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

Percentage Accurate: 89.6% → 93.7%

Time: 27.6s

Alternatives: 16

Speedup: 0.5×

• 48.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(c \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(i \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -4e+70)
   (* 2.0 (fma z t (- (* x y) (* i (* c (fma b c a))))))
   (* 2.0 (fma y x (- (* z t) (* c (* i (fma b c a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -4e+70) {
		tmp = 2.0 * fma(z, t, ((x * y) - (i * (c * fma(b, c, a)))));
	} else {
		tmp = 2.0 * fma(y, x, ((z * t) - (c * (i * fma(b, c, a)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -4e+70)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(x * y) - Float64(i * Float64(c * fma(b, c, a))))));
	else
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(z * t) - Float64(c * Float64(i * fma(b, c, a))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -4e+70], N[(2.0 * N[(z * t + N[(N[(x * y), $MachinePrecision] - N[(i * N[(c * N[(b * c + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x + N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(b * c + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.00000000000000029e70

   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. Step-by-step derivation

      1. associate--l+ 96.2%

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

      2. *-commutative 96.2%

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

      3. associate--l+ 96.2%

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

      4. associate--l+ 96.2%

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

      5. *-commutative 96.2%

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

      6. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

      1. associate-+r- 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-*r* 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-*r* 85.1%

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

      6. associate-+r- 85.1%

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

      7. fma-define 87.1%

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

      8. +-commutative 87.1%

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

      9. fma-define 87.1%

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

   6. Applied egg-rr 87.1%

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

      1. associate-*r* 98.2%

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

      2. *-commutative 98.2%

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

   8. Simplified 98.2%

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

   if -4.00000000000000029e70 < i

   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. Step-by-step derivation

      1. associate--l+ 87.1%

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

      2. *-commutative 87.1%

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

      3. associate--l+ 87.1%

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

      4. associate--l+ 87.1%

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

      5. *-commutative 87.1%

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

      6. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. fma-define 96.1%

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

      3. associate-*r* 89.6%

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

      4. *-commutative 89.6%

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

      5. associate-*r* 95.6%

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

      6. +-commutative 95.6%

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

      7. fma-define 95.6%

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

   6. Applied egg-rr 95.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(c \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(i \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.3%

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

      1. associate--l+ 93.3%

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

      2. *-commutative 93.3%

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

      3. associate--l+ 93.3%

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

      4. associate--l+ 93.3%

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

      5. *-commutative 93.3%

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

      6. associate-*l* 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y + \left(z \cdot t - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)} \]
   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 a around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in x around 0 43.3%

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

      1. *-commutative 43.3%

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

      2. *-commutative 43.3%

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

      3. associate-*r* 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 96.1%

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

Alternative 3: 44.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= (* x y) -5e+80)
     t_2
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 5e-217)
         (* 2.0 (* i (* a (- c))))
         (if (<= (* x y) 4e+59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -5e+80) {
		tmp = t_2;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-217) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 4e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if ((x * y) <= (-5d+80)) then
        tmp = t_2
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 5d-217) then
        tmp = 2.0d0 * (i * (a * -c))
    else if ((x * y) <= 4d+59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -5e+80) {
		tmp = t_2;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-217) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 4e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -5e+80:
		tmp = t_2
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 5e-217:
		tmp = 2.0 * (i * (a * -c))
	elif (x * y) <= 4e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -5e+80)
		tmp = t_2;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-217)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	elseif (Float64(x * y) <= 4e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -5e+80)
		tmp = t_2;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 5e-217)
		tmp = 2.0 * (i * (a * -c));
	elseif ((x * y) <= 4e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+80], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-217], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999961e80 or 3.99999999999999989e59 < (*.f64 x y)

   1. Initial program 88.8%

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

      1. associate--l+ 88.8%

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

      2. *-commutative 88.8%

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

      3. associate--l+ 88.8%

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

      4. associate--l+ 88.8%

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

      5. *-commutative 88.8%

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

      6. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 65.1%

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

   if -4.99999999999999961e80 < (*.f64 x y) < 0.0 or 5.0000000000000002e-217 < (*.f64 x y) < 3.99999999999999989e59

   1. Initial program 89.2%

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

      1. associate--l+ 89.2%

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

      2. *-commutative 89.2%

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

      3. associate--l+ 89.2%

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

      4. associate--l+ 89.2%

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

      5. *-commutative 89.2%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 41.4%

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

   if 0.0 < (*.f64 x y) < 5.0000000000000002e-217

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in x around 0 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*l* 40.5%

