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

Percentage Accurate: 90.5% → 96.2%

Time: 19.1s

Alternatives: 17

Speedup: 0.5×

• 47.0% 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: 90.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. fma-define 97.2%

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

      2. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   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 y around inf 14.3%

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

   4. Taylor expanded in c around 0 50.0%

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

   5. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 97.4%

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

Alternative 2: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_3 := 2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.02 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 820000000000 \lor \neg \left(c \leq 1.35 \cdot 10^{+161}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* a (* c i)))))
        (t_2 (* (+ (* x y) (* z t)) 2.0))
        (t_3 (* 2.0 (* (* (+ a (* b c)) i) (- c)))))
   (if (<= c -2.9e-22)
     t_3
     (if (<= c -1.1e-185)
       t_2
       (if (<= c -2.02e-221)
         t_1
         (if (<= c 5.6e-126)
           t_2
           (if (<= c 6.4e-59)
             t_1
             (if (or (<= c 820000000000.0) (not (<= c 1.35e+161)))
               (* 2.0 (- (* x y) (* c (* b (* c i)))))
               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 * ((z * t) - (a * (c * i)));
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -2.9e-22) {
		tmp = t_3;
	} else if (c <= -1.1e-185) {
		tmp = t_2;
	} else if (c <= -2.02e-221) {
		tmp = t_1;
	} else if (c <= 5.6e-126) {
		tmp = t_2;
	} else if (c <= 6.4e-59) {
		tmp = t_1;
	} else if ((c <= 820000000000.0) || !(c <= 1.35e+161)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} 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 * ((z * t) - (a * (c * i)))
    t_2 = ((x * y) + (z * t)) * 2.0d0
    t_3 = 2.0d0 * (((a + (b * c)) * i) * -c)
    if (c <= (-2.9d-22)) then
        tmp = t_3
    else if (c <= (-1.1d-185)) then
        tmp = t_2
    else if (c <= (-2.02d-221)) then
        tmp = t_1
    else if (c <= 5.6d-126) then
        tmp = t_2
    else if (c <= 6.4d-59) then
        tmp = t_1
    else if ((c <= 820000000000.0d0) .or. (.not. (c <= 1.35d+161))) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    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 * ((z * t) - (a * (c * i)));
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -2.9e-22) {
		tmp = t_3;
	} else if (c <= -1.1e-185) {
		tmp = t_2;
	} else if (c <= -2.02e-221) {
		tmp = t_1;
	} else if (c <= 5.6e-126) {
		tmp = t_2;
	} else if (c <= 6.4e-59) {
		tmp = t_1;
	} else if ((c <= 820000000000.0) || !(c <= 1.35e+161)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (a * (c * i)))
	t_2 = ((x * y) + (z * t)) * 2.0
	t_3 = 2.0 * (((a + (b * c)) * i) * -c)
	tmp = 0
	if c <= -2.9e-22:
		tmp = t_3
	elif c <= -1.1e-185:
		tmp = t_2
	elif c <= -2.02e-221:
		tmp = t_1
	elif c <= 5.6e-126:
		tmp = t_2
	elif c <= 6.4e-59:
		tmp = t_1
	elif (c <= 820000000000.0) or not (c <= 1.35e+161):
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_3 = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)))
	tmp = 0.0
	if (c <= -2.9e-22)
		tmp = t_3;
	elseif (c <= -1.1e-185)
		tmp = t_2;
	elseif (c <= -2.02e-221)
		tmp = t_1;
	elseif (c <= 5.6e-126)
		tmp = t_2;
	elseif (c <= 6.4e-59)
		tmp = t_1;
	elseif ((c <= 820000000000.0) || !(c <= 1.35e+161))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	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 * ((z * t) - (a * (c * i)));
	t_2 = ((x * y) + (z * t)) * 2.0;
	t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	tmp = 0.0;
	if (c <= -2.9e-22)
		tmp = t_3;
	elseif (c <= -1.1e-185)
		tmp = t_2;
	elseif (c <= -2.02e-221)
		tmp = t_1;
	elseif (c <= 5.6e-126)
		tmp = t_2;
	elseif (c <= 6.4e-59)
		tmp = t_1;
	elseif ((c <= 820000000000.0) || ~((c <= 1.35e+161)))
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.9e-22], t$95$3, If[LessEqual[c, -1.1e-185], t$95$2, If[LessEqual[c, -2.02e-221], t$95$1, If[LessEqual[c, 5.6e-126], t$95$2, If[LessEqual[c, 6.4e-59], t$95$1, If[Or[LessEqual[c, 820000000000.0], N[Not[LessEqual[c, 1.35e+161]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9000000000000002e-22 or 8.2e11 < c < 1.3499999999999999e161

