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

Percentage Accurate: 90.0% → 93.9%

Time: 15.9s

Alternatives: 12

Speedup: 0.9×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \frac{c \cdot i}{\frac{-1}{a + c \cdot b}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (+ (+ (* x y) (* z t)) (/ (* c i) (/ -1.0 (+ a (* c b)))))))

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)) + ((c * i) / (-1.0 / (a + (c * b)))));
}

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)) + ((c * i) / ((-1.0d0) / (a + (c * b)))))
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)) + ((c * i) / (-1.0 / (a + (c * b)))));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / (a + (c * b)))))

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(c * i) / Float64(-1.0 / Float64(a + Float64(c * b))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / (a + (c * b)))));
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[(c * i), $MachinePrecision] / N[(-1.0 / N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.9%

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

   1. associate-*l* N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(a + b \cdot c\right) \cdot \color{blue}{\left(c \cdot i\right)}\right)\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \color{blue}{\left(a + b \cdot c\right)}\right)\right)\right) \]

   3. flip-+ N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{\color{blue}{a - b \cdot c}}\right)\right)\right) \]

   4. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \frac{1}{\color{blue}{\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}}}\right)\right)\right) \]

   5. un-div-inv N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\frac{c \cdot i}{\color{blue}{\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}}}\right)\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\left(c \cdot i\right), \color{blue}{\left(\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}\right)}\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{\color{blue}{a - b \cdot c}}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}\right)\right)\right)\right) \]

   8. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{1}{\color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}}\right)\right)\right)\right) \]

   9. flip-+ N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{1}{a + \color{blue}{b \cdot c}}\right)\right)\right)\right) \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \color{blue}{\left(a + b \cdot c\right)}\right)\right)\right)\right) \]

   11. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot c\right)}\right)\right)\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \left(c \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

   13. *-lowering-*.f64 97.5%

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

4. Applied egg-rr 97.5%

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

5. Final simplification 97.5%

   \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \frac{c \cdot i}{\frac{-1}{a + c \cdot b}}\right) \]
6. Add Preprocessing

Alternative 2: 92.3% accurate, 0.6× speedup

Math

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

FPCore

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

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 t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (i * t_1))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	}
	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 t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (i * t_1))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (i * t_1))));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	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]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 78.2%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 90.0%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 90.0%

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

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

   1. Initial program 97.6%

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

4. Final simplification 96.1%

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

Alternative 3: 92.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (- (* z t) (* c (* i (+ a (* c b)))))))))
   (if (<= c -7.5e-115)
     t_1
     (if (<= c 2e-181) (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (c * b))))));
	double tmp;
	if (c <= -7.5e-115) {
		tmp = t_1;
	} else if (c <= 2e-181) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + ((z * t) - (c * (i * (a + (c * b))))))
    if (c <= (-7.5d-115)) then
        tmp = t_1
    else if (c <= 2d-181) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (c * b))))));
	double tmp;
	if (c <= -7.5e-115) {
		tmp = t_1;
	} else if (c <= 2e-181) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (c * b))))))
	tmp = 0
	if c <= -7.5e-115:
		tmp = t_1
	elif c <= 2e-181:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b)))))))
	tmp = 0.0
	if (c <= -7.5e-115)
		tmp = t_1;
	elseif (c <= 2e-181)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (c * b))))));
	tmp = 0.0;
	if (c <= -7.5e-115)
		tmp = t_1;
	elseif (c <= 2e-181)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e-115], t$95$1, If[LessEqual[c, 2e-181], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -7.50000000000000038e-115 or 2.00000000000000009e-181 < c

   1. Initial program 91.3%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 95.0%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 95.0%

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

   if -7.50000000000000038e-115 < c < 2.00000000000000009e-181

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\color{blue}{\left(a \cdot c\right)}, i\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\left(c \cdot a\right), i\right)\right)\right) \]

      2. *-lowering-*.f64 98.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, a\right), i\right)\right)\right) \]