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

   8. Simplified 40.5%

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

   9. Taylor expanded in t around 0 40.3%

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

       1. neg-mul-1 40.3%

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

       2. distribute-rgt-neg-in 40.3%

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

       3. *-commutative 40.3%

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

       4. distribute-rgt-neg-out 40.3%

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

       5. *-commutative 40.3%

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

       6. associate-*l* 45.8%

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

   11. Simplified 45.8%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+148}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(i \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+185}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (* i (+ a (* c b)))) -2.0)))
   (if (<= c -5.2e+34)
     t_1
     (if (<= c 2.35e-77)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 1.12e+148)
         (* 2.0 (- (* x y) (* a (* i c))))
         (if (<= c 3.4e+185) (* 2.0 (- (* z t) (* (* c b) (* i c)))) 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 * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -5.2e+34) {
		tmp = t_1;
	} else if (c <= 2.35e-77) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.12e+148) {
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	} else if (c <= 3.4e+185) {
		tmp = 2.0 * ((z * t) - ((c * b) * (i * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * (i * (a + (c * b)))) * (-2.0d0)
    if (c <= (-5.2d+34)) then
        tmp = t_1
    else if (c <= 2.35d-77) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 1.12d+148) then
        tmp = 2.0d0 * ((x * y) - (a * (i * c)))
    else if (c <= 3.4d+185) then
        tmp = 2.0d0 * ((z * t) - ((c * b) * (i * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -5.2e+34) {
		tmp = t_1;
	} else if (c <= 2.35e-77) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.12e+148) {
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	} else if (c <= 3.4e+185) {
		tmp = 2.0 * ((z * t) - ((c * b) * (i * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (i * (a + (c * b)))) * -2.0
	tmp = 0
	if c <= -5.2e+34:
		tmp = t_1
	elif c <= 2.35e-77:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 1.12e+148:
		tmp = 2.0 * ((x * y) - (a * (i * c)))
	elif c <= 3.4e+185:
		tmp = 2.0 * ((z * t) - ((c * b) * (i * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(i * Float64(a + Float64(c * b)))) * -2.0)
	tmp = 0.0
	if (c <= -5.2e+34)
		tmp = t_1;
	elseif (c <= 2.35e-77)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 1.12e+148)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(i * c))));
	elseif (c <= 3.4e+185)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(Float64(c * b) * Float64(i * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (i * (a + (c * b)))) * -2.0;
	tmp = 0.0;
	if (c <= -5.2e+34)
		tmp = t_1;
	elseif (c <= 2.35e-77)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 1.12e+148)
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	elseif (c <= 3.4e+185)
		tmp = 2.0 * ((z * t) - ((c * b) * (i * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -5.2e+34], t$95$1, If[LessEqual[c, 2.35e-77], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.12e+148], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+185], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.19999999999999995e34 or 3.40000000000000017e185 < c

   1. Initial program 73.7%

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

      1. associate--l+ 73.7%

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

      2. *-commutative 73.7%

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

      3. associate--l+ 73.7%

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

      4. associate--l+ 73.7%

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

      5. *-commutative 73.7%

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

      6. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. associate-*r* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 79.4%

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

   if -5.19999999999999995e34 < c < 2.3499999999999999e-77

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in c around 0 80.4%

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

      1. +-commutative 80.4%

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

   7. Simplified 80.4%

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

   if 2.3499999999999999e-77 < c < 1.12e148

   1. Initial program 93.2%

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

      1. associate--l+ 93.2%

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

      2. *-commutative 93.2%

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

      3. associate--l+ 93.2%

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

      4. associate--l+ 93.2%

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

      5. *-commutative 93.2%

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

      6. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. associate-*r* 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in a around inf 65.6%

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

   if 1.12e148 < c < 3.40000000000000017e185

   1. Initial program 80.5%

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

      1. associate--l+ 80.5%

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

      2. *-commutative 80.5%

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

      3. associate--l+ 80.5%

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

      4. associate--l+ 80.5%

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

      5. *-commutative 80.5%

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

      6. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. associate-+r- 90.0%

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

      2. +-commutative 90.0%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-*r* 89.8%

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

      6. associate-+r- 89.8%

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

      7. fma-define 89.8%

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

      8. +-commutative 89.8%

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

      9. fma-define 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in x around 0 70.5%