   1. Initial program 86.3%

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

   3. Taylor expanded in i around inf 75.8%

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

   if -2.9000000000000002e-22 < c < -1.1e-185 or -2.0199999999999999e-221 < c < 5.59999999999999983e-126

   1. Initial program 95.7%

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

   3. Taylor expanded in c around 0 80.8%

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

   if -1.1e-185 < c < -2.0199999999999999e-221 or 5.59999999999999983e-126 < c < 6.3999999999999998e-59

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 69.3%

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

   4. Taylor expanded in c around 0 88.1%

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

      1. +-commutative 88.1%

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

      2. mul-1-neg 88.1%

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

      3. sub-neg 88.1%

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

   6. Simplified 88.1%

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

   if 6.3999999999999998e-59 < c < 8.2e11 or 1.3499999999999999e161 < c

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 88.0%

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

   4. Taylor expanded in a around 0 81.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{-22}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-185}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -2.02 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 820000000000 \lor \neg \left(c \leq 1.35 \cdot 10^{+161}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.8% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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

   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 y around inf 14.3%

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

   4. Taylor expanded in c around 0 50.0%

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

   5. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 95.4%

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

Alternative 4: 96.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. fma-define 97.2%

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

      2. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

      1. fma-define 99.3%

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

      2. +-commutative 99.3%

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

   6. Applied egg-rr 99.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 14.3%

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

   4. Taylor expanded in c around 0 50.0%

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

   5. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 97.4%

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

Alternative 5: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_3 := 2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i)))
        (t_2 (* (+ (* x y) (* z t)) 2.0))
        (t_3 (* 2.0 (* (* (+ a (* b c)) i) (- c)))))
   (if (<= c -9.5e-22)
     t_3
     (if (<= c -2.4e-186)
       t_2
       (if (<= c -1.2e-221)
         (* 2.0 (- (* z t) t_1))
         (if (<= c 2e-119)
           t_2
           (if (<= c 1.15e-9) (* 2.0 (- (* x y) t_1)) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -9.5e-22) {
		tmp = t_3;
	} else if (c <= -2.4e-186) {
		tmp = t_2;
	} else if (c <= -1.2e-221) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2e-119) {
		tmp = t_2;
	} else if (c <= 1.15e-9) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (c * i)
    t_2 = ((x * y) + (z * t)) * 2.0d0
    t_3 = 2.0d0 * (((a + (b * c)) * i) * -c)
    if (c <= (-9.5d-22)) then
        tmp = t_3
    else if (c <= (-2.4d-186)) then
        tmp = t_2
    else if (c <= (-1.2d-221)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 2d-119) then
        tmp = t_2
    else if (c <= 1.15d-9) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -9.5e-22) {
		tmp = t_3;
	} else if (c <= -2.4e-186) {
		tmp = t_2;
	} else if (c <= -1.2e-221) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2e-119) {
		tmp = t_2;
	} else if (c <= 1.15e-9) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	t_2 = ((x * y) + (z * t)) * 2.0
	t_3 = 2.0 * (((a + (b * c)) * i) * -c)
	tmp = 0
	if c <= -9.5e-22:
		tmp = t_3
	elif c <= -2.4e-186:
		tmp = t_2
	elif c <= -1.2e-221:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 2e-119:
		tmp = t_2
	elif c <= 1.15e-9:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_3 = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)))
	tmp = 0.0
	if (c <= -9.5e-22)
		tmp = t_3;
	elseif (c <= -2.4e-186)
		tmp = t_2;
	elseif (c <= -1.2e-221)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 2e-119)
		tmp = t_2;
	elseif (c <= 1.15e-9)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	t_2 = ((x * y) + (z * t)) * 2.0;
	t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	tmp = 0.0;
	if (c <= -9.5e-22)
		tmp = t_3;
	elseif (c <= -2.4e-186)
		tmp = t_2;
	elseif (c <= -1.2e-221)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 2e-119)
		tmp = t_2;
	elseif (c <= 1.15e-9)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e-22], t$95$3, If[LessEqual[c, -2.4e-186], t$95$2, If[LessEqual[c, -1.2e-221], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-119], t$95$2, If[LessEqual[c, 1.15e-9], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.4999999999999994e-22 or 1.15e-9 < c

