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

Percentage Accurate: 90.0% → 95.9%

Time: 17.3s

Alternatives: 15

Speedup: 0.5×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i))))
     (* t (* 2.0 (+ 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)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = t * (2.0 * (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(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(t * Float64(2.0 * 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[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(2.0 * 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 93.5%

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

      1. fma-define 93.5%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   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 c around 0 66.7%

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

   4. Taylor expanded in t around inf 77.8%

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

      1. distribute-lft-out 77.8%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 98.1%

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

Alternative 2: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -4.7 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.85 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* a -2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1.55e+52)
     t_3
     (if (<= (* x y) -4.7e-11)
       t_1
       (if (<= (* x y) -1.85e-65)
         t_2
         (if (<= (* x y) -6.4e-242)
           t_1
           (if (<= (* x y) 4.8e-77)
             t_2
             (if (<= (* x y) 2.5e+37) 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 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.55e+52) {
		tmp = t_3;
	} else if ((x * y) <= -4.7e-11) {
		tmp = t_1;
	} else if ((x * y) <= -1.85e-65) {
		tmp = t_2;
	} else if ((x * y) <= -6.4e-242) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e-77) {
		tmp = t_2;
	} else if ((x * y) <= 2.5e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * i) * (a * (-2.0d0))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1.55d+52)) then
        tmp = t_3
    else if ((x * y) <= (-4.7d-11)) then
        tmp = t_1
    else if ((x * y) <= (-1.85d-65)) then
        tmp = t_2
    else if ((x * y) <= (-6.4d-242)) then
        tmp = t_1
    else if ((x * y) <= 4.8d-77) then
        tmp = t_2
    else if ((x * y) <= 2.5d+37) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.55e+52) {
		tmp = t_3;
	} else if ((x * y) <= -4.7e-11) {
		tmp = t_1;
	} else if ((x * y) <= -1.85e-65) {
		tmp = t_2;
	} else if ((x * y) <= -6.4e-242) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e-77) {
		tmp = t_2;
	} else if ((x * y) <= 2.5e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (a * -2.0)
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.55e+52:
		tmp = t_3
	elif (x * y) <= -4.7e-11:
		tmp = t_1
	elif (x * y) <= -1.85e-65:
		tmp = t_2
	elif (x * y) <= -6.4e-242:
		tmp = t_1
	elif (x * y) <= 4.8e-77:
		tmp = t_2
	elif (x * y) <= 2.5e+37:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.55e+52)
		tmp = t_3;
	elseif (Float64(x * y) <= -4.7e-11)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.85e-65)
		tmp = t_2;
	elseif (Float64(x * y) <= -6.4e-242)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.8e-77)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.5e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (a * -2.0);
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.55e+52)
		tmp = t_3;
	elseif ((x * y) <= -4.7e-11)
		tmp = t_1;
	elseif ((x * y) <= -1.85e-65)
		tmp = t_2;
	elseif ((x * y) <= -6.4e-242)
		tmp = t_1;
	elseif ((x * y) <= 4.8e-77)
		tmp = t_2;
	elseif ((x * y) <= 2.5e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.55e+52], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4.7e-11], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e-65], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6.4e-242], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.8e-77], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+37], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.55e52 or 2.49999999999999994e37 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf 60.1%

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

   if -1.55e52 < (*.f64 x y) < -4.69999999999999993e-11 or -1.85e-65 < (*.f64 x y) < -6.39999999999999997e-242 or 4.7999999999999998e-77 < (*.f64 x y) < 2.49999999999999994e37

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 43.8%

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

      1. mul-1-neg 43.8%

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

      2. *-commutative 43.8%

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

      3. associate-*l* 37.4%

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

      4. *-commutative 37.4%

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

      5. distribute-rgt-neg-in 37.4%

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

      6. *-commutative 37.4%

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

      7. distribute-rgt-neg-in 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in c around 0 43.8%

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

      1. associate-*r* 43.8%

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

   8. Simplified 43.8%

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

   if -4.69999999999999993e-11 < (*.f64 x y) < -1.85e-65 or -6.39999999999999997e-242 < (*.f64 x y) < 4.7999999999999998e-77