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

       1. *-commutative 70.5%

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

       2. *-commutative 70.5%

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

       3. associate-*l* 70.7%

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

       4. *-commutative 70.7%

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

       5. *-commutative 70.7%

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

   11. Simplified 70.7%

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

   12. Taylor expanded in a around 0 70.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+148}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(i \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+185}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := \left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+159}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(i \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* (* c (* i (+ a (* c b)))) -2.0)))
   (if (<= c -1.9e+29)
     t_2
     (if (<= c 2.6e-77)
       t_1
       (if (<= c 5.4e+159)
         (* 2.0 (- (* x y) (* a (* i c))))
         (if (<= c 5.4e+183) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = (c * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -1.9e+29) {
		tmp = t_2;
	} else if (c <= 2.6e-77) {
		tmp = t_1;
	} else if (c <= 5.4e+159) {
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	} else if (c <= 5.4e+183) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (c * (i * (a + (c * b)))) * (-2.0d0)
    if (c <= (-1.9d+29)) then
        tmp = t_2
    else if (c <= 2.6d-77) then
        tmp = t_1
    else if (c <= 5.4d+159) then
        tmp = 2.0d0 * ((x * y) - (a * (i * c)))
    else if (c <= 5.4d+183) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = (c * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -1.9e+29) {
		tmp = t_2;
	} else if (c <= 2.6e-77) {
		tmp = t_1;
	} else if (c <= 5.4e+159) {
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	} else if (c <= 5.4e+183) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = (c * (i * (a + (c * b)))) * -2.0
	tmp = 0
	if c <= -1.9e+29:
		tmp = t_2
	elif c <= 2.6e-77:
		tmp = t_1
	elif c <= 5.4e+159:
		tmp = 2.0 * ((x * y) - (a * (i * c)))
	elif c <= 5.4e+183:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(Float64(c * Float64(i * Float64(a + Float64(c * b)))) * -2.0)
	tmp = 0.0
	if (c <= -1.9e+29)
		tmp = t_2;
	elseif (c <= 2.6e-77)
		tmp = t_1;
	elseif (c <= 5.4e+159)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(i * c))));
	elseif (c <= 5.4e+183)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = (c * (i * (a + (c * b)))) * -2.0;
	tmp = 0.0;
	if (c <= -1.9e+29)
		tmp = t_2;
	elseif (c <= 2.6e-77)
		tmp = t_1;
	elseif (c <= 5.4e+159)
		tmp = 2.0 * ((x * y) - (a * (i * c)));
	elseif (c <= 5.4e+183)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -1.9e+29], t$95$2, If[LessEqual[c, 2.6e-77], t$95$1, If[LessEqual[c, 5.4e+159], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e+183], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.89999999999999985e29 or 5.39999999999999964e183 < c

   1. Initial program 73.7%

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

      1. associate--l+ 73.7%

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

      2. *-commutative 73.7%

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

      3. associate--l+ 73.7%

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

      4. associate--l+ 73.7%

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

      5. *-commutative 73.7%

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

      6. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. associate-*r* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 79.4%

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

   if -1.89999999999999985e29 < c < 2.6000000000000001e-77 or 5.40000000000000016e159 < c < 5.39999999999999964e183

   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. Step-by-step derivation

      1. associate--l+ 97.7%

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

      2. *-commutative 97.7%

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

      3. associate--l+ 97.7%

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

      4. associate--l+ 97.7%

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

      5. *-commutative 97.7%

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

      6. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in c around 0 80.1%

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

      1. +-commutative 80.1%

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

   7. Simplified 80.1%

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

   if 2.6000000000000001e-77 < c < 5.40000000000000016e159

   1. Initial program 93.5%

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

      1. associate--l+ 93.5%

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

      2. *-commutative 93.5%

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

      3. associate--l+ 93.5%

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

      4. associate--l+ 93.5%

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

      5. *-commutative 93.5%

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

      6. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 83.2%

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

      1. associate-*r* 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in a around inf 63.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+159}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(i \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+183}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ a (* c b)) (* i c))))
   (if (or (<= (* x y) -5e+80) (not (<= (* x y) 4e+59)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a + (c * b)) * (i * c);
	double tmp;
	if (((x * y) <= -5e+80) || !((x * y) <= 4e+59)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + (c * b)) * (i * c)
    if (((x * y) <= (-5d+80)) .or. (.not. ((x * y) <= 4d+59))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a + (c * b)) * (i * c);
	double tmp;
	if (((x * y) <= -5e+80) || !((x * y) <= 4e+59)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a + (c * b)) * (i * c)
	tmp = 0
	if ((x * y) <= -5e+80) or not ((x * y) <= 4e+59):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a + Float64(c * b)) * Float64(i * c))
	tmp = 0.0
	if ((Float64(x * y) <= -5e+80) || !(Float64(x * y) <= 4e+59))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a + (c * b)) * (i * c);
	tmp = 0.0;
	if (((x * y) <= -5e+80) || ~(((x * y) <= 4e+59)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+80], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+59]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999961e80 or 3.99999999999999989e59 < (*.f64 x y)