   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 i around inf 74.5%

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

   if -9.4999999999999994e-22 < c < -2.40000000000000003e-186 or -1.20000000000000012e-221 < c < 2.00000000000000003e-119

   1. Initial program 95.8%

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

   3. Taylor expanded in c around 0 81.2%

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

   if -2.40000000000000003e-186 < c < -1.20000000000000012e-221

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 56.8%

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

   4. Taylor expanded in c around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. mul-1-neg 90.4%

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

      3. sub-neg 90.4%

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

   6. Simplified 90.4%

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

   if 2.00000000000000003e-119 < c < 1.15e-9

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 73.8%

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

   4. Taylor expanded in b around 0 67.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-186}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+92}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+221} \lor \neg \left(a \leq 1.02 \cdot 10^{+300}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -7.8e+92)
   (* -2.0 (* i (* a c)))
   (if (<= a 3.6e+179)
     (* (+ (* x y) (* z t)) 2.0)
     (if (or (<= a 2.05e+221) (not (<= a 1.02e+300)))
       (* (* a (* c i)) -2.0)
       (* 2.0 (* t (+ z (* x (/ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -7.8e+92) {
		tmp = -2.0 * (i * (a * c));
	} else if (a <= 3.6e+179) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((a <= 2.05e+221) || !(a <= 1.02e+300)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-7.8d+92)) then
        tmp = (-2.0d0) * (i * (a * c))
    else if (a <= 3.6d+179) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((a <= 2.05d+221) .or. (.not. (a <= 1.02d+300))) then
        tmp = (a * (c * i)) * (-2.0d0)
    else
        tmp = 2.0d0 * (t * (z + (x * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -7.8e+92) {
		tmp = -2.0 * (i * (a * c));
	} else if (a <= 3.6e+179) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((a <= 2.05e+221) || !(a <= 1.02e+300)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -7.8e+92:
		tmp = -2.0 * (i * (a * c))
	elif a <= 3.6e+179:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (a <= 2.05e+221) or not (a <= 1.02e+300):
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = 2.0 * (t * (z + (x * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -7.8e+92)
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	elseif (a <= 3.6e+179)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif ((a <= 2.05e+221) || !(a <= 1.02e+300))
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	else
		tmp = Float64(2.0 * Float64(t * Float64(z + Float64(x * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -7.8e+92)
		tmp = -2.0 * (i * (a * c));
	elseif (a <= 3.6e+179)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((a <= 2.05e+221) || ~((a <= 1.02e+300)))
		tmp = (a * (c * i)) * -2.0;
	else
		tmp = 2.0 * (t * (z + (x * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -7.8e+92], N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+179], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[Or[LessEqual[a, 2.05e+221], N[Not[LessEqual[a, 1.02e+300]], $MachinePrecision]], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(t * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.80000000000000022e92

   1. Initial program 92.5%

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

   3. Taylor expanded in a around inf 51.3%

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

   4. Taylor expanded in a around 0 51.3%

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

      1. associate-*r* 56.3%

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

      2. *-commutative 56.3%

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

      3. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   if -7.80000000000000022e92 < a < 3.5999999999999998e179