   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 inf 48.7%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -4.7 \cdot 10^{-11}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq -1.85 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-242}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-242}:\\ \;\;\;\;i \cdot \left(a \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* a -2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1.05e+49)
     t_3
     (if (<= (* x y) -3.4e-9)
       t_1
       (if (<= (* x y) -3.2e-67)
         t_2
         (if (<= (* x y) -5.8e-242)
           (* i (* a (* c -2.0)))
           (if (<= (* x y) 8.2e-81)
             t_2
             (if (<= (* x y) 1.7e+37) 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 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.05e+49) {
		tmp = t_3;
	} else if ((x * y) <= -3.4e-9) {
		tmp = t_1;
	} else if ((x * y) <= -3.2e-67) {
		tmp = t_2;
	} else if ((x * y) <= -5.8e-242) {
		tmp = i * (a * (c * -2.0));
	} else if ((x * y) <= 8.2e-81) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * i) * (a * (-2.0d0))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1.05d+49)) then
        tmp = t_3
    else if ((x * y) <= (-3.4d-9)) then
        tmp = t_1
    else if ((x * y) <= (-3.2d-67)) then
        tmp = t_2
    else if ((x * y) <= (-5.8d-242)) then
        tmp = i * (a * (c * (-2.0d0)))
    else if ((x * y) <= 8.2d-81) then
        tmp = t_2
    else if ((x * y) <= 1.7d+37) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.05e+49) {
		tmp = t_3;
	} else if ((x * y) <= -3.4e-9) {
		tmp = t_1;
	} else if ((x * y) <= -3.2e-67) {
		tmp = t_2;
	} else if ((x * y) <= -5.8e-242) {
		tmp = i * (a * (c * -2.0));
	} else if ((x * y) <= 8.2e-81) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e+37) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (a * -2.0)
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.05e+49:
		tmp = t_3
	elif (x * y) <= -3.4e-9:
		tmp = t_1
	elif (x * y) <= -3.2e-67:
		tmp = t_2
	elif (x * y) <= -5.8e-242:
		tmp = i * (a * (c * -2.0))
	elif (x * y) <= 8.2e-81:
		tmp = t_2
	elif (x * y) <= 1.7e+37:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.05e+49)
		tmp = t_3;
	elseif (Float64(x * y) <= -3.4e-9)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.2e-67)
		tmp = t_2;
	elseif (Float64(x * y) <= -5.8e-242)
		tmp = Float64(i * Float64(a * Float64(c * -2.0)));
	elseif (Float64(x * y) <= 8.2e-81)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.7e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (a * -2.0);
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.05e+49)
		tmp = t_3;
	elseif ((x * y) <= -3.4e-9)
		tmp = t_1;
	elseif ((x * y) <= -3.2e-67)
		tmp = t_2;
	elseif ((x * y) <= -5.8e-242)
		tmp = i * (a * (c * -2.0));
	elseif ((x * y) <= 8.2e-81)
		tmp = t_2;
	elseif ((x * y) <= 1.7e+37)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.05e+49], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -3.4e-9], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e-67], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5.8e-242], N[(i * N[(a * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.2e-81], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.7e+37], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.05000000000000005e49 or 1.70000000000000003e37 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf 60.1%

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

   if -1.05000000000000005e49 < (*.f64 x y) < -3.3999999999999998e-9 or 8.19999999999999968e-81 < (*.f64 x y) < 1.70000000000000003e37

   1. Initial program 84.6%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. *-commutative 49.5%

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

      3. associate-*l* 39.4%

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

      4. *-commutative 39.4%

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

      5. distribute-rgt-neg-in 39.4%

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

      6. *-commutative 39.4%

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

      7. distribute-rgt-neg-in 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in c around 0 49.5%

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

      1. associate-*r* 49.5%

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

   8. Simplified 49.5%

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

   if -3.3999999999999998e-9 < (*.f64 x y) < -3.20000000000000021e-67 or -5.8000000000000002e-242 < (*.f64 x y) < 8.19999999999999968e-81