   1. Initial program 88.8%

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

      1. associate--l+ 88.8%

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

      2. *-commutative 88.8%

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

      3. associate--l+ 88.8%

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

      4. associate--l+ 88.8%

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

      5. *-commutative 88.8%

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

      6. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around 0 85.0%

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

      1. associate-*r* 86.9%

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

   7. Simplified 86.9%

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

   if -4.99999999999999961e80 < (*.f64 x y) < 3.99999999999999989e59

   1. Initial program 89.1%

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

      1. associate--l+ 89.1%

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

      2. *-commutative 89.1%

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

      3. associate--l+ 89.1%

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

      4. associate--l+ 89.1%

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

      5. *-commutative 89.1%

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

      6. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

      1. associate-+r- 96.0%

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

      2. +-commutative 96.0%

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

      3. associate-*r* 89.1%

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

      4. *-commutative 89.1%

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

      5. associate-*r* 92.8%

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

      6. associate-+r- 92.8%

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

      7. fma-define 92.9%

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

      8. +-commutative 92.9%

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

      9. fma-define 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*r* 89.1%

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

      2. *-commutative 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in x around 0 86.8%

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

       1. *-commutative 86.8%

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

       2. *-commutative 86.8%

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

       3. associate-*l* 89.9%

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

       4. *-commutative 89.9%

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

       5. *-commutative 89.9%

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

   11. Simplified 89.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+96)
   (* 2.0 (+ (* x y) (* z t)))
   (if (<= (* x y) 5e+115)
     (* 2.0 (- (* z t) (* c (* i (+ a (* c b))))))
     (* 2.0 (- (* x y) (* (* c b) (* i c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 5e+115) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * 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 ((x * y) <= (-2d+96)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if ((x * y) <= 5d+115) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (c * b)))))
    else
        tmp = 2.0d0 * ((x * y) - ((c * b) * (i * 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 ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 5e+115) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+96:
		tmp = 2.0 * ((x * y) + (z * t))
	elif (x * y) <= 5e+115:
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))))
	else:
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+96)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 5e+115)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * b) * Float64(i * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+96)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif ((x * y) <= 5e+115)
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	else
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+96], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+115], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e96

   1. Initial program 90.2%

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

      1. associate--l+ 90.2%

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

      2. *-commutative 90.2%

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

      3. associate--l+ 90.2%

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

      4. associate--l+ 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in c around 0 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -2.0000000000000001e96 < (*.f64 x y) < 5.00000000000000008e115

   1. Initial program 89.5%

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

      1. associate--l+ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate--l+ 89.5%

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

      4. associate--l+ 89.5%

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

      5. *-commutative 89.5%

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

      6. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 85.6%

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

   if 5.00000000000000008e115 < (*.f64 x y)

   1. Initial program 86.3%

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

      1. associate--l+ 86.3%

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

      2. *-commutative 86.3%

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

      3. associate--l+ 86.3%

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

      4. associate--l+ 86.3%

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

      5. *-commutative 86.3%

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

      6. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 86.3%

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

      1. associate-*r* 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in a around 0 84.5%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+96)
   (* 2.0 (+ (* x y) (* z t)))
   (if (<= (* x y) 5e+115)
     (* 2.0 (- (* z t) (* (+ a (* c b)) (* i c))))
     (* 2.0 (- (* x y) (* (* c b) (* i c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 5e+115) {
		tmp = 2.0 * ((z * t) - ((a + (c * b)) * (i * c)));
	} else {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * 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 ((x * y) <= (-2d+96)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if ((x * y) <= 5d+115) then
        tmp = 2.0d0 * ((z * t) - ((a + (c * b)) * (i * c)))
    else
        tmp = 2.0d0 * ((x * y) - ((c * b) * (i * 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 ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 5e+115) {
		tmp = 2.0 * ((z * t) - ((a + (c * b)) * (i * c)));
	} else {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+96:
		tmp = 2.0 * ((x * y) + (z * t))
	elif (x * y) <= 5e+115:
		tmp = 2.0 * ((z * t) - ((a + (c * b)) * (i * c)))
	else:
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+96)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 5e+115)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(Float64(a + Float64(c * b)) * Float64(i * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * b) * Float64(i * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+96)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif ((x * y) <= 5e+115)
		tmp = 2.0 * ((z * t) - ((a + (c * b)) * (i * c)));
	else
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+96], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+115], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e96