   5. Simplified 98.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \frac{c \cdot i}{\frac{-1}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* c b)) (- 0.0 i))))))
   (if (<= c -1.55e+109)
     t_1
     (if (<= c 1.85e+74)
       (* 2.0 (+ (+ (* x y) (* z t)) (/ (* c i) (/ -1.0 a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -1.55e+109) {
		tmp = t_1;
	} else if (c <= 1.85e+74) {
		tmp = 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (c * b)) * (0.0d0 - i)))
    if (c <= (-1.55d+109)) then
        tmp = t_1
    else if (c <= 1.85d+74) then
        tmp = 2.0d0 * (((x * y) + (z * t)) + ((c * i) / ((-1.0d0) / a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -1.55e+109) {
		tmp = t_1;
	} else if (c <= 1.85e+74) {
		tmp = 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)))
	tmp = 0
	if c <= -1.55e+109:
		tmp = t_1
	elif c <= 1.85e+74:
		tmp = 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(c * b)) * Float64(0.0 - i))))
	tmp = 0.0
	if (c <= -1.55e+109)
		tmp = t_1;
	elseif (c <= 1.85e+74)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(Float64(c * i) / Float64(-1.0 / a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	tmp = 0.0;
	if (c <= -1.55e+109)
		tmp = t_1;
	elseif (c <= 1.85e+74)
		tmp = 2.0 * (((x * y) + (z * t)) + ((c * i) / (-1.0 / a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(0.0 - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+109], t$95$1, If[LessEqual[c, 1.85e+74], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] / N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.54999999999999996e109 or 1.8500000000000001e74 < c

   1. Initial program 84.6%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 93.8%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(-1 \cdot c\right) \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(i \cdot \left(a + b \cdot c\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \left(a + b \cdot c\right)\right), \left(\color{blue}{-1} \cdot c\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(b \cdot c\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(c \cdot b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(0 - \color{blue}{c}\right)\right)\right) \]

      10. --lowering--.f64 84.6%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{c}\right)\right)\right) \]

   7. Simplified 84.6%

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

   if -1.54999999999999996e109 < c < 1.8500000000000001e74

   1. Initial program 99.3%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(a + b \cdot c\right) \cdot \color{blue}{\left(c \cdot i\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \color{blue}{\left(a + b \cdot c\right)}\right)\right)\right) \]

      3. flip-+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{\color{blue}{a - b \cdot c}}\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\left(c \cdot i\right) \cdot \frac{1}{\color{blue}{\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}}}\right)\right)\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \left(\frac{c \cdot i}{\color{blue}{\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}}}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\left(c \cdot i\right), \color{blue}{\left(\frac{a - b \cdot c}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{\color{blue}{a - b \cdot c}}{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}\right)\right)\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{1}{\color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}}\right)\right)\right)\right) \]

      9. flip-+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(\frac{1}{a + \color{blue}{b \cdot c}}\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \color{blue}{\left(a + b \cdot c\right)}\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot c\right)}\right)\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \left(c \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \color{blue}{\left(\frac{1}{a}\right)}\right)\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 91.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{/.f64}\left(1, \color{blue}{a}\right)\right)\right)\right) \]

   7. Simplified 91.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+109}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) + \frac{c \cdot i}{\frac{-1}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* c b)) (- 0.0 i))))))
   (if (<= c -1.8e+103)
     t_1
     (if (<= c 6.2e+75) (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -1.8e+103) {
		tmp = t_1;
	} else if (c <= 6.2e+75) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (c * b)) * (0.0d0 - i)))
    if (c <= (-1.8d+103)) then
        tmp = t_1
    else if (c <= 6.2d+75) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -1.8e+103) {
		tmp = t_1;
	} else if (c <= 6.2e+75) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)))
	tmp = 0
	if c <= -1.8e+103:
		tmp = t_1
	elif c <= 6.2e+75:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(c * b)) * Float64(0.0 - i))))
	tmp = 0.0
	if (c <= -1.8e+103)
		tmp = t_1;
	elseif (c <= 6.2e+75)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	tmp = 0.0;
	if (c <= -1.8e+103)
		tmp = t_1;
	elseif (c <= 6.2e+75)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(0.0 - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+103], t$95$1, If[LessEqual[c, 6.2e+75], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.80000000000000008e103 or 6.2000000000000002e75 < c

