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

Percentage Accurate: 90.8% → 96.2%

Time: 10.9s

Alternatives: 12

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.1× speedup

Math

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

FPCore

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

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 ((((z * t) + (x * y)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	}
	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(z * t) + Float64(x * y)) - 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(i * Float64(Float64(-a) - Float64(b * c)))));
	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[(z * t), $MachinePrecision] + N[(x * y), $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[(i * N[((-a) - N[(b * c), $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 95.4%

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

      1. associate-*l* 98.0%

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

      2. fma-def 98.0%

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

   3. Simplified 98.0%

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

   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. Taylor expanded in i around inf 66.8%

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

4. Final simplification 96.1%

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

Alternative 2: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+277}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_1\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (+ a (* b c))) i)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+277)))
     (* 2.0 (* c (* i (- (- a) (* b c)))))
     (* (- (+ (* z t) (* x y)) t_1) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+277)) {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	} else {
		tmp = (((z * t) + (x * y)) - t_1) * 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+277)) {
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	} else {
		tmp = (((z * t) + (x * y)) - t_1) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (a + (b * c))) * i
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+277):
		tmp = 2.0 * (c * (i * (-a - (b * c))))
	else:
		tmp = (((z * t) + (x * y)) - t_1) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+277))
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))));
	else
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - t_1) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (a + (b * c))) * i;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+277)))
		tmp = 2.0 * (c * (i * (-a - (b * c))));
	else
		tmp = (((z * t) + (x * y)) - t_1) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+277]], $MachinePrecision]], N[(2.0 * N[(c * N[(i * N[((-a) - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 1e277 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.5%

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

   2. Taylor expanded in i around inf 90.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e277

   1. Initial program 98.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+277}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]

Alternative 3: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))))
   (if (<= c -3.5e+53)
     (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
     (if (<= c 4.5e-64)
       (* 2.0 (- t_1 (* i (* a c))))
       (* 2.0 (- t_1 (* c (* c (* b i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if (c <= -3.5e+53) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else if (c <= 4.5e-64) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - (c * (c * (b * 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 = (z * t) + (x * y)
    if (c <= (-3.5d+53)) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else if (c <= 4.5d-64) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * (t_1 - (c * (c * (b * 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 = (z * t) + (x * y);
	double tmp;
	if (c <= -3.5e+53) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else if (c <= 4.5e-64) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	tmp = 0
	if c <= -3.5e+53:
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	elif c <= 4.5e-64:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * (t_1 - (c * (c * (b * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (c <= -3.5e+53)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	elseif (c <= 4.5e-64)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(b * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	tmp = 0.0;
	if (c <= -3.5e+53)
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	elseif (c <= 4.5e-64)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+53], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e-64], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.50000000000000019e53

   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. Taylor expanded in z around 0 86.3%

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

   if -3.50000000000000019e53 < c < 4.5000000000000001e-64

   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. Taylor expanded in a around inf 95.1%

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

   if 4.5000000000000001e-64 < c

   1. Initial program 85.0%

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

   2. Taylor expanded in a around 0 76.7%

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

      1. unpow2 76.7%

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

      2. associate-*r* 85.4%

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

   4. Simplified 85.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t + x \cdot y\right) \cdot 2\\ t_2 := 2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* z t) (* x y)) 2.0))
        (t_2 (* 2.0 (* c (* i (- (- a) (* b c)))))))
   (if (<= c -3.2e+63)
     t_2
     (if (<= c -4.1e-11)
       t_1
       (if (<= c -5.8e-34)
         (* 2.0 (- (* x y) (* c (* a i))))
         (if (<= c 9.2e+127) 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 = ((z * t) + (x * y)) * 2.0;
	double t_2 = 2.0 * (c * (i * (-a - (b * c))));
	double tmp;
	if (c <= -3.2e+63) {
		tmp = t_2;
	} else if (c <= -4.1e-11) {
		tmp = t_1;
	} else if (c <= -5.8e-34) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= 9.2e+127) {
		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 = ((z * t) + (x * y)) * 2.0d0
    t_2 = 2.0d0 * (c * (i * (-a - (b * c))))
    if (c <= (-3.2d+63)) then
        tmp = t_2
    else if (c <= (-4.1d-11)) then
        tmp = t_1
    else if (c <= (-5.8d-34)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if (c <= 9.2d+127) 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 = ((z * t) + (x * y)) * 2.0;
	double t_2 = 2.0 * (c * (i * (-a - (b * c))));
	double tmp;
	if (c <= -3.2e+63) {
		tmp = t_2;
	} else if (c <= -4.1e-11) {
		tmp = t_1;
	} else if (c <= -5.8e-34) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= 9.2e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z * t) + (x * y)) * 2.0
	t_2 = 2.0 * (c * (i * (-a - (b * c))))
	tmp = 0
	if c <= -3.2e+63:
		tmp = t_2
	elif c <= -4.1e-11:
		tmp = t_1
	elif c <= -5.8e-34:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif c <= 9.2e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0)
	t_2 = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-a) - Float64(b * c)))))
	tmp = 0.0
	if (c <= -3.2e+63)
		tmp = t_2;
	elseif (c <= -4.1e-11)
		tmp = t_1;
	elseif (c <= -5.8e-34)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (c <= 9.2e+127)
		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 = ((z * t) + (x * y)) * 2.0;
	t_2 = 2.0 * (c * (i * (-a - (b * c))));
	tmp = 0.0;
	if (c <= -3.2e+63)
		tmp = t_2;
	elseif (c <= -4.1e-11)
		tmp = t_1;
	elseif (c <= -5.8e-34)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif (c <= 9.2e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(i * N[((-a) - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+63], t$95$2, If[LessEqual[c, -4.1e-11], t$95$1, If[LessEqual[c, -5.8e-34], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+127], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.20000000000000011e63 or 9.2000000000000007e127 < c