   1. Initial program 90.2%

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

      1. associate--l+ 90.2%

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

      2. *-commutative 90.2%

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

      3. associate--l+ 90.2%

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

      4. associate--l+ 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in c around 0 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -2.0000000000000001e96 < (*.f64 x y) < 5.00000000000000008e115

   1. Initial program 89.5%

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

      1. associate--l+ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate--l+ 89.5%

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

      4. associate--l+ 89.5%

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

      5. *-commutative 89.5%

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

      6. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

      1. associate-+r- 96.3%

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

      2. +-commutative 96.3%

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

      3. associate-*r* 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-*r* 93.5%

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

      6. associate-+r- 93.5%

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

      7. fma-define 93.5%

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

      8. +-commutative 93.5%

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

      9. fma-define 93.5%

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

   6. Applied egg-rr 93.5%

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

      1. associate-*r* 89.5%

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

      2. *-commutative 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in x around 0 85.6%

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

       1. *-commutative 85.6%

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

       2. *-commutative 85.6%

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

       3. associate-*l* 88.4%

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

       4. *-commutative 88.4%

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

       5. *-commutative 88.4%

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

   11. Simplified 88.4%

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

   if 5.00000000000000008e115 < (*.f64 x y)

   1. Initial program 86.3%

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

      1. associate--l+ 86.3%

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

      2. *-commutative 86.3%

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

      3. associate--l+ 86.3%

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

      4. associate--l+ 86.3%

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

      5. *-commutative 86.3%

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

      6. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 86.3%

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

      1. associate-*r* 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in a around 0 84.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+72}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1 \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(c \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= (* x y) -2e+96)
     (* 2.0 (+ (* x y) (* z t)))
     (if (<= (* x y) 1e+72)
       (* 2.0 (- (* z t) (* t_1 (* i c))))
       (* 2.0 (- (* x y) (* i (* c t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 1e+72) {
		tmp = 2.0 * ((z * t) - (t_1 * (i * c)));
	} else {
		tmp = 2.0 * ((x * y) - (i * (c * 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 = a + (c * b)
    if ((x * y) <= (-2d+96)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if ((x * y) <= 1d+72) then
        tmp = 2.0d0 * ((z * t) - (t_1 * (i * c)))
    else
        tmp = 2.0d0 * ((x * y) - (i * (c * 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 = a + (c * b);
	double tmp;
	if ((x * y) <= -2e+96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if ((x * y) <= 1e+72) {
		tmp = 2.0 * ((z * t) - (t_1 * (i * c)));
	} else {
		tmp = 2.0 * ((x * y) - (i * (c * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	tmp = 0
	if (x * y) <= -2e+96:
		tmp = 2.0 * ((x * y) + (z * t))
	elif (x * y) <= 1e+72:
		tmp = 2.0 * ((z * t) - (t_1 * (i * c)))
	else:
		tmp = 2.0 * ((x * y) - (i * (c * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (Float64(x * y) <= -2e+96)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 1e+72)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(t_1 * Float64(i * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(c * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	tmp = 0.0;
	if ((x * y) <= -2e+96)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif ((x * y) <= 1e+72)
		tmp = 2.0 * ((z * t) - (t_1 * (i * c)));
	else
		tmp = 2.0 * ((x * y) - (i * (c * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+96], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+72], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(t$95$1 * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e96

   1. Initial program 90.2%

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

      1. associate--l+ 90.2%

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

      2. *-commutative 90.2%

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

      3. associate--l+ 90.2%

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

      4. associate--l+ 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in c around 0 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -2.0000000000000001e96 < (*.f64 x y) < 9.99999999999999944e71

   1. Initial program 88.9%

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

      1. associate--l+ 88.9%

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

      2. *-commutative 88.9%

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

      3. associate--l+ 88.9%

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

      4. associate--l+ 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

      1. associate-+r- 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-*r* 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-*r* 93.1%

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

      6. associate-+r- 93.1%

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

      7. fma-define 93.1%

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

      8. +-commutative 93.1%

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

      9. fma-define 93.1%

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

   6. Applied egg-rr 93.1%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

   8. Simplified 88.9%

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

   9. Taylor expanded in x around 0 86.6%

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

       1. *-commutative 86.6%

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

       2. *-commutative 86.6%

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

       3. associate-*l* 89.6%

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

       4. *-commutative 89.6%

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

       5. *-commutative 89.6%

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

   11. Simplified 89.6%

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

   if 9.99999999999999944e71 < (*.f64 x y)

