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

Percentage Accurate: 89.6% → 95.7%

Time: 15.6s

Alternatives: 15

Speedup: 0.5×

• 46.2% 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: 89.6% 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: 95.7% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $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 92.9%

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

      1. associate--l+ 92.9%

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

      2. *-commutative 92.9%

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

      3. associate--l+ 92.9%

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

      4. associate--l+ 92.9%

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

      5. *-commutative 92.9%

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

      6. associate--l+ 92.9%

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

      7. fma-def 92.9%

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

      8. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 57.5%

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

   4. Taylor expanded in a around 0 57.6%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.1%

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

Alternative 2: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+282} \lor \neg \left(t_2 \leq 10^{+307}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t_2\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 -5e+282) (not (<= t_2 1e+307)))
     (* 2.0 (* c (* t_1 (- i))))
     (* (- (+ (* x y) (* z t)) t_2) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -5e+282) || !(t_2 <= 1e+307)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (c * t_1) * i
    if ((t_2 <= (-5d+282)) .or. (.not. (t_2 <= 1d+307))) then
        tmp = 2.0d0 * (c * (t_1 * -i))
    else
        tmp = (((x * y) + (z * t)) - t_2) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -5e+282) || !(t_2 <= 1e+307)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if (t_2 <= -5e+282) or not (t_2 <= 1e+307):
		tmp = 2.0 * (c * (t_1 * -i))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if ((t_2 <= -5e+282) || !(t_2 <= 1e+307))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if ((t_2 <= -5e+282) || ~((t_2 <= 1e+307)))
		tmp = 2.0 * (c * (t_1 * -i));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+282], N[Not[LessEqual[t$95$2, 1e+307]], $MachinePrecision]], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.99999999999999978e282 or 9.99999999999999986e306 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 67.8%

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

   3. Taylor expanded in i around inf 87.5%

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

   if -4.99999999999999978e282 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999986e306

   1. Initial program 99.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+282} \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+307}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(\left(a \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+31}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -2.6e+153)
     t_1
     (if (<= (* x y) -3.35e-9)
       (* 2.0 (* z t))
       (if (<= (* x y) -2.1e-45)
         (* c (* (* a i) -2.0))
         (if (<= (* x y) 5e-98)
           (* t (* z 2.0))
           (if (<= (* x y) 6e+31) (* (* a (* c i)) -2.0) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2.6e+153) {
		tmp = t_1;
	} else if ((x * y) <= -3.35e-9) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= -2.1e-45) {
		tmp = c * ((a * i) * -2.0);
	} else if ((x * y) <= 5e-98) {
		tmp = t * (z * 2.0);
	} else if ((x * y) <= 6e+31) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) * 2.0d0
    if ((x * y) <= (-2.6d+153)) then
        tmp = t_1
    else if ((x * y) <= (-3.35d-9)) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= (-2.1d-45)) then
        tmp = c * ((a * i) * (-2.0d0))
    else if ((x * y) <= 5d-98) then
        tmp = t * (z * 2.0d0)
    else if ((x * y) <= 6d+31) then
        tmp = (a * (c * i)) * (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2.6e+153) {
		tmp = t_1;
	} else if ((x * y) <= -3.35e-9) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= -2.1e-45) {
		tmp = c * ((a * i) * -2.0);
	} else if ((x * y) <= 5e-98) {
		tmp = t * (z * 2.0);
	} else if ((x * y) <= 6e+31) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2.6e+153:
		tmp = t_1
	elif (x * y) <= -3.35e-9:
		tmp = 2.0 * (z * t)
	elif (x * y) <= -2.1e-45:
		tmp = c * ((a * i) * -2.0)
	elif (x * y) <= 5e-98:
		tmp = t * (z * 2.0)
	elif (x * y) <= 6e+31:
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2.6e+153)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.35e-9)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= -2.1e-45)
		tmp = Float64(c * Float64(Float64(a * i) * -2.0));
	elseif (Float64(x * y) <= 5e-98)
		tmp = Float64(t * Float64(z * 2.0));
	elseif (Float64(x * y) <= 6e+31)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2.6e+153)
		tmp = t_1;
	elseif ((x * y) <= -3.35e-9)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= -2.1e-45)
		tmp = c * ((a * i) * -2.0);
	elseif ((x * y) <= 5e-98)
		tmp = t * (z * 2.0);
	elseif ((x * y) <= 6e+31)
		tmp = (a * (c * i)) * -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e+153], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.35e-9], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.1e-45], N[(c * N[(N[(a * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-98], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e+31], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2.5999999999999999e153 or 5.99999999999999978e31 < (*.f64 x y)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf 64.9%