   1. Initial program 94.0%

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

   3. Taylor expanded in c around 0 59.7%

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

   if 3.5999999999999998e179 < a < 2.04999999999999985e221 or 1.02000000000000002e300 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 81.4%

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

   4. Taylor expanded in a around 0 81.4%

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

   if 2.04999999999999985e221 < a < 1.02000000000000002e300

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 76.5%

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

   4. Taylor expanded in c around 0 54.1%

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

   5. Taylor expanded in t around inf 53.8%

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

      1. associate-/l* 58.3%

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

   7. Simplified 58.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+92}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+179}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+221} \lor \neg \left(a \leq 1.02 \cdot 10^{+300}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+185} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+97}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1e+185) (not (<= (* x y) 2e+97)))
   (* 2.0 (- (* x y) (* c (* b (* c i)))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e+185) || !((x * y) <= 2e+97)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1d+185)) .or. (.not. ((x * y) <= 2d+97))) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e+185) || !((x * y) <= 2e+97)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1e+185) or not ((x * y) <= 2e+97):
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+185) || !(Float64(x * y) <= 2e+97))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1e+185) || ~(((x * y) <= 2e+97)))
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+185], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+97]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999998e184 or 2.0000000000000001e97 < (*.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in a around 0 82.3%

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

   if -9.9999999999999998e184 < (*.f64 x y) < 2.0000000000000001e97

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 81.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+185} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+97}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(\frac{z \cdot t}{i} - c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= a -5.8e+92)
     (* 2.0 (* i (- (/ (* z t) i) (* c (+ a (* b c))))))
     (if (<= a 1.25e+115)
       (* 2.0 (- t_1 (* (* b c) (* c i))))
       (* 2.0 (- t_1 (* a (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (a <= -5.8e+92) {
		tmp = 2.0 * (i * (((z * t) / i) - (c * (a + (b * c)))));
	} else if (a <= 1.25e+115) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (a <= (-5.8d+92)) then
        tmp = 2.0d0 * (i * (((z * t) / i) - (c * (a + (b * c)))))
    else if (a <= 1.25d+115) then
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (a <= -5.8e+92) {
		tmp = 2.0 * (i * (((z * t) / i) - (c * (a + (b * c)))));
	} else if (a <= 1.25e+115) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (a * (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 <= -5.8e+92:
		tmp = 2.0 * (i * (((z * t) / i) - (c * (a + (b * c)))))
	elif a <= 1.25e+115:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	else:
		tmp = 2.0 * (t_1 - (a * (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 <= -5.8e+92)
		tmp = Float64(2.0 * Float64(i * Float64(Float64(Float64(z * t) / i) - Float64(c * Float64(a + Float64(b * c))))));
	elseif (a <= 1.25e+115)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * 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 <= -5.8e+92)
		tmp = 2.0 * (i * (((z * t) / i) - (c * (a + (b * c)))));
	elseif (a <= 1.25e+115)
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	else
		tmp = 2.0 * (t_1 - (a * (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[LessEqual[a, -5.8e+92], N[(2.0 * N[(i * N[(N[(N[(z * t), $MachinePrecision] / i), $MachinePrecision] - N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+115], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8000000000000001e92

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 76.0%

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

   4. Taylor expanded in i around inf 87.9%

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

   if -5.8000000000000001e92 < a < 1.25000000000000002e115

   1. Initial program 94.9%

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

      1. fma-define 95.5%

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

      2. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

      1. fma-define 97.5%

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

      2. +-commutative 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in a around 0 90.5%