   1. Initial program 88.4%

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

      1. associate--l+ 88.4%

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

      2. *-commutative 88.4%

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

      3. associate--l+ 88.4%

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

      4. associate--l+ 88.4%

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

      5. *-commutative 88.4%

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

      6. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. *-commutative 90.0%

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

      2. fma-define 96.7%

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

      3. associate-*r* 95.1%

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

      4. *-commutative 95.1%

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

      5. associate-*r* 95.0%

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

      6. +-commutative 95.0%

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

      7. fma-define 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in z around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. associate-*r* 95.0%

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

      3. distribute-rgt-neg-in 95.0%

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

      4. *-commutative 95.0%

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

   9. Simplified 95.0%

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

   10. Taylor expanded in y around 0 86.7%

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

       1. +-commutative 86.7%

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

       2. mul-1-neg 86.7%

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

       3. unsub-neg 86.7%

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

       4. associate-*r* 88.3%

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

       5. *-commutative 88.3%

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

       6. associate-*l* 86.7%

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

   12. Simplified 86.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+72}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(z \cdot t + \left(x \cdot y - c \cdot \left(b \cdot \left(i \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ a (* c b)) (* i c))))
   (if (<= (* x y) -5e-19)
     (* 2.0 (+ (* z t) (- (* x y) (* c (* b (* i c))))))
     (if (<= (* x y) 4e+59) (* 2.0 (- (* z t) t_1)) (* 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 = (a + (c * b)) * (i * c);
	double tmp;
	if ((x * y) <= -5e-19) {
		tmp = 2.0 * ((z * t) + ((x * y) - (c * (b * (i * c)))));
	} else if ((x * y) <= 4e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} 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 = (a + (c * b)) * (i * c)
    if ((x * y) <= (-5d-19)) then
        tmp = 2.0d0 * ((z * t) + ((x * y) - (c * (b * (i * c)))))
    else if ((x * y) <= 4d+59) then
        tmp = 2.0d0 * ((z * t) - t_1)
    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 = (a + (c * b)) * (i * c);
	double tmp;
	if ((x * y) <= -5e-19) {
		tmp = 2.0 * ((z * t) + ((x * y) - (c * (b * (i * c)))));
	} else if ((x * y) <= 4e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a + (c * b)) * (i * c)
	tmp = 0
	if (x * y) <= -5e-19:
		tmp = 2.0 * ((z * t) + ((x * y) - (c * (b * (i * c)))))
	elif (x * y) <= 4e+59:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a + Float64(c * b)) * Float64(i * c))
	tmp = 0.0
	if (Float64(x * y) <= -5e-19)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(Float64(x * y) - Float64(c * Float64(b * Float64(i * c))))));
	elseif (Float64(x * y) <= 4e+59)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	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 = (a + (c * b)) * (i * c);
	tmp = 0.0;
	if ((x * y) <= -5e-19)
		tmp = 2.0 * ((z * t) + ((x * y) - (c * (b * (i * c)))));
	elseif ((x * y) <= 4e+59)
		tmp = 2.0 * ((z * t) - t_1);
	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[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-19], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+59], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000004e-19

   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. Step-by-step derivation

      1. +-commutative 89.8%

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

      2. associate--l+ 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around 0 92.4%

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

   if -5.0000000000000004e-19 < (*.f64 x y) < 3.99999999999999989e59

   1. Initial program 89.3%

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

      1. associate--l+ 89.3%

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

      2. *-commutative 89.3%

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

      3. associate--l+ 89.3%

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

      4. associate--l+ 89.3%

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

      5. *-commutative 89.3%

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

      6. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

      1. associate-+r- 95.3%

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

      2. +-commutative 95.3%

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

      3. associate-*r* 89.3%

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

      4. *-commutative 89.3%

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

      5. associate-*r* 91.6%

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

      6. associate-+r- 91.6%

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

      7. fma-define 91.6%

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

      8. +-commutative 91.6%

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

      9. fma-define 91.6%

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

   6. Applied egg-rr 91.6%

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

      1. associate-*r* 89.3%

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

      2. *-commutative 89.3%

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

   8. Simplified 89.3%

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

   9. Taylor expanded in x around 0 88.1%

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

       1. *-commutative 88.1%

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

       2. *-commutative 88.1%

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

       3. associate-*l* 91.9%

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

       4. *-commutative 91.9%

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

       5. *-commutative 91.9%

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

   11. Simplified 91.9%

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

   if 3.99999999999999989e59 < (*.f64 x y)

   1. Initial program 87.3%

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

      1. associate--l+ 87.3%

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

      2. *-commutative 87.3%

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

      3. associate--l+ 87.3%

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

      4. associate--l+ 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around 0 87.1%