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

   if -2.5999999999999999e153 < (*.f64 x y) < -3.34999999999999981e-9

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 37.2%

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

   if -3.34999999999999981e-9 < (*.f64 x y) < -2.09999999999999995e-45

   1. Initial program 62.3%

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

   3. Taylor expanded in a around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. *-commutative 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around 0 52.5%

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

      1. *-commutative 52.5%

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

      2. associate-*r* 42.5%

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

      3. *-commutative 42.5%

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

      4. associate-*r* 52.7%

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

      5. metadata-eval 52.7%

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

      6. distribute-rgt-neg-in 52.7%

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

      7. associate-*r* 52.7%

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

      8. distribute-rgt-neg-in 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-neg-in 52.7%

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

      11. metadata-eval 52.7%

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

   8. Simplified 52.7%

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

   if -2.09999999999999995e-45 < (*.f64 x y) < 5.00000000000000018e-98

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 44.9%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. expm1-log1p-u 24.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(t \cdot z\right)\right)\right)} \]

      2. expm1-udef 16.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(t \cdot z\right)\right)} - 1} \]

      3. *-commutative 16.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot z\right) \cdot 2}\right)} - 1 \]

      4. associate-*l* 16.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{t \cdot \left(z \cdot 2\right)}\right)} - 1 \]

   5. Applied egg-rr 16.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(z \cdot 2\right)\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 24.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(z \cdot 2\right)\right)\right)} \]

      2. expm1-log1p 44.9%

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

      3. *-commutative 44.9%

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

   7. Simplified 44.9%

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

   if 5.00000000000000018e-98 < (*.f64 x y) < 5.99999999999999978e31

   1. Initial program 85.5%

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

   3. Taylor expanded in a around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. *-commutative 43.7%

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

      3. distribute-rgt-neg-in 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in c around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(\left(a \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+31}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.7 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(\left(a \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -1.95e+153)
     t_2
     (if (<= (* x y) -2.5e-12)
       t_1
       (if (<= (* x y) -2.7e-44)
         (* c (* (* a i) -2.0))
         (if (<= (* x y) 2.95e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.95e+153) {
		tmp = t_2;
	} else if ((x * y) <= -2.5e-12) {
		tmp = t_1;
	} else if ((x * y) <= -2.7e-44) {
		tmp = c * ((a * i) * -2.0);
	} else if ((x * y) <= 2.95e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-1.95d+153)) then
        tmp = t_2
    else if ((x * y) <= (-2.5d-12)) then
        tmp = t_1
    else if ((x * y) <= (-2.7d-44)) then
        tmp = c * ((a * i) * (-2.0d0))
    else if ((x * y) <= 2.95d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.95e+153) {
		tmp = t_2;
	} else if ((x * y) <= -2.5e-12) {
		tmp = t_1;
	} else if ((x * y) <= -2.7e-44) {
		tmp = c * ((a * i) * -2.0);
	} else if ((x * y) <= 2.95e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.95e+153:
		tmp = t_2
	elif (x * y) <= -2.5e-12:
		tmp = t_1
	elif (x * y) <= -2.7e-44:
		tmp = c * ((a * i) * -2.0)
	elif (x * y) <= 2.95e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.95e+153)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.5e-12)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.7e-44)
		tmp = Float64(c * Float64(Float64(a * i) * -2.0));
	elseif (Float64(x * y) <= 2.95e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.95e+153)
		tmp = t_2;
	elseif ((x * y) <= -2.5e-12)
		tmp = t_1;
	elseif ((x * y) <= -2.7e-44)
		tmp = c * ((a * i) * -2.0);
	elseif ((x * y) <= 2.95e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.95e+153], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.5e-12], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.7e-44], N[(c * N[(N[(a * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.95e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.94999999999999992e153 or 2.95000000000000002e69 < (*.f64 x y)