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

   if 1.25000000000000002e115 < a

   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 a around inf 83.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(\frac{z \cdot t}{i} - c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-116}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)) (t_2 (* 2.0 (* z t))))
   (if (<= t -1.5e-101)
     t_2
     (if (<= t -7.5e-308)
       t_1
       (if (<= t 8.2e-116)
         (* (* a (* c i)) -2.0)
         (if (<= t 3.85e+105) 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 = (x * y) * 2.0;
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.5e-101) {
		tmp = t_2;
	} else if (t <= -7.5e-308) {
		tmp = t_1;
	} else if (t <= 8.2e-116) {
		tmp = (a * (c * i)) * -2.0;
	} else if (t <= 3.85e+105) {
		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 = (x * y) * 2.0d0
    t_2 = 2.0d0 * (z * t)
    if (t <= (-1.5d-101)) then
        tmp = t_2
    else if (t <= (-7.5d-308)) then
        tmp = t_1
    else if (t <= 8.2d-116) then
        tmp = (a * (c * i)) * (-2.0d0)
    else if (t <= 3.85d+105) 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 = (x * y) * 2.0;
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.5e-101) {
		tmp = t_2;
	} else if (t <= -7.5e-308) {
		tmp = t_1;
	} else if (t <= 8.2e-116) {
		tmp = (a * (c * i)) * -2.0;
	} else if (t <= 3.85e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.5e-101:
		tmp = t_2
	elif t <= -7.5e-308:
		tmp = t_1
	elif t <= 8.2e-116:
		tmp = (a * (c * i)) * -2.0
	elif t <= 3.85e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1.5e-101)
		tmp = t_2;
	elseif (t <= -7.5e-308)
		tmp = t_1;
	elseif (t <= 8.2e-116)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	elseif (t <= 3.85e+105)
		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 = (x * y) * 2.0;
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1.5e-101)
		tmp = t_2;
	elseif (t <= -7.5e-308)
		tmp = t_1;
	elseif (t <= 8.2e-116)
		tmp = (a * (c * i)) * -2.0;
	elseif (t <= 3.85e+105)
		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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-101], t$95$2, If[LessEqual[t, -7.5e-308], t$95$1, If[LessEqual[t, 8.2e-116], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, 3.85e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5000000000000002e-101 or 3.85000000000000006e105 < t

   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. Add Preprocessing

   3. Taylor expanded in z around inf 46.2%

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

   if -1.5000000000000002e-101 < t < -7.4999999999999998e-308 or 8.1999999999999998e-116 < t < 3.85000000000000006e105

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 42.6%

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

   if -7.4999999999999998e-308 < t < 8.1999999999999998e-116

   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. Add Preprocessing

   3. Taylor expanded in a around inf 50.0%

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

   4. Taylor expanded in a around 0 50.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-116}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+105}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + \frac{z \cdot t}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+98)
   (* 2.0 (* t (+ z (* x (/ y t)))))
   (if (<= (* x y) 5e+57)
     (* 2.0 (- (* z t) (* a (* c i))))
     (* 2.0 (* x (+ y (/ (* z t) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+98) {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	} else if ((x * y) <= 5e+57) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (x * (y + ((z * t) / x)));
	}
	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) <= (-5d+98)) then
        tmp = 2.0d0 * (t * (z + (x * (y / t))))
    else if ((x * y) <= 5d+57) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = 2.0d0 * (x * (y + ((z * t) / x)))
    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) <= -5e+98) {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	} else if ((x * y) <= 5e+57) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (x * (y + ((z * t) / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+98:
		tmp = 2.0 * (t * (z + (x * (y / t))))
	elif (x * y) <= 5e+57:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = 2.0 * (x * (y + ((z * t) / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+98)
		tmp = Float64(2.0 * Float64(t * Float64(z + Float64(x * Float64(y / t)))));
	elseif (Float64(x * y) <= 5e+57)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(x * Float64(y + Float64(Float64(z * t) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+98)
		tmp = 2.0 * (t * (z + (x * (y / t))));
	elseif ((x * y) <= 5e+57)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = 2.0 * (x * (y + ((z * t) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+98], N[(2.0 * N[(t * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+57], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * N[(y + N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999998e98

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 87.7%

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

   4. Taylor expanded in c around 0 73.6%

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

   5. Taylor expanded in t around inf 75.7%

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

      1. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   if -4.9999999999999998e98 < (*.f64 x y) < 4.99999999999999972e57

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 83.5%

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

   4. Taylor expanded in c around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. sub-neg 66.5%

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

   6. Simplified 66.5%

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

   if 4.99999999999999972e57 < (*.f64 x y)