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

      1. associate-*r* 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(z \cdot t + \left(x \cdot y - c \cdot \left(b \cdot \left(i \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -4 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 10^{+198}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (* i (+ a (* c b)))) -2.0)))
   (if (<= c -4e+32)
     t_1
     (if (<= c 2.9e-53)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 1e+198) (* 2.0 (- (* x y) (* (* c b) (* i c)))) 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 * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -4e+32) {
		tmp = t_1;
	} else if (c <= 2.9e-53) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1e+198) {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * (i * (a + (c * b)))) * (-2.0d0)
    if (c <= (-4d+32)) then
        tmp = t_1
    else if (c <= 2.9d-53) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 1d+198) then
        tmp = 2.0d0 * ((x * y) - ((c * b) * (i * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (i * (a + (c * b)))) * -2.0;
	double tmp;
	if (c <= -4e+32) {
		tmp = t_1;
	} else if (c <= 2.9e-53) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1e+198) {
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (i * (a + (c * b)))) * -2.0
	tmp = 0
	if c <= -4e+32:
		tmp = t_1
	elif c <= 2.9e-53:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 1e+198:
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(i * Float64(a + Float64(c * b)))) * -2.0)
	tmp = 0.0
	if (c <= -4e+32)
		tmp = t_1;
	elseif (c <= 2.9e-53)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 1e+198)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * b) * Float64(i * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (i * (a + (c * b)))) * -2.0;
	tmp = 0.0;
	if (c <= -4e+32)
		tmp = t_1;
	elseif (c <= 2.9e-53)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 1e+198)
		tmp = 2.0 * ((x * y) - ((c * b) * (i * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -4e+32], t$95$1, If[LessEqual[c, 2.9e-53], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e+198], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.00000000000000021e32 or 1.00000000000000002e198 < c

   1. Initial program 72.4%

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

      1. associate--l+ 72.4%

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

      2. *-commutative 72.4%

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

      3. associate--l+ 72.4%

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

      4. associate--l+ 72.4%

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

      5. *-commutative 72.4%

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

      6. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around 0 79.5%

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

      1. associate-*r* 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in x around 0 80.8%

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

   if -4.00000000000000021e32 < c < 2.8999999999999998e-53

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in c around 0 79.3%

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

      1. +-commutative 79.3%

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

   7. Simplified 79.3%

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

   if 2.8999999999999998e-53 < c < 1.00000000000000002e198

   1. Initial program 91.0%

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

      1. associate--l+ 91.0%

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

      2. *-commutative 91.0%

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

      3. associate--l+ 91.0%

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

      4. associate--l+ 91.0%

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

      5. *-commutative 91.0%

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

      6. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. associate-*r* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in a around 0 70.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+32}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 10^{+198}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot t\_1\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1 \cdot \left(i \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= c -4.2e+71)
     (* 2.0 (- (* z t) (* c (* i t_1))))
     (if (<= c 3.3e-53)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a))))
       (* 2.0 (- (* x y) (* t_1 (* i c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if (c <= -4.2e+71) {
		tmp = 2.0 * ((z * t) - (c * (i * t_1)));
	} else if (c <= 3.3e-53) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((x * y) - (t_1 * (i * 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) :: t_1
    real(8) :: tmp
    t_1 = a + (c * b)
    if (c <= (-4.2d+71)) then
        tmp = 2.0d0 * ((z * t) - (c * (i * t_1)))
    else if (c <= 3.3d-53) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    else
        tmp = 2.0d0 * ((x * y) - (t_1 * (i * 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 t_1 = a + (c * b);
	double tmp;
	if (c <= -4.2e+71) {
		tmp = 2.0 * ((z * t) - (c * (i * t_1)));
	} else if (c <= 3.3e-53) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((x * y) - (t_1 * (i * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	tmp = 0
	if c <= -4.2e+71:
		tmp = 2.0 * ((z * t) - (c * (i * t_1)))
	elif c <= 3.3e-53:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	else:
		tmp = 2.0 * ((x * y) - (t_1 * (i * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (c <= -4.2e+71)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * t_1))));
	elseif (c <= 3.3e-53)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(t_1 * Float64(i * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	tmp = 0.0;
	if (c <= -4.2e+71)
		tmp = 2.0 * ((z * t) - (c * (i * t_1)));
	elseif (c <= 3.3e-53)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	else
		tmp = 2.0 * ((x * y) - (t_1 * (i * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+71], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e-53], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(t$95$1 * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.19999999999999978e71

   1. Initial program 73.9%

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

      1. associate--l+ 73.9%

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

      2. *-commutative 73.9%

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

      3. associate--l+ 73.9%

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

      4. associate--l+ 73.9%

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

      5. *-commutative 73.9%

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

      6. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around 0 91.9%

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

   if -4.19999999999999978e71 < c < 3.30000000000000004e-53

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   if 3.30000000000000004e-53 < c