   1. Initial program 83.6%

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

   3. Taylor expanded in x around inf 68.2%

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

   if -1.94999999999999992e153 < (*.f64 x y) < -2.49999999999999985e-12 or -2.6999999999999999e-44 < (*.f64 x y) < 2.95000000000000002e69

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 39.5%

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

   if -2.49999999999999985e-12 < (*.f64 x y) < -2.6999999999999999e-44

   1. Initial program 62.3%

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

   3. Taylor expanded in a around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. *-commutative 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around 0 52.5%

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

      1. *-commutative 52.5%

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

      2. associate-*r* 42.5%

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

      3. *-commutative 42.5%

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

      4. associate-*r* 52.7%

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

      5. metadata-eval 52.7%

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

      6. distribute-rgt-neg-in 52.7%

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

      7. associate-*r* 52.7%

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

      8. distribute-rgt-neg-in 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-neg-in 52.7%

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

      11. metadata-eval 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.7 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(\left(a \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -7.2e+109)
     t_1
     (if (<= c -1.25e+14)
       (* 2.0 (- (* z t) (* c (* c (* b i)))))
       (if (<= c -3e-18)
         (* 2.0 (- (* x y) (* c (* a i))))
         (if (<= c 6.8e-17) (* (+ (* x y) (* z t)) 2.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -7.2e+109) {
		tmp = t_1;
	} else if (c <= -1.25e+14) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -3e-18) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= 6.8e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-7.2d+109)) then
        tmp = t_1
    else if (c <= (-1.25d+14)) then
        tmp = 2.0d0 * ((z * t) - (c * (c * (b * i))))
    else if (c <= (-3d-18)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if (c <= 6.8d-17) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -7.2e+109) {
		tmp = t_1;
	} else if (c <= -1.25e+14) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -3e-18) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= 6.8e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -7.2e+109:
		tmp = t_1
	elif c <= -1.25e+14:
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))))
	elif c <= -3e-18:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif c <= 6.8e-17:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -7.2e+109)
		tmp = t_1;
	elseif (c <= -1.25e+14)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(c * Float64(b * i)))));
	elseif (c <= -3e-18)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (c <= 6.8e-17)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -7.2e+109)
		tmp = t_1;
	elseif (c <= -1.25e+14)
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	elseif (c <= -3e-18)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif (c <= 6.8e-17)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.2e+109], t$95$1, If[LessEqual[c, -1.25e+14], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-18], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-17], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.2e109 or 6.7999999999999996e-17 < c

   1. Initial program 73.1%

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

   3. Taylor expanded in i around inf 79.0%

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

   if -7.2e109 < c < -1.25e14

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0 91.5%

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

   4. Taylor expanded in a around 0 81.4%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

   6. Simplified 85.3%

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

   if -1.25e14 < c < -2.99999999999999983e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   if -2.99999999999999983e-18 < c < 6.7999999999999996e-17

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0 79.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-131} \lor \neg \left(c \leq 2.06 \cdot 10^{-26}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3e-131) (not (<= c 2.06e-26)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3e-131) || !(c <= 2.06e-26)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3d-131)) .or. (.not. (c <= 2.06d-26))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3e-131) || !(c <= 2.06e-26)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3e-131) or not (c <= 2.06e-26):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3e-131) || !(c <= 2.06e-26))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3e-131) || ~((c <= 2.06e-26)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3e-131], N[Not[LessEqual[c, 2.06e-26]], $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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.99999999999999996e-131 or 2.0599999999999999e-26 < 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 82.5%