   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 inf 48.7%

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

   if -3.20000000000000021e-67 < (*.f64 x y) < -5.8000000000000002e-242

   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 a around inf 35.3%

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

      1. mul-1-neg 35.3%

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

      2. *-commutative 35.3%

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

      3. associate-*l* 34.4%

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

      4. *-commutative 34.4%

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

      5. distribute-rgt-neg-in 34.4%

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

      6. *-commutative 34.4%

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

      7. distribute-rgt-neg-in 34.4%

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

   5. Simplified 34.4%

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

   6. Taylor expanded in c around 0 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 35.3%

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

      3. *-commutative 35.3%

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

      4. associate-*r* 35.3%

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

      5. associate-*r* 35.3%

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

      6. *-commutative 35.3%

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

   8. Simplified 35.3%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-242}:\\ \;\;\;\;i \cdot \left(a \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+300}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c t_1)))
   (if (<= t_2 (- INFINITY))
     (* c (+ (* -2.0 (* a i)) (* -2.0 (* b (* c i)))))
     (if (<= t_2 1e+300)
       (* (- (+ (* x y) (* z t)) (* t_2 i)) 2.0)
       (* 2.0 (- (* z t) (* c (* t_1 i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = c * ((-2.0 * (a * i)) + (-2.0 * (b * (c * i))));
	} else if (t_2 <= 1e+300) {
		tmp = (((x * y) + (z * t)) - (t_2 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = c * ((-2.0 * (a * i)) + (-2.0 * (b * (c * i))));
	} else if (t_2 <= 1e+300) {
		tmp = (((x * y) + (z * t)) - (t_2 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = c * ((-2.0 * (a * i)) + (-2.0 * (b * (c * i))))
	elif t_2 <= 1e+300:
		tmp = (((x * y) + (z * t)) - (t_2 * i)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(c * Float64(Float64(-2.0 * Float64(a * i)) + Float64(-2.0 * Float64(b * Float64(c * i)))));
	elseif (t_2 <= 1e+300)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_2 * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = c * ((-2.0 * (a * i)) + (-2.0 * (b * (c * i))));
	elseif (t_2 <= 1e+300)
		tmp = (((x * y) + (z * t)) - (t_2 * i)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(c * N[(N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+300], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.6%

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

   3. Taylor expanded in i around inf 91.7%

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

   4. Taylor expanded in c around 0 94.4%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 1.0000000000000001e300

   1. Initial program 97.7%

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

   if 1.0000000000000001e300 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 10^{+300}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 0.5× speedup

Math

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

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 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* t (* 2.0 (+ 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 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = t * (2.0 * (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 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = t * (2.0 * (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 - ((c * t_1) * i)) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = t * (2.0 * (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(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(t * Float64(2.0 * 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 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = t * (2.0 * (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[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(2.0 * 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 93.5%

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

      1. fma-define 93.5%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

      1. fma-define 98.8%

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

      2. +-commutative 98.8%

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

   6. Applied egg-rr 98.8%

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

   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 c around 0 66.7%

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

   4. Taylor expanded in t around inf 77.8%

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

      1. distribute-lft-out 77.8%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 98.1%

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

Alternative 6: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -4.1 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -4.1e+135)
     t_2
     (if (<= c -4e+111)
       t_1
       (if (<= c -3.2e+46)
         t_2
         (if (<= c 3.3e+28)
           t_1
           (* 2.0 (* x (- y (/ (* c (* (* b c) i)) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -4.1e+135) {
		tmp = t_2;
	} else if (c <= -4e+111) {
		tmp = t_1;
	} else if (c <= -3.2e+46) {
		tmp = t_2;
	} else if (c <= 3.3e+28) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-4.1d+135)) then
        tmp = t_2
    else if (c <= (-4d+111)) then
        tmp = t_1
    else if (c <= (-3.2d+46)) then
        tmp = t_2
    else if (c <= 3.3d+28) then
        tmp = t_1
    else
        tmp = 2.0d0 * (x * (y - ((c * ((b * c) * i)) / 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 t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -4.1e+135) {
		tmp = t_2;
	} else if (c <= -4e+111) {
		tmp = t_1;
	} else if (c <= -3.2e+46) {
		tmp = t_2;
	} else if (c <= 3.3e+28) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -4.1e+135:
		tmp = t_2
	elif c <= -4e+111:
		tmp = t_1
	elif c <= -3.2e+46:
		tmp = t_2
	elif c <= 3.3e+28:
		tmp = t_1
	else:
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -4.1e+135)
		tmp = t_2;
	elseif (c <= -4e+111)
		tmp = t_1;
	elseif (c <= -3.2e+46)
		tmp = t_2;
	elseif (c <= 3.3e+28)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(Float64(c * Float64(Float64(b * c) * i)) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -4.1e+135)
		tmp = t_2;
	elseif (c <= -4e+111)
		tmp = t_1;
	elseif (c <= -3.2e+46)
		tmp = t_2;
	elseif (c <= 3.3e+28)
		tmp = t_1;
	else
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.1e+135], t$95$2, If[LessEqual[c, -4e+111], t$95$1, If[LessEqual[c, -3.2e+46], t$95$2, If[LessEqual[c, 3.3e+28], t$95$1, N[(2.0 * N[(x * N[(y - N[(N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.1e135 or -3.99999999999999983e111 < c < -3.1999999999999998e46