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 89.3%

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

   4. Taylor expanded in c around 0 63.1%

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

   5. Taylor expanded in x around inf 63.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + \frac{z \cdot t}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= t -1.7e-33)
     (* 2.0 (- (* z t) (* a (* c i))))
     (if (<= t 2.7e+106) (* 2.0 (- (* x y) t_1)) (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (t <= -1.7e-33) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (t <= 2.7e+106) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (t <= (-1.7d-33)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (t <= 2.7d+106) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (t <= -1.7e-33) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (t <= 2.7e+106) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if t <= -1.7e-33:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif t <= 2.7e+106:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (t <= -1.7e-33)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (t <= 2.7e+106)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (t <= -1.7e-33)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (t <= 2.7e+106)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-33], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+106], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e-33

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 79.4%

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

   4. Taylor expanded in c around 0 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. sub-neg 66.0%

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

   6. Simplified 66.0%

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

   if -1.7e-33 < t < 2.70000000000000006e106

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 82.3%

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

   if 2.70000000000000006e106 < t

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 77.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -2.75e+29)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 7e-58)
       (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
       (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.75e+29) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-58) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-2.75d+29)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 7d-58) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.75e+29) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-58) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -2.75e+29:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 7e-58:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -2.75e+29)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 7e-58)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -2.75e+29)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 7e-58)
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.75e+29], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-58], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.75e29

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 88.2%

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

   if -2.75e29 < c < 6.9999999999999998e-58

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 90.0%

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

   if 6.9999999999999998e-58 < c

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 85.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 36000000000 \lor \neg \left(i \leq 5.5 \cdot 10^{+57}\right) \land i \leq 7 \cdot 10^{+168}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i 36000000000.0) (and (not (<= i 5.5e+57)) (<= i 7e+168)))
   (* (+ (* x y) (* z t)) 2.0)
   (* (* a (* c i)) -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 <= 36000000000.0) || (!(i <= 5.5e+57) && (i <= 7e+168))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -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 <= 36000000000.0d0) .or. (.not. (i <= 5.5d+57)) .and. (i <= 7d+168)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (a * (c * i)) * (-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 <= 36000000000.0) || (!(i <= 5.5e+57) && (i <= 7e+168))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= 36000000000.0) or (not (i <= 5.5e+57) and (i <= 7e+168)):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (a * (c * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= 36000000000.0) || (!(i <= 5.5e+57) && (i <= 7e+168)))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= 36000000000.0) || (~((i <= 5.5e+57)) && (i <= 7e+168)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (a * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, 36000000000.0], And[N[Not[LessEqual[i, 5.5e+57]], $MachinePrecision], LessEqual[i, 7e+168]]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 3.6e10 or 5.5000000000000002e57 < i < 7.0000000000000004e168

   1. Initial program 93.3%

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

   3. Taylor expanded in c around 0 60.6%

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

   if 3.6e10 < i < 5.5000000000000002e57 or 7.0000000000000004e168 < i

   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 a around inf 55.1%

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

   4. Taylor expanded in a around 0 55.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 36000000000 \lor \neg \left(i \leq 5.5 \cdot 10^{+57}\right) \land i \leq 7 \cdot 10^{+168}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i))))
   (if (<= t -1.4e-101)
     (* 2.0 (- (* z t) t_1))
     (if (<= t 4.8e+114)
       (* 2.0 (- (* x y) t_1))
       (* 2.0 (* t (+ z (* x (/ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double tmp;
	if (t <= -1.4e-101) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (t <= 4.8e+114) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * i)
    if (t <= (-1.4d-101)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (t <= 4.8d+114) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * (t * (z + (x * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double tmp;
	if (t <= -1.4e-101) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (t <= 4.8e+114) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * (t * (z + (x * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	tmp = 0
	if t <= -1.4e-101:
		tmp = 2.0 * ((z * t) - t_1)
	elif t <= 4.8e+114:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * (t * (z + (x * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	tmp = 0.0
	if (t <= -1.4e-101)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (t <= 4.8e+114)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(t * Float64(z + Float64(x * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	tmp = 0.0;
	if (t <= -1.4e-101)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (t <= 4.8e+114)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * (t * (z + (x * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-101], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+114], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999995e-101

