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

Percentage Accurate: 90.3% → 96.8%

Time: 18.9s

Alternatives: 12

Speedup: 0.5×

• 46.4% 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: 90.3% 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: 96.8% accurate, 0.1× speedup

Math

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

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 (fma y x (* 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 * fma(y, x, (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 * fma(y, x, 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[(y * x + N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

      1. associate--l+ 97.6%

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

      2. *-commutative 97.6%

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

      3. associate--l+ 97.6%

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

      4. associate--l+ 97.6%

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

      5. *-commutative 97.6%

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

      6. associate--l+ 97.6%

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

      7. fma-define 97.6%

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

      8. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   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 z around 0 33.3%

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

   4. Taylor expanded in a around 0 50.0%

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

      1. cancel-sign-sub-inv 50.0%

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

      2. *-commutative 50.0%

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

      3. fma-define 83.3%

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

   6. Applied egg-rr 83.3%

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

4. Final simplification 98.4%

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

Alternative 2: 93.3% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * Float64(a + Float64(b * c))) * i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 * 2.0);
	else
		tmp = Float64(2.0 * fma(y, x, 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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 * 2.0), $MachinePrecision], N[(2.0 * N[(y * x + N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

   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 z around 0 33.3%

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

   4. Taylor expanded in a around 0 50.0%

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

      1. cancel-sign-sub-inv 50.0%

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

      2. *-commutative 50.0%

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

      3. fma-define 83.3%

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

   6. Applied egg-rr 83.3%

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

4. Final simplification 96.9%

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

Alternative 3: 92.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

   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 z around 0 33.3%

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

   4. Taylor expanded in c around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-*l* 59.2%

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

      4. *-commutative 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 95.8%

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

Alternative 4: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

   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 a around inf 8.6%

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

      1. add0 8.6%

         \[\leadsto \color{blue}{2 \cdot \left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right) + 0} \]

      2. add-sqr-sqrt 0.2%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \cdot \sqrt{-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)}\right)} + 0 \]

      3. sqrt-unprod 33.7%

         \[\leadsto 2 \cdot \color{blue}{\sqrt{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right) \cdot \left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)}} + 0 \]

      4. mul-1-neg 33.7%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \cdot \left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} + 0 \]

      5. mul-1-neg 33.7%

         \[\leadsto 2 \cdot \sqrt{\left(-a \cdot \left(c \cdot i\right)\right) \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)}} + 0 \]

      6. sqr-neg 33.7%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(a \cdot \left(c \cdot i\right)\right)}} + 0 \]

      7. sqrt-unprod 18.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{a \cdot \left(c \cdot i\right)} \cdot \sqrt{a \cdot \left(c \cdot i\right)}\right)} + 0 \]

      8. add-sqr-sqrt 44.2%

         \[\leadsto 2 \cdot \color{blue}{\left(a \cdot \left(c \cdot i\right)\right)} + 0 \]

      9. *-commutative 44.2%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} + 0 \]

      10. associate-*l* 36.6%

          \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(i \cdot a\right)\right)} + 0 \]

   5. Applied egg-rr 36.6%

      \[\leadsto \color{blue}{2 \cdot \left(c \cdot \left(i \cdot a\right)\right) + 0} \]
   6. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot a\right)\right) \cdot 2} + 0 \]

      2. add0 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-*r* 51.7%

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

      5. *-commutative 51.7%

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

      6. associate-*l* 51.7%

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

   7. Simplified 51.7%

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

4. Final simplification 95.5%

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

Alternative 5: 86.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot t\_2\\ \mathbf{elif}\;c \leq -96000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 10^{-31}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (- (* z t) (* (* b c) (* c i))))))
        (t_2 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.8e+204)
     (* -2.0 t_2)
     (if (<= c -96000000000000.0)
       t_1
       (if (<= c 1e-31)
         (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
         (if (<= c 3.2e+159) t_1 (* 2.0 (- (* x y) 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 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.8e+204) {
		tmp = -2.0 * t_2;
	} else if (c <= -96000000000000.0) {
		tmp = t_1;
	} else if (c <= 1e-31) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else if (c <= 3.2e+159) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - 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 * ((x * y) + ((z * t) - ((b * c) * (c * i))))
    t_2 = c * ((a + (b * c)) * i)
    if (c <= (-1.8d+204)) then
        tmp = (-2.0d0) * t_2
    else if (c <= (-96000000000000.0d0)) then
        tmp = t_1
    else if (c <= 1d-31) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else if (c <= 3.2d+159) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) - 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 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.8e+204) {
		tmp = -2.0 * t_2;
	} else if (c <= -96000000000000.0) {
		tmp = t_1;
	} else if (c <= 1e-31) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else if (c <= 3.2e+159) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))))
	t_2 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.8e+204:
		tmp = -2.0 * t_2
	elif c <= -96000000000000.0:
		tmp = t_1
	elif c <= 1e-31:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	elif c <= 3.2e+159:
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(Float64(b * c) * Float64(c * i)))))
	t_2 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.8e+204)
		tmp = Float64(-2.0 * t_2);
	elseif (c <= -96000000000000.0)
		tmp = t_1;
	elseif (c <= 1e-31)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	elseif (c <= 3.2e+159)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	t_2 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.8e+204)
		tmp = -2.0 * t_2;
	elseif (c <= -96000000000000.0)
		tmp = t_1;
	elseif (c <= 1e-31)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	elseif (c <= 3.2e+159)
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+204], N[(-2.0 * t$95$2), $MachinePrecision], If[LessEqual[c, -96000000000000.0], t$95$1, If[LessEqual[c, 1e-31], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+159], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.8000000000000001e204