   1. Initial program 79.5%

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

   2. Taylor expanded in i around inf 86.0%

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

   if -3.20000000000000011e63 < c < -4.1000000000000001e-11 or -5.8000000000000004e-34 < c < 9.2000000000000007e127

   1. Initial program 96.6%

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

   2. Taylor expanded in c around 0 77.1%

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

   if -4.1000000000000001e-11 < c < -5.8000000000000004e-34

   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. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in c around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+63}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-11}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+127}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-a\right) - b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-34} \lor \neg \left(c \leq 1.8 \cdot 10^{-81}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.8e-34) (not (<= c 1.8e-81)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.8e-34) || !(c <= 1.8e-81)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.8d-34)) .or. (.not. (c <= 1.8d-81))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.8e-34) || !(c <= 1.8e-81)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.8e-34) or not (c <= 1.8e-81):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.8e-34) || !(c <= 1.8e-81))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.8e-34) || ~((c <= 1.8e-81)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.8e-34], N[Not[LessEqual[c, 1.8e-81]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.79999999999999997e-34 or 1.7999999999999999e-81 < c

   1. Initial program 84.3%

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

   2. Taylor expanded in z around 0 82.2%

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

   if -2.79999999999999997e-34 < c < 1.7999999999999999e-81

   1. Initial program 98.0%

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

   2. Taylor expanded in c around 0 84.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-34} \lor \neg \left(c \leq 1.8 \cdot 10^{-81}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 6: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+49} \lor \neg \left(c \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.8e+49) (not (<= c 5e+93)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* z t) (* x y)) (* 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 <= -3.8e+49) || !(c <= 5e+93)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (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 <= (-3.8d+49)) .or. (.not. (c <= 5d+93))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (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 <= -3.8e+49) || !(c <= 5e+93)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.8e+49) or not (c <= 5e+93):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.8e+49) || !(c <= 5e+93))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - 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 <= -3.8e+49) || ~((c <= 5e+93)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.8e+49], N[Not[LessEqual[c, 5e+93]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.7999999999999999e49 or 5.0000000000000001e93 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in z around 0 89.1%

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

   if -3.7999999999999999e49 < c < 5.0000000000000001e93

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf 89.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+49} \lor \neg \left(c \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 7: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+212} \lor \neg \left(a \leq 3.6 \cdot 10^{+100} \lor \neg \left(a \leq 2.75 \cdot 10^{+167}\right) \land a \leq 3.2 \cdot 10^{+227}\right):\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= a -2.5e+212)
         (not
          (or (<= a 3.6e+100) (and (not (<= a 2.75e+167)) (<= a 3.2e+227)))))
   (* 2.0 (* i (* a (- c))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= -2.5e+212) || !((a <= 3.6e+100) || (!(a <= 2.75e+167) && (a <= 3.2e+227)))) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a <= (-2.5d+212)) .or. (.not. (a <= 3.6d+100) .or. (.not. (a <= 2.75d+167)) .and. (a <= 3.2d+227))) then
        tmp = 2.0d0 * (i * (a * -c))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= -2.5e+212) || !((a <= 3.6e+100) || (!(a <= 2.75e+167) && (a <= 3.2e+227)))) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a <= -2.5e+212) or not ((a <= 3.6e+100) or (not (a <= 2.75e+167) and (a <= 3.2e+227))):
		tmp = 2.0 * (i * (a * -c))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((a <= -2.5e+212) || !((a <= 3.6e+100) || (!(a <= 2.75e+167) && (a <= 3.2e+227))))
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a <= -2.5e+212) || ~(((a <= 3.6e+100) || (~((a <= 2.75e+167)) && (a <= 3.2e+227)))))
		tmp = 2.0 * (i * (a * -c));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[a, -2.5e+212], N[Not[Or[LessEqual[a, 3.6e+100], And[N[Not[LessEqual[a, 2.75e+167]], $MachinePrecision], LessEqual[a, 3.2e+227]]]], $MachinePrecision]], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.49999999999999996e212 or 3.6e100 < a < 2.7500000000000002e167 or 3.19999999999999988e227 < a