   1. Initial program 84.6%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 93.8%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(-1 \cdot c\right) \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(i \cdot \left(a + b \cdot c\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \left(a + b \cdot c\right)\right), \left(\color{blue}{-1} \cdot c\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(b \cdot c\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(c \cdot b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(0 - \color{blue}{c}\right)\right)\right) \]

      10. --lowering--.f64 84.6%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{c}\right)\right)\right) \]

   7. Simplified 84.6%

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

   if -1.80000000000000008e103 < c < 6.2000000000000002e75

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\color{blue}{\left(a \cdot c\right)}, i\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\left(c \cdot a\right), i\right)\right)\right) \]

      2. *-lowering-*.f64 91.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, a\right), i\right)\right)\right) \]

   5. Simplified 91.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* c b)) (- 0.0 i))))))
   (if (<= c -5.8e+102)
     t_1
     (if (<= c 7.2e+60) (* 2.0 (+ (* x y) (* 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 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -5.8e+102) {
		tmp = t_1;
	} else if (c <= 7.2e+60) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (c * b)) * (0.0d0 - i)))
    if (c <= (-5.8d+102)) then
        tmp = t_1
    else if (c <= 7.2d+60) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	double tmp;
	if (c <= -5.8e+102) {
		tmp = t_1;
	} else if (c <= 7.2e+60) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)))
	tmp = 0
	if c <= -5.8e+102:
		tmp = t_1
	elif c <= 7.2e+60:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(c * b)) * Float64(0.0 - i))))
	tmp = 0.0
	if (c <= -5.8e+102)
		tmp = t_1;
	elseif (c <= 7.2e+60)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (c * b)) * (0.0 - i)));
	tmp = 0.0;
	if (c <= -5.8e+102)
		tmp = t_1;
	elseif (c <= 7.2e+60)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(0.0 - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.8e+102], t$95$1, If[LessEqual[c, 7.2e+60], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -5.8000000000000005e102 or 7.19999999999999935e60 < c

   1. Initial program 85.5%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 94.1%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 94.1%

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

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(-1 \cdot c\right) \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(i \cdot \left(a + b \cdot c\right)\right), \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \left(a + b \cdot c\right)\right), \left(\color{blue}{-1} \cdot c\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(b \cdot c\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \left(c \cdot b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(-1 \cdot c\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \left(0 - \color{blue}{c}\right)\right)\right) \]

      10. --lowering--.f64 83.5%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{c}\right)\right)\right) \]

   7. Simplified 83.5%

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

   if -5.8000000000000005e102 < c < 7.19999999999999935e60

   1. Initial program 99.3%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 91.9%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 91.9%

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

   5. Taylor expanded in c around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z + x \cdot y\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 76.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + c \cdot b\right) \cdot \left(0 - i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -1.8e+137)
     t_1
     (if (<= z 9.8e-262)
       (* 2.0 (* x y))
       (if (<= z 1.05e-32) (* a (* c (* i -2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.8e+137) {
		tmp = t_1;
	} else if (z <= 9.8e-262) {
		tmp = 2.0 * (x * y);
	} else if (z <= 1.05e-32) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (z <= (-1.8d+137)) then
        tmp = t_1
    else if (z <= 9.8d-262) then
        tmp = 2.0d0 * (x * y)
    else if (z <= 1.05d-32) then
        tmp = a * (c * (i * (-2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.8e+137) {
		tmp = t_1;
	} else if (z <= 9.8e-262) {
		tmp = 2.0 * (x * y);
	} else if (z <= 1.05e-32) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -1.8e+137:
		tmp = t_1
	elif z <= 9.8e-262:
		tmp = 2.0 * (x * y)
	elif z <= 1.05e-32:
		tmp = a * (c * (i * -2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -1.8e+137)
		tmp = t_1;
	elseif (z <= 9.8e-262)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (z <= 1.05e-32)
		tmp = Float64(a * Float64(c * Float64(i * -2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -1.8e+137)
		tmp = t_1;
	elseif (z <= 9.8e-262)
		tmp = 2.0 * (x * y);
	elseif (z <= 1.05e-32)
		tmp = a * (c * (i * -2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+137], t$95$1, If[LessEqual[z, 9.8e-262], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-32], N[(a * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e137 or 1.05e-32 < z