   1. Initial program 83.0%

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

      1. associate--l+ 83.0%

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

      2. *-commutative 83.0%

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

      3. associate--l+ 83.0%

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

      4. associate--l+ 83.0%

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

      5. *-commutative 83.0%

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

      6. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. associate-*r* 80.9%

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

   7. Simplified 80.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(a + c \cdot b\right) \cdot \left(i \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+33} \lor \neg \left(c \leq 18.5\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.15e+33) (not (<= c 18.5)))
   (* (* c (* i (+ a (* c b)))) -2.0)
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.15e+33) || !(c <= 18.5)) {
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.15d+33)) .or. (.not. (c <= 18.5d0))) then
        tmp = (c * (i * (a + (c * b)))) * (-2.0d0)
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.15e+33) || !(c <= 18.5)) {
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.15e+33) or not (c <= 18.5):
		tmp = (c * (i * (a + (c * b)))) * -2.0
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.15e+33) || !(c <= 18.5))
		tmp = Float64(Float64(c * Float64(i * Float64(a + Float64(c * b)))) * -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.15e+33) || ~((c <= 18.5)))
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.15e+33], N[Not[LessEqual[c, 18.5]], $MachinePrecision]], N[(N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.15000000000000014e33 or 18.5 < c

   1. Initial program 78.4%

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

      1. associate--l+ 78.4%

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

      2. *-commutative 78.4%

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

      3. associate--l+ 78.4%

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

      4. associate--l+ 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 80.6%

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

      1. associate-*r* 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in x around 0 71.7%

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

   if -2.15000000000000014e33 < c < 18.5

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in c around 0 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+33} \lor \neg \left(c \leq 18.5\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+80) (not (<= (* x y) 4e+59)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -5e+80) || !((x * y) <= 4e+59)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-5d+80)) .or. (.not. ((x * y) <= 4d+59))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -5e+80) || !((x * y) <= 4e+59)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -5e+80) or not ((x * y) <= 4e+59):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+80) || !(Float64(x * y) <= 4e+59))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -5e+80) || ~(((x * y) <= 4e+59)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+80], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+59]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999961e80 or 3.99999999999999989e59 < (*.f64 x y)

   1. Initial program 88.8%

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

      1. associate--l+ 88.8%

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

      2. *-commutative 88.8%

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

      3. associate--l+ 88.8%

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

      4. associate--l+ 88.8%

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

      5. *-commutative 88.8%

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

      6. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 65.1%

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

   if -4.99999999999999961e80 < (*.f64 x y) < 3.99999999999999989e59

   1. Initial program 89.1%

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

      1. associate--l+ 89.1%

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

      2. *-commutative 89.1%

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

      3. associate--l+ 89.1%

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

      4. associate--l+ 89.1%

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

      5. *-commutative 89.1%

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

      6. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 38.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.3e+154) (* a (* (* i c) -2.0)) (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.3e+154) {
		tmp = a * ((i * c) * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-1.3d+154)) then
        tmp = a * ((i * c) * (-2.0d0))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.3e+154) {
		tmp = a * ((i * c) * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.3e+154:
		tmp = a * ((i * c) * -2.0)
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.3e+154)
		tmp = Float64(a * Float64(Float64(i * c) * -2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.3e+154)
		tmp = a * ((i * c) * -2.0);
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.3e+154], N[(a * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.29999999999999994e154

   1. Initial program 94.4%

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

      1. associate--l+ 94.4%

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

      2. *-commutative 94.4%

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

      3. associate--l+ 94.4%

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

      4. associate--l+ 94.4%

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

      5. *-commutative 94.4%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. associate-*r* 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in a around inf 57.3%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 57.3%

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

      4. associate-*l* 57.3%

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

   10. Simplified 57.3%

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

   if -1.29999999999999994e154 < i

   1. Initial program 88.1%

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

      1. associate--l+ 88.1%

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

      2. *-commutative 88.1%

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

      3. associate--l+ 88.1%

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

      4. associate--l+ 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in c around 0 61.5%

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

      1. +-commutative 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.8% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. associate--l+ 89.0%

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

   2. *-commutative 89.0%

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

   3. associate--l+ 89.0%

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

   4. associate--l+ 89.0%

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

   5. *-commutative 89.0%

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

   6. associate-*l* 94.1%

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

3. Simplified 94.1%

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

5. Taylor expanded in z around inf 27.9%

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

6. Final simplification 27.9%

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

Developer target: 93.6% 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 2024048 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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