   1. Initial program 82.8%

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

   2. Taylor expanded in z around 0 72.4%

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

   3. Taylor expanded in a around inf 53.5%

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

      1. associate-*r* 53.5%

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

      2. neg-mul-1 53.5%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

      5. associate-*l* 65.3%

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

   5. Simplified 65.3%

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

   if -2.49999999999999996e212 < a < 3.6e100 or 2.7500000000000002e167 < a < 3.19999999999999988e227

   1. Initial program 91.7%

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

   2. Taylor expanded in c around 0 61.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+212} \lor \neg \left(a \leq 3.6 \cdot 10^{+100} \lor \neg \left(a \leq 2.75 \cdot 10^{+167}\right) \land a \leq 3.2 \cdot 10^{+227}\right):\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 8: 69.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.4 \cdot 10^{+64} \lor \neg \left(c \leq 3.1 \cdot 10^{+142}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(i \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -9.4e+64) (not (<= c 3.1e+142)))
   (* 2.0 (* c (* b (* i (- c)))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.4e+64) || !(c <= 3.1e+142)) {
		tmp = 2.0 * (c * (b * (i * -c)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-9.4d+64)) .or. (.not. (c <= 3.1d+142))) then
        tmp = 2.0d0 * (c * (b * (i * -c)))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.4e+64) || !(c <= 3.1e+142)) {
		tmp = 2.0 * (c * (b * (i * -c)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -9.4e+64) or not (c <= 3.1e+142):
		tmp = 2.0 * (c * (b * (i * -c)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -9.4e+64) || !(c <= 3.1e+142))
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(i * Float64(-c)))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -9.4e+64) || ~((c <= 3.1e+142)))
		tmp = 2.0 * (c * (b * (i * -c)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -9.4e+64], N[Not[LessEqual[c, 3.1e+142]], $MachinePrecision]], N[(2.0 * N[(c * N[(b * N[(i * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.40000000000000058e64 or 3.0999999999999999e142 < c

   1. Initial program 79.8%

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

   2. Taylor expanded in a around 0 67.8%

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

      1. unpow2 67.8%

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

      2. associate-*r* 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in c around inf 71.1%

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

      1. unpow2 71.1%

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

      2. associate-*r* 77.1%

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

      3. *-commutative 77.1%

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

      4. associate-*l* 77.1%

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

      5. neg-mul-1 77.1%

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

      6. *-commutative 77.1%

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

      7. distribute-rgt-neg-in 77.1%

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

      8. distribute-lft-neg-in 77.1%

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

      9. associate-*r* 79.1%

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

   7. Simplified 79.1%

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

   if -9.40000000000000058e64 < c < 3.0999999999999999e142

   1. Initial program 96.2%

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

   2. Taylor expanded in c around 0 74.1%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.4 \cdot 10^{+64} \lor \neg \left(c \leq 3.1 \cdot 10^{+142}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(i \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 9: 39.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-57} \lor \neg \left(y \leq 2.3 \cdot 10^{+91} \lor \neg \left(y \leq 8.5 \cdot 10^{+194}\right) \land y \leq 1.95 \cdot 10^{+210}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1e-57)
         (not
          (or (<= y 2.3e+91) (and (not (<= y 8.5e+194)) (<= y 1.95e+210)))))
   (* 2.0 (* 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 ((y <= -1e-57) || !((y <= 2.3e+91) || (!(y <= 8.5e+194) && (y <= 1.95e+210)))) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = (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 ((y <= (-1d-57)) .or. (.not. (y <= 2.3d+91) .or. (.not. (y <= 8.5d+194)) .and. (y <= 1.95d+210))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = (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 ((y <= -1e-57) || !((y <= 2.3e+91) || (!(y <= 8.5e+194) && (y <= 1.95e+210)))) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = (z * t) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1e-57) or not ((y <= 2.3e+91) or (not (y <= 8.5e+194) and (y <= 1.95e+210))):
		tmp = 2.0 * (x * y)
	else:
		tmp = (z * t) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1e-57) || !((y <= 2.3e+91) || (!(y <= 8.5e+194) && (y <= 1.95e+210))))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(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 ((y <= -1e-57) || ~(((y <= 2.3e+91) || (~((y <= 8.5e+194)) && (y <= 1.95e+210)))))
		tmp = 2.0 * (x * y);
	else
		tmp = (z * t) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1e-57], N[Not[Or[LessEqual[y, 2.3e+91], And[N[Not[LessEqual[y, 8.5e+194]], $MachinePrecision], LessEqual[y, 1.95e+210]]]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999955e-58 or 2.29999999999999991e91 < y < 8.50000000000000026e194 or 1.95e210 < y