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

   if -2.99999999999999996e-131 < c < 2.0599999999999999e-26

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0 84.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-131} \lor \neg \left(c \leq 2.06 \cdot 10^{-26}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+14} \lor \neg \left(c \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.2e+14) (not (<= c 9e-25)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* c (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.2e+14) || !(c <= 9e-25)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.2d+14)) .or. (.not. (c <= 9d-25))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (c * (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.2e+14) || !(c <= 9e-25)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.2e+14) or not (c <= 9e-25):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.2e+14) || !(c <= 9e-25))
		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(c * Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.2e+14) || ~((c <= 9e-25)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.2e+14], N[Not[LessEqual[c, 9e-25]], $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[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.2e14 or 9.0000000000000002e-25 < c

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0 85.0%

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

   if -1.2e14 < c < 9.0000000000000002e-25

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l* 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+14} \lor \neg \left(c \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -68000000000000 \lor \neg \left(c \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -68000000000000.0) (not (<= c 3.2e-24)))
   (* 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 <= -68000000000000.0) || !(c <= 3.2e-24)) {
		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 <= (-68000000000000.0d0)) .or. (.not. (c <= 3.2d-24))) 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 <= -68000000000000.0) || !(c <= 3.2e-24)) {
		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 <= -68000000000000.0) or not (c <= 3.2e-24):
		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 <= -68000000000000.0) || !(c <= 3.2e-24))
		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 <= -68000000000000.0) || ~((c <= 3.2e-24)))
		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, -68000000000000.0], N[Not[LessEqual[c, 3.2e-24]], $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 < -6.8e13 or 3.20000000000000012e-24 < c

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0 85.0%

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

   if -6.8e13 < c < 3.20000000000000012e-24

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 94.0%

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

      1. *-commutative 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -68000000000000 \lor \neg \left(c \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -54000000000000 \lor \neg \left(c \leq 1.04 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -54000000000000.0) (not (<= c 1.04e-16)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -54000000000000.0) || !(c <= 1.04e-16)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-54000000000000.0d0)) .or. (.not. (c <= 1.04d-16))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -54000000000000.0) || !(c <= 1.04e-16)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -54000000000000.0) or not (c <= 1.04e-16):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -54000000000000.0) || !(c <= 1.04e-16))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -54000000000000.0) || ~((c <= 1.04e-16)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -54000000000000.0], N[Not[LessEqual[c, 1.04e-16]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.4e13 or 1.04000000000000001e-16 < c

   1. Initial program 74.5%

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

   3. Taylor expanded in i around inf 76.9%

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

   if -5.4e13 < c < 1.04000000000000001e-16

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0 78.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -54000000000000 \lor \neg \left(c \leq 1.04 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -58000000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -58000000000000.0)
   (* 2.0 (* c (* b (* c (- i)))))
   (if (<= c 1.26e-23)
     (* (+ (* x y) (* z t)) 2.0)
     (* 2.0 (- (* 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 <= -58000000000000.0) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 1.26e-23) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((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 <= (-58000000000000.0d0)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= 1.26d-23) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((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 <= -58000000000000.0) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 1.26e-23) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -58000000000000.0:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= 1.26e-23:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -58000000000000.0)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= 1.26e-23)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(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 <= -58000000000000.0)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= 1.26e-23)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -58000000000000.0], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.26e-23], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.8e13

   1. Initial program 73.0%

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

   3. Taylor expanded in i around inf 77.1%

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

   4. Taylor expanded in a around 0 67.5%

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

   if -5.8e13 < c < 1.25999999999999996e-23

   1. Initial program 99.2%

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

   3. Taylor expanded in c around 0 79.1%

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

   if 1.25999999999999996e-23 < 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 85.1%

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

   4. Taylor expanded in c around 0 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. sub-neg 59.3%

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

   6. Simplified 59.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -58000000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -65000000000000 \lor \neg \left(c \leq 2.15 \cdot 10^{+155}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -65000000000000.0) (not (<= c 2.15e+155)))
   (* 2.0 (* c (* b (* c (- i)))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -65000000000000.0) || !(c <= 2.15e+155)) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-65000000000000.0d0)) .or. (.not. (c <= 2.15d+155))) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -65000000000000.0) || !(c <= 2.15e+155)) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -65000000000000.0) or not (c <= 2.15e+155):
		tmp = 2.0 * (c * (b * (c * -i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -65000000000000.0) || !(c <= 2.15e+155))
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -65000000000000.0) || ~((c <= 2.15e+155)))
		tmp = 2.0 * (c * (b * (c * -i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -65000000000000.0], N[Not[LessEqual[c, 2.15e+155]], $MachinePrecision]], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.5e13 or 2.1500000000000001e155 < c