   1. Initial program 81.2%

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

   3. Taylor expanded in i around inf 87.9%

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

   4. Taylor expanded in i around 0 87.9%

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

   if -4.1e135 < c < -3.99999999999999983e111 or -3.1999999999999998e46 < c < 3.3e28

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0 81.2%

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

   if 3.3e28 < c

   1. Initial program 80.6%

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

   3. Taylor expanded in x around inf 86.9%

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

   4. Taylor expanded in t around 0 83.7%

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

   5. Taylor expanded in a around 0 78.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{+135}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -2.6e+135)
     t_2
     (if (<= c -2.75e+112)
       t_1
       (if (<= c -1.35e+47)
         t_2
         (if (<= c 2.15e+39) t_1 (* 2.0 (- (* z t) (* c (* (* b c) i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -2.6e+135) {
		tmp = t_2;
	} else if (c <= -2.75e+112) {
		tmp = t_1;
	} else if (c <= -1.35e+47) {
		tmp = t_2;
	} else if (c <= 2.15e+39) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((z * t) - (c * ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-2.6d+135)) then
        tmp = t_2
    else if (c <= (-2.75d+112)) then
        tmp = t_1
    else if (c <= (-1.35d+47)) then
        tmp = t_2
    else if (c <= 2.15d+39) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((z * t) - (c * ((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 t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -2.6e+135) {
		tmp = t_2;
	} else if (c <= -2.75e+112) {
		tmp = t_1;
	} else if (c <= -1.35e+47) {
		tmp = t_2;
	} else if (c <= 2.15e+39) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -2.6e+135:
		tmp = t_2
	elif c <= -2.75e+112:
		tmp = t_1
	elif c <= -1.35e+47:
		tmp = t_2
	elif c <= 2.15e+39:
		tmp = t_1
	else:
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -2.6e+135)
		tmp = t_2;
	elseif (c <= -2.75e+112)
		tmp = t_1;
	elseif (c <= -1.35e+47)
		tmp = t_2;
	elseif (c <= 2.15e+39)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(b * c) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -2.6e+135)
		tmp = t_2;
	elseif (c <= -2.75e+112)
		tmp = t_1;
	elseif (c <= -1.35e+47)
		tmp = t_2;
	elseif (c <= 2.15e+39)
		tmp = t_1;
	else
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.6e+135], t$95$2, If[LessEqual[c, -2.75e+112], t$95$1, If[LessEqual[c, -1.35e+47], t$95$2, If[LessEqual[c, 2.15e+39], t$95$1, N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.6e135 or -2.75000000000000013e112 < c < -1.34999999999999998e47

   1. Initial program 81.2%

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

   3. Taylor expanded in i around inf 87.9%

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

   4. Taylor expanded in i around 0 87.9%

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

   if -2.6e135 < c < -2.75000000000000013e112 or -1.34999999999999998e47 < c < 2.15e39

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0 81.4%

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

   if 2.15e39 < c

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 87.9%

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

   4. Taylor expanded in a around 0 79.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+135}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{+112}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+135} \lor \neg \left(c \leq -8.2 \cdot 10^{+112}\right) \land \left(c \leq -1.2 \cdot 10^{+45} \lor \neg \left(c \leq 1.05 \cdot 10^{+37}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.6e+135)
         (and (not (<= c -8.2e+112))
              (or (<= c -1.2e+45) (not (<= c 1.05e+37)))))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.6e+135) || (!(c <= -8.2e+112) && ((c <= -1.2e+45) || !(c <= 1.05e+37)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.6d+135)) .or. (.not. (c <= (-8.2d+112))) .and. (c <= (-1.2d+45)) .or. (.not. (c <= 1.05d+37))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.6e+135) || (!(c <= -8.2e+112) && ((c <= -1.2e+45) || !(c <= 1.05e+37)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.6e+135) or (not (c <= -8.2e+112) and ((c <= -1.2e+45) or not (c <= 1.05e+37))):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.6e+135) || (!(c <= -8.2e+112) && ((c <= -1.2e+45) || !(c <= 1.05e+37))))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.6e+135) || (~((c <= -8.2e+112)) && ((c <= -1.2e+45) || ~((c <= 1.05e+37)))))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.6e+135], And[N[Not[LessEqual[c, -8.2e+112]], $MachinePrecision], Or[LessEqual[c, -1.2e+45], N[Not[LessEqual[c, 1.05e+37]], $MachinePrecision]]]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.6e135 or -8.19999999999999951e112 < c < -1.19999999999999995e45 or 1.0500000000000001e37 < c