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 80.4%

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

   4. Taylor expanded in x around 0 92.9%

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

   if -1.8000000000000001e204 < c < -9.6e13 or 1e-31 < c < 3.19999999999999985e159

   1. Initial program 90.8%

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

      1. associate--l+ 90.8%

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

      2. fma-neg 90.8%

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

      3. *-commutative 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-undefine 90.8%

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

      6. associate-*r* 93.7%

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

      7. *-commutative 93.7%

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

      8. *-commutative 93.7%

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

      9. fma-define 95.3%

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

      10. *-commutative 95.3%

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

      11. associate-*r* 92.4%

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

      12. fma-undefine 92.4%

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

      13. +-commutative 92.4%

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

      14. *-commutative 92.4%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in b around inf 94.0%

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

      1. fma-undefine 92.4%

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

      2. associate-*r* 91.0%

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

   7. Applied egg-rr 91.0%

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

   if -9.6e13 < c < 1e-31

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 93.3%

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

      1. *-commutative 93.3%

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

   5. Simplified 93.3%

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

   if 3.19999999999999985e159 < c

   1. Initial program 84.9%

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

   3. Taylor expanded in z around 0 99.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -96000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 10^{-31}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-80} \lor \neg \left(c \leq 9.8 \cdot 10^{+72}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6e-80) (not (<= c 9.8e+72)))
   (* 2.0 (- (* x y) (* 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 <= -6e-80) || !(c <= 9.8e+72)) {
		tmp = 2.0 * ((x * y) - (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 <= (-6d-80)) .or. (.not. (c <= 9.8d+72))) then
        tmp = 2.0d0 * ((x * y) - (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 <= -6e-80) || !(c <= 9.8e+72)) {
		tmp = 2.0 * ((x * y) - (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 <= -6e-80) or not (c <= 9.8e+72):
		tmp = 2.0 * ((x * y) - (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 <= -6e-80) || !(c <= 9.8e+72))
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 <= -6e-80) || ~((c <= 9.8e+72)))
		tmp = 2.0 * ((x * y) - (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, -6e-80], N[Not[LessEqual[c, 9.8e+72]], $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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.00000000000000014e-80 or 9.80000000000000012e72 < c

   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. Add Preprocessing

   3. Taylor expanded in z around 0 81.9%

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

   if -6.00000000000000014e-80 < c < 9.80000000000000012e72

   1. Initial program 97.7%

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

   3. Taylor expanded in c around 0 80.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-80} \lor \neg \left(c \leq 9.8 \cdot 10^{+72}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+96}:\\ \;\;\;\;-2 \cdot t\_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.5e+96)
     (* -2.0 t_1)
     (if (<= c 1.6e+76)
       (* 2.0 (- (+ (* x y) (* z t)) (* c (* a i))))
       (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.5e+96) {
		tmp = -2.0 * t_1;
	} else if (c <= 1.6e+76) {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-1.5d+96)) then
        tmp = (-2.0d0) * t_1
    else if (c <= 1.6d+76) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (c * (a * i)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.5e+96) {
		tmp = -2.0 * t_1;
	} else if (c <= 1.6e+76) {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.5e+96:
		tmp = -2.0 * t_1
	elif c <= 1.6e+76:
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.5e+96)
		tmp = Float64(-2.0 * t_1);
	elseif (c <= 1.6e+76)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(c * Float64(a * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.5e+96)
		tmp = -2.0 * t_1;
	elseif (c <= 1.6e+76)
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+96], N[(-2.0 * t$95$1), $MachinePrecision], If[LessEqual[c, 1.6e+76], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5e96