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf 45.1%

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

   if -9.99999999999999955e-58 < y < 2.29999999999999991e91 or 8.50000000000000026e194 < y < 1.95e210

   1. Initial program 91.6%

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

   2. Taylor expanded in z around inf 40.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-57} \lor \neg \left(y \leq 2.3 \cdot 10^{+91} \lor \neg \left(y \leq 8.5 \cdot 10^{+194}\right) \land y \leq 1.95 \cdot 10^{+210}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 10: 69.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.25 \cdot 10^{+62} \lor \neg \left(c \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.25e+62) (not (<= c 7e+135)))
   (* b (* i (* c (* c -2.0))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.25e+62) || !(c <= 7e+135)) {
		tmp = b * (i * (c * (c * -2.0)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.25d+62)) .or. (.not. (c <= 7d+135))) then
        tmp = b * (i * (c * (c * (-2.0d0))))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.25e+62) || !(c <= 7e+135)) {
		tmp = b * (i * (c * (c * -2.0)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.25e+62) or not (c <= 7e+135):
		tmp = b * (i * (c * (c * -2.0)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.25e+62) || !(c <= 7e+135))
		tmp = Float64(b * Float64(i * Float64(c * Float64(c * -2.0))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.25e+62) || ~((c <= 7e+135)))
		tmp = b * (i * (c * (c * -2.0)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.25e+62], N[Not[LessEqual[c, 7e+135]], $MachinePrecision]], N[(b * N[(i * N[(c * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.2500000000000001e62 or 7.0000000000000005e135 < c

   1. Initial program 79.8%

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

   2. Taylor expanded in b around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. *-commutative 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

      4. unpow2 71.1%

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

      5. distribute-rgt-neg-in 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in i around 0 71.1%

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

      1. unpow2 71.1%

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

      2. associate-*r* 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in c around 0 71.1%

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

      1. associate-*r* 71.1%

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

      2. unpow2 71.1%

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

      3. *-commutative 71.1%

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

      4. *-commutative 71.1%

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

      5. associate-*l* 72.3%

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

      6. associate-*r* 72.3%

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

      7. *-commutative 72.3%

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

      8. *-commutative 72.3%

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

   10. Simplified 72.3%

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

   if -3.2500000000000001e62 < c < 7.0000000000000005e135

   1. Initial program 96.2%

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

   2. Taylor expanded in c around 0 74.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.25 \cdot 10^{+62} \lor \neg \left(c \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 11: 68.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.45 \cdot 10^{+52} \lor \neg \left(c \leq 8.2 \cdot 10^{+135}\right):\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.45e+52) (not (<= c 8.2e+135)))
   (* c (* (* c (* b i)) -2.0))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.45e+52) || !(c <= 8.2e+135)) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.45d+52)) .or. (.not. (c <= 8.2d+135))) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.45e+52) || !(c <= 8.2e+135)) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.45e+52) or not (c <= 8.2e+135):
		tmp = c * ((c * (b * i)) * -2.0)
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.45e+52) || !(c <= 8.2e+135))
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.45e+52) || ~((c <= 8.2e+135)))
		tmp = c * ((c * (b * i)) * -2.0);
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.45e+52], N[Not[LessEqual[c, 8.2e+135]], $MachinePrecision]], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.44999999999999998e52 or 8.2e135 < c

   1. Initial program 79.8%

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

   2. Taylor expanded in b around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. *-commutative 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

      4. unpow2 71.1%

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

      5. distribute-rgt-neg-in 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in i around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. unpow2 71.1%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-*r* 77.3%

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

      6. associate-*l* 77.3%

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

      7. associate-*r* 77.1%

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

      8. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   if -3.44999999999999998e52 < c < 8.2e135

   1. Initial program 96.2%

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

   2. Taylor expanded in c around 0 74.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.45 \cdot 10^{+52} \lor \neg \left(c \leq 8.2 \cdot 10^{+135}\right):\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 12: 29.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

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 = (z * t) * 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

2. Taylor expanded in z around inf 31.1%

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

3. Final simplification 31.1%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023221 
(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))))