   1. Initial program 80.6%

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

   3. Taylor expanded in i around inf 83.5%

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

   4. Taylor expanded in i around 0 83.5%

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

   if -2.6e135 < c < -8.19999999999999951e112 or -1.19999999999999995e45 < c < 1.0500000000000001e37

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0 81.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+135} \lor \neg \left(c \leq -8.2 \cdot 10^{+112}\right) \land \left(c \leq -1.2 \cdot 10^{+45} \lor \neg \left(c \leq 1.05 \cdot 10^{+37}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+113}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+54)
   (* y (* 2.0 (+ x (* t (/ z y)))))
   (if (<= (* x y) 2e+113)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* 2.0 (* x (- y (/ (* c (* (* b c) i)) 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) <= -1e+54) {
		tmp = y * (2.0 * (x + (t * (z / y))));
	} else if ((x * y) <= 2e+113) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / 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) <= (-1d+54)) then
        tmp = y * (2.0d0 * (x + (t * (z / y))))
    else if ((x * y) <= 2d+113) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (x * (y - ((c * ((b * c) * i)) / 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) <= -1e+54) {
		tmp = y * (2.0 * (x + (t * (z / y))));
	} else if ((x * y) <= 2e+113) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+54:
		tmp = y * (2.0 * (x + (t * (z / y))))
	elif (x * y) <= 2e+113:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+54)
		tmp = Float64(y * Float64(2.0 * Float64(x + Float64(t * Float64(z / y)))));
	elseif (Float64(x * y) <= 2e+113)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(Float64(c * Float64(Float64(b * c) * i)) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+54)
		tmp = y * (2.0 * (x + (t * (z / y))));
	elseif ((x * y) <= 2e+113)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (x * (y - ((c * ((b * c) * i)) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+54], N[(y * N[(2.0 * N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+113], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * N[(y - N[(N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.0000000000000001e54

   1. Initial program 95.3%

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

   3. Taylor expanded in c around 0 79.9%

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

   4. Taylor expanded in y around inf 79.9%

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

      1. distribute-lft-out 79.9%

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

      2. associate-/l* 79.8%

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

   6. Simplified 79.8%

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

   if -1.0000000000000001e54 < (*.f64 x y) < 2e113

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 85.6%

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

   if 2e113 < (*.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 89.1%

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

   4. Taylor expanded in t around 0 82.7%

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

   5. Taylor expanded in a around 0 84.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+113}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -29000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(t\_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= c -29000000000.0)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (if (<= c 1.45e-80)
       (* 2.0 (- t_1 (* a (* c i))))
       (* 2.0 (- t_1 (* (* b c) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -29000000000.0) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else if (c <= 1.45e-80) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-29000000000.0d0)) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else if (c <= 1.45d-80) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -29000000000.0) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else if (c <= 1.45e-80) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if c <= -29000000000.0:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	elif c <= 1.45e-80:
		tmp = 2.0 * (t_1 - (a * (c * i)))
	else:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -29000000000.0)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	elseif (c <= 1.45e-80)
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -29000000000.0)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	elseif (c <= 1.45e-80)
		tmp = 2.0 * (t_1 - (a * (c * i)));
	else
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -29000000000.0], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-80], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9e10

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -2.9e10 < c < 1.44999999999999999e-80