   1. Initial program 91.6%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 93.4%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 56.4%

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

   if -1.8e137 < z < 9.8000000000000005e-262

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 90.4%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 36.2%

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

   if 9.8000000000000005e-262 < z < 1.05e-32

   1. Initial program 99.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 96.2%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 96.2%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-2 \cdot \left(c \cdot i\right)\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(\left(c \cdot i\right) \cdot \color{blue}{-2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot \color{blue}{\left(i \cdot -2\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{\left(i \cdot -2\right)}\right)\right) \]

      8. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(i, \color{blue}{-2}\right)\right)\right) \]

   7. Simplified 33.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(a + c \cdot b\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ a (* c b)) (* c -2.0)))))
   (if (<= c -4.8e+102)
     t_1
     (if (<= c 3.9e+59) (* 2.0 (+ (* x y) (* 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 = i * ((a + (c * b)) * (c * -2.0));
	double tmp;
	if (c <= -4.8e+102) {
		tmp = t_1;
	} else if (c <= 3.9e+59) {
		tmp = 2.0 * ((x * y) + (z * t));
	} 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 = i * ((a + (c * b)) * (c * (-2.0d0)))
    if (c <= (-4.8d+102)) then
        tmp = t_1
    else if (c <= 3.9d+59) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    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 = i * ((a + (c * b)) * (c * -2.0));
	double tmp;
	if (c <= -4.8e+102) {
		tmp = t_1;
	} else if (c <= 3.9e+59) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * ((a + (c * b)) * (c * -2.0))
	tmp = 0
	if c <= -4.8e+102:
		tmp = t_1
	elif c <= 3.9e+59:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(a + Float64(c * b)) * Float64(c * -2.0)))
	tmp = 0.0
	if (c <= -4.8e+102)
		tmp = t_1;
	elseif (c <= 3.9e+59)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i * ((a + (c * b)) * (c * -2.0));
	tmp = 0.0;
	if (c <= -4.8e+102)
		tmp = t_1;
	elseif (c <= 3.9e+59)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e+102], t$95$1, If[LessEqual[c, 3.9e+59], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -4.79999999999999989e102 or 3.90000000000000021e59 < c

   1. Initial program 85.5%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 94.1%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 94.1%

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

   5. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-2 \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(\left(-2 \cdot c\right) \cdot \color{blue}{\left(a + b \cdot c\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(\left(a + b \cdot c\right) \cdot \color{blue}{\left(-2 \cdot c\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(a + b \cdot c\right), \color{blue}{\left(-2 \cdot c\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), \left(\color{blue}{-2} \cdot c\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(c \cdot b\right)\right), \left(-2 \cdot c\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right), \left(-2 \cdot c\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right), \left(c \cdot \color{blue}{-2}\right)\right)\right) \]

      14. *-lowering-*.f64 79.8%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(c, b\right)\right), \mathsf{*.f64}\left(c, \color{blue}{-2}\right)\right)\right) \]

   7. Simplified 79.8%

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

   if -4.79999999999999989e102 < c < 3.90000000000000021e59

   1. Initial program 99.3%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 91.9%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 91.9%