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 73.4%

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

   4. Taylor expanded in c around 0 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. sub-neg 63.6%

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

   6. Simplified 63.6%

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

   if -1.39999999999999995e-101 < t < 4.8e114

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 82.8%

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

   4. Taylor expanded in b around 0 64.6%

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

   if 4.8e114 < t

   1. Initial program 81.8%

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

   3. Taylor expanded in y around inf 73.5%

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

   4. Taylor expanded in c around 0 58.1%

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

   5. Taylor expanded in t around inf 64.5%

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

      1. associate-/l* 69.0%

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

   7. Simplified 69.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+106}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -5e-23)
     t_1
     (if (<= t 1.3e-188)
       (* -2.0 (* i (* a c)))
       (if (<= t 1.55e+106) (* (* x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -5e-23) {
		tmp = t_1;
	} else if (t <= 1.3e-188) {
		tmp = -2.0 * (i * (a * c));
	} else if (t <= 1.55e+106) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-5d-23)) then
        tmp = t_1
    else if (t <= 1.3d-188) then
        tmp = (-2.0d0) * (i * (a * c))
    else if (t <= 1.55d+106) then
        tmp = (x * y) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -5e-23) {
		tmp = t_1;
	} else if (t <= 1.3e-188) {
		tmp = -2.0 * (i * (a * c));
	} else if (t <= 1.55e+106) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -5e-23:
		tmp = t_1
	elif t <= 1.3e-188:
		tmp = -2.0 * (i * (a * c))
	elif t <= 1.55e+106:
		tmp = (x * y) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -5e-23)
		tmp = t_1;
	elseif (t <= 1.3e-188)
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	elseif (t <= 1.55e+106)
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -5e-23)
		tmp = t_1;
	elseif (t <= 1.3e-188)
		tmp = -2.0 * (i * (a * c));
	elseif (t <= 1.55e+106)
		tmp = (x * y) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-23], t$95$1, If[LessEqual[t, 1.3e-188], N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+106], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e-23 or 1.55e106 < t

   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 z around inf 50.8%

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

   if -5.0000000000000002e-23 < t < 1.3e-188

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 38.1%

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

   4. Taylor expanded in a around 0 38.1%

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

      1. associate-*r* 41.1%

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

      2. *-commutative 41.1%

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

      3. *-commutative 41.1%

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

   6. Simplified 41.1%

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

   if 1.3e-188 < t < 1.55e106

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+106}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-110} \lor \neg \left(t \leq 1.32 \cdot 10^{+106}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -2.35e-110) (not (<= t 1.32e+106)))
   (* 2.0 (* z t))
   (* (* 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 ((t <= -2.35e-110) || !(t <= 1.32e+106)) {
		tmp = 2.0 * (z * t);
	} 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 ((t <= (-2.35d-110)) .or. (.not. (t <= 1.32d+106))) then
        tmp = 2.0d0 * (z * t)
    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 ((t <= -2.35e-110) || !(t <= 1.32e+106)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -2.35e-110) or not (t <= 1.32e+106):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -2.35e-110) || !(t <= 1.32e+106))
		tmp = Float64(2.0 * Float64(z * t));
	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 ((t <= -2.35e-110) || ~((t <= 1.32e+106)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -2.35e-110], N[Not[LessEqual[t, 1.32e+106]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.34999999999999996e-110 or 1.31999999999999999e106 < t

   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. Add Preprocessing

   3. Taylor expanded in z around inf 46.2%

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

   if -2.34999999999999996e-110 < t < 1.31999999999999999e106

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 35.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-110} \lor \neg \left(t \leq 1.32 \cdot 10^{+106}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

3. Taylor expanded in z around inf 28.9%

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

4. Final simplification 28.9%

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

Developer target: 94.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(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))))