

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

Developer target: 94.1% 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 2024106 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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