   1. Initial program 72.4%

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

   3. Taylor expanded in i around inf 80.8%

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

   4. Taylor expanded in a around 0 69.8%

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

   if -6.5e13 < c < 2.1500000000000001e155

   1. Initial program 96.3%

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

   3. Taylor expanded in c around 0 72.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -65000000000000 \lor \neg \left(c \leq 2.15 \cdot 10^{+155}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -58000000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -58000000000000.0)
   (* 2.0 (* c (* b (* c (- i)))))
   (if (<= c 1.45e+37)
     (* (+ (* x y) (* z t)) 2.0)
     (* (* c (* c (* b i))) (- 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -58000000000000.0) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 1.45e+37) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-58000000000000.0d0)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= 1.45d+37) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (c * (c * (b * i))) * -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -58000000000000.0) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 1.45e+37) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -58000000000000.0:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= 1.45e+37:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (c * (c * (b * i))) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -58000000000000.0)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= 1.45e+37)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(c * Float64(c * Float64(b * i))) * Float64(-2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -58000000000000.0)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= 1.45e+37)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (c * (c * (b * i))) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -58000000000000.0], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e+37], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.8e13

   1. Initial program 73.0%

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

   3. Taylor expanded in i around inf 77.1%

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

   4. Taylor expanded in a around 0 67.5%

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

   if -5.8e13 < c < 1.44999999999999989e37

   1. Initial program 98.6%

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

   3. Taylor expanded in c around 0 75.7%

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

   if 1.44999999999999989e37 < c

   1. Initial program 72.6%

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

   3. Taylor expanded in i around inf 83.4%

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

   4. Taylor expanded in a around 0 58.1%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*r* 60.8%

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

      4. *-commutative 60.8%

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

   6. Simplified 60.8%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(c \cdot \left(i \cdot b\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -58000000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.15 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+67}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4.15e+152) (not (<= (* x y) 3.9e+67)))
   (* (* 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) <= -4.15e+152) || !((x * y) <= 3.9e+67)) {
		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) <= (-4.15d+152)) .or. (.not. ((x * y) <= 3.9d+67))) 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) <= -4.15e+152) || !((x * y) <= 3.9e+67)) {
		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) <= -4.15e+152) or not ((x * y) <= 3.9e+67):
		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) <= -4.15e+152) || !(Float64(x * y) <= 3.9e+67))
		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) <= -4.15e+152) || ~(((x * y) <= 3.9e+67)))
		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], -4.15e+152], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.9e+67]], $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) < -4.1500000000000001e152 or 3.90000000000000007e67 < (*.f64 x y)

   1. Initial program 83.6%

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

   3. Taylor expanded in x around inf 68.2%

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

   if -4.1500000000000001e152 < (*.f64 x y) < 3.90000000000000007e67

   1. Initial program 89.7%

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

   3. Taylor expanded in z around inf 37.9%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.15 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+67}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 2.3 \cdot 10^{+174}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i 2.3e+174) (* (+ (* x y) (* z t)) 2.0) (* (* a (* c i)) -2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= 2.3e+174) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= 2.3d+174) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (a * (c * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= 2.3e+174) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= 2.3e+174:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (a * (c * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= 2.3e+174)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= 2.3e+174)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (a * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, 2.3e+174], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 2.2999999999999998e174

   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 c around 0 59.4%

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

   if 2.2999999999999998e174 < i

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. *-commutative 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in c around 0 55.0%

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

      1. *-commutative 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 2.3 \cdot 10^{+174}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

3. Taylor expanded in z around inf 31.3%

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

4. Final simplification 31.3%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
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 2024019 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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