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-define 99.9%

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

      2. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in c around 0 91.9%

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

   8. Taylor expanded in c around 0 96.6%

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

   if 1.44999999999999999e-80 < c

   1. Initial program 83.1%

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

      1. fma-define 83.1%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

      1. fma-define 94.9%

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

      2. +-commutative 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in a around 0 88.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -29000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -65000000000000 \lor \neg \left(c \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -65000000000000.0) (not (<= c 6.2e+34)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -65000000000000.0) || !(c <= 6.2e+34)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-65000000000000.0d0)) .or. (.not. (c <= 6.2d+34))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -65000000000000.0) || !(c <= 6.2e+34)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -65000000000000.0) or not (c <= 6.2e+34):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -65000000000000.0) || !(c <= 6.2e+34))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -65000000000000.0) || ~((c <= 6.2e+34)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -65000000000000.0], N[Not[LessEqual[c, 6.2e+34]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.5e13 or 6.19999999999999955e34 < c

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 88.4%

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

   if -6.5e13 < c < 6.19999999999999955e34

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -65000000000000 \lor \neg \left(c \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4400000000000 \lor \neg \left(c \leq 2.75 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4400000000000.0) (not (<= c 2.75e+38)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4400000000000.0) || !(c <= 2.75e+38)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4400000000000.0d0)) .or. (.not. (c <= 2.75d+38))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4400000000000.0) || !(c <= 2.75e+38)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4400000000000.0) or not (c <= 2.75e+38):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4400000000000.0) || !(c <= 2.75e+38))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4400000000000.0) || ~((c <= 2.75e+38)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4400000000000.0], N[Not[LessEqual[c, 2.75e+38]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.4e12 or 2.7500000000000002e38 < c

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 88.4%

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

   if -4.4e12 < c < 2.7500000000000002e38

   1. Initial program 98.3%

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

      1. fma-define 98.4%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in c around 0 91.8%

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

   8. Taylor expanded in c around 0 94.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4400000000000 \lor \neg \left(c \leq 2.75 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+146} \lor \neg \left(c \leq -5.8 \cdot 10^{+109}\right) \land c \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -5.5e+146) (and (not (<= c -5.8e+109)) (<= c -1.3e+51)))
   (* (* c i) (* a -2.0))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.5e+146) || (!(c <= -5.8e+109) && (c <= -1.3e+51))) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-5.5d+146)) .or. (.not. (c <= (-5.8d+109))) .and. (c <= (-1.3d+51))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.5e+146) || (!(c <= -5.8e+109) && (c <= -1.3e+51))) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -5.5e+146) or (not (c <= -5.8e+109) and (c <= -1.3e+51)):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -5.5e+146) || (!(c <= -5.8e+109) && (c <= -1.3e+51)))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -5.5e+146) || (~((c <= -5.8e+109)) && (c <= -1.3e+51)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -5.5e+146], And[N[Not[LessEqual[c, -5.8e+109]], $MachinePrecision], LessEqual[c, -1.3e+51]]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.5000000000000004e146 or -5.8e109 < c < -1.3000000000000001e51

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. *-commutative 49.8%

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

      3. associate-*l* 42.7%

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

      4. *-commutative 42.7%

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

      5. distribute-rgt-neg-in 42.7%

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

      6. *-commutative 42.7%

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

      7. distribute-rgt-neg-in 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in c around 0 49.8%

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

      1. associate-*r* 49.8%

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

   8. Simplified 49.8%

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

   if -5.5000000000000004e146 < c < -5.8e109 or -1.3000000000000001e51 < c

   1. Initial program 92.3%

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

   3. Taylor expanded in c around 0 65.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+146} \lor \neg \left(c \leq -5.8 \cdot 10^{+109}\right) \land c \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -122 \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+115}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -122.0) (not (<= (* x y) 7.2e+115)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -122.0) || !((x * y) <= 7.2e+115)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-122.0d0)) .or. (.not. ((x * y) <= 7.2d+115))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -122.0) || !((x * y) <= 7.2e+115)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -122.0) or not ((x * y) <= 7.2e+115):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -122.0) || !(Float64(x * y) <= 7.2e+115))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -122.0) || ~(((x * y) <= 7.2e+115)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -122.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.2e+115]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -122 or 7.2000000000000001e115 < (*.f64 x y)

   1. Initial program 91.2%

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

   3. Taylor expanded in x around inf 59.4%

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

   if -122 < (*.f64 x y) < 7.2000000000000001e115

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 37.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -122 \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+115}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in z around inf 28.7%

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

4. Final simplification 28.7%

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

Developer target: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024059 
(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))))