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 77.7%

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

   4. Taylor expanded in x around 0 82.4%

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

   if -1.5e96 < c < 1.59999999999999988e76

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l* 83.6%

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

   5. Simplified 83.6%

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

   if 1.59999999999999988e76 < c

   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 z around 0 91.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+96}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;-2 \cdot t\_1\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.05e+94)
     (* -2.0 t_1)
     (if (<= c 4.6e+73)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.05e+94) {
		tmp = -2.0 * t_1;
	} else if (c <= 4.6e+73) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-1.05d+94)) then
        tmp = (-2.0d0) * t_1
    else if (c <= 4.6d+73) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.05e+94) {
		tmp = -2.0 * t_1;
	} else if (c <= 4.6e+73) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.05e+94:
		tmp = -2.0 * t_1
	elif c <= 4.6e+73:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.05e+94)
		tmp = Float64(-2.0 * t_1);
	elseif (c <= 4.6e+73)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.05e+94)
		tmp = -2.0 * t_1;
	elseif (c <= 4.6e+73)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e+94], N[(-2.0 * t$95$1), $MachinePrecision], If[LessEqual[c, 4.6e+73], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.04999999999999995e94

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 77.7%

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

   4. Taylor expanded in x around 0 82.4%

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

   if -1.04999999999999995e94 < c < 4.6e73

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 89.8%

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

      1. *-commutative 89.8%

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

   5. Simplified 89.8%

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

   if 4.6e73 < c

   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 z around 0 91.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+73}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -0.022 \lor \neg \left(c \leq 5.4 \cdot 10^{+73}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -0.022) (not (<= c 5.4e+73)))
   (* -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 <= -0.022) || !(c <= 5.4e+73)) {
		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 <= (-0.022d0)) .or. (.not. (c <= 5.4d+73))) 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 <= -0.022) || !(c <= 5.4e+73)) {
		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 <= -0.022) or not (c <= 5.4e+73):
		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 <= -0.022) || !(c <= 5.4e+73))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -0.022) || ~((c <= 5.4e+73)))
		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, -0.022], N[Not[LessEqual[c, 5.4e+73]], $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 < -0.021999999999999999 or 5.3999999999999998e73 < c

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 83.2%

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

   4. Taylor expanded in x around 0 79.8%

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

   if -0.021999999999999999 < c < 5.3999999999999998e73

   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. Add Preprocessing

   3. Taylor expanded in c around 0 79.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -0.022 \lor \neg \left(c \leq 5.4 \cdot 10^{+73}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{-54} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+146}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -8.2e-54) (not (<= (* x y) 3.8e+146)))
   (* (* x y) 2.0)
   (* (* 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 (((x * y) <= -8.2e-54) || !((x * y) <= 3.8e+146)) {
		tmp = (x * y) * 2.0;
	} 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 (((x * y) <= (-8.2d-54)) .or. (.not. ((x * y) <= 3.8d+146))) then
        tmp = (x * y) * 2.0d0
    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 (((x * y) <= -8.2e-54) || !((x * y) <= 3.8e+146)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = (z * t) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -8.2e-54) or not ((x * y) <= 3.8e+146):
		tmp = (x * y) * 2.0
	else:
		tmp = (z * t) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -8.2e-54) || !(Float64(x * y) <= 3.8e+146))
		tmp = Float64(Float64(x * y) * 2.0);
	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 (((x * y) <= -8.2e-54) || ~(((x * y) <= 3.8e+146)))
		tmp = (x * y) * 2.0;
	else
		tmp = (z * t) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -8.2e-54], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.8e+146]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -8.2000000000000001e-54 or 3.79999999999999979e146 < (*.f64 x y)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 52.6%

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

   if -8.2000000000000001e-54 < (*.f64 x y) < 3.79999999999999979e146

   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. Add Preprocessing

   3. Taylor expanded in z around inf 46.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{-54} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+146}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+156} \lor \neg \left(i \leq 1.16 \cdot 10^{+15}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.55e+156) (not (<= i 1.16e+15)))
   (* (* c i) (* a -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 ((i <= -1.55e+156) || !(i <= 1.16e+15)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.55d+156)) .or. (.not. (i <= 1.16d+15))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.55e+156) || !(i <= 1.16e+15)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.55e+156) or not (i <= 1.16e+15):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.55e+156) || !(i <= 1.16e+15))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.55e+156) || ~((i <= 1.16e+15)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.55e+156], N[Not[LessEqual[i, 1.16e+15]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.5500000000000001e156 or 1.16e15 < i

   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. Add Preprocessing

   3. Taylor expanded in a around inf 47.4%

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

   4. Taylor expanded in a around 0 47.4%

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

      1. associate-*r* 47.4%

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

   6. Simplified 47.4%

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

   if -1.5500000000000001e156 < i < 1.16e15

   1. Initial program 93.1%

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

   3. Taylor expanded in c around 0 70.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+156} \lor \neg \left(i \leq 1.16 \cdot 10^{+15}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.5% 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 93.0%

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

3. Taylor expanded in z around inf 34.0%

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

4. Final simplification 34.0%

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

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 2024034 
(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))))