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

   5. Taylor expanded in c around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z + x \cdot y\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 76.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(\left(a + c \cdot b\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(a + c \cdot b\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (* -2.0 (* c (* c i))))))
   (if (<= c -2.2e+107)
     t_1
     (if (<= c 4.2e+102) (* 2.0 (+ (* x y) (* 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 = b * (-2.0 * (c * (c * i)));
	double tmp;
	if (c <= -2.2e+107) {
		tmp = t_1;
	} else if (c <= 4.2e+102) {
		tmp = 2.0 * ((x * y) + (z * t));
	} 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 = b * ((-2.0d0) * (c * (c * i)))
    if (c <= (-2.2d+107)) then
        tmp = t_1
    else if (c <= 4.2d+102) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    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 = b * (-2.0 * (c * (c * i)));
	double tmp;
	if (c <= -2.2e+107) {
		tmp = t_1;
	} else if (c <= 4.2e+102) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * (-2.0 * (c * (c * i)))
	tmp = 0
	if c <= -2.2e+107:
		tmp = t_1
	elif c <= 4.2e+102:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * Float64(-2.0 * Float64(c * Float64(c * i))))
	tmp = 0.0
	if (c <= -2.2e+107)
		tmp = t_1;
	elseif (c <= 4.2e+102)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * (-2.0 * (c * (c * i)));
	tmp = 0.0;
	if (c <= -2.2e+107)
		tmp = t_1;
	elseif (c <= 4.2e+102)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[(-2.0 * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+107], t$95$1, If[LessEqual[c, 4.2e+102], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.2e107 or 4.20000000000000003e102 < c

   1. Initial program 84.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 93.3%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 93.3%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(b \cdot \left({c}^{2} \cdot i\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(b \cdot \color{blue}{\left(\mathsf{neg}\left({c}^{2} \cdot i\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(b \cdot \left(-1 \cdot \color{blue}{\left({c}^{2} \cdot i\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot i\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left({c}^{2} \cdot i\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(0 - \color{blue}{{c}^{2} \cdot i}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \color{blue}{\left({c}^{2} \cdot i\right)}\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \left(\left(c \cdot c\right) \cdot i\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \left(c \cdot \color{blue}{\left(c \cdot i\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \color{blue}{\left(c \cdot i\right)}\right)\right)\right)\right) \]

      11. *-lowering-*.f64 75.7%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(c, \color{blue}{i}\right)\right)\right)\right)\right) \]

   7. Simplified 75.7%

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

   8. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot -2\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left({c}^{2} \cdot i\right), \color{blue}{-2}\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(\left(c \cdot c\right) \cdot i\right), -2\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(c \cdot \left(c \cdot i\right)\right), -2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, \left(c \cdot i\right)\right), -2\right)\right) \]

      8. *-lowering-*.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(c, i\right)\right), -2\right)\right) \]

   10. Simplified 75.7%

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

   if -2.2e107 < c < 4.20000000000000003e102

   1. Initial program 98.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in c around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z + x \cdot y\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 74.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -1.6e-159) t_1 (if (<= t 2.35e+54) (* 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 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.6e-159) {
		tmp = t_1;
	} else if (t <= 2.35e+54) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-1.6d-159)) then
        tmp = t_1
    else if (t <= 2.35d+54) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.6e-159) {
		tmp = t_1;
	} else if (t <= 2.35e+54) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.6e-159:
		tmp = t_1
	elif t <= 2.35e+54:
		tmp = 2.0 * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1.6e-159)
		tmp = t_1;
	elseif (t <= 2.35e+54)
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1.6e-159)
		tmp = t_1;
	elseif (t <= 2.35e+54)
		tmp = 2.0 * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-159], t$95$1, If[LessEqual[t, 2.35e+54], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-159 or 2.34999999999999996e54 < t

   1. Initial program 92.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 92.1%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 45.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 45.5%

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

   if -1.6e-159 < t < 2.34999999999999996e54

   1. Initial program 95.2%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 93.6%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 40.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 40.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.55 \cdot 10^{+255}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.55e+255) (* 2.0 (+ (* x y) (* z t))) (* a (* c (* i -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.55e+255) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = a * (c * (i * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.55d+255) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = a * (c * (i * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.55e+255) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = a * (c * (i * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.55e+255:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = a * (c * (i * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.55e+255)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(a * Float64(c * Float64(i * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.55e+255)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = a * (c * (i * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.55e+255], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5500000000000001e255

   1. Initial program 93.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 92.8%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 92.8%

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

   5. Taylor expanded in c around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z + x \cdot y\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 59.3%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 59.3%

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

   if 1.5500000000000001e255 < a

   1. Initial program 93.0%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

      7. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

      19. *-lowering-*.f64 92.5%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-2 \cdot \left(c \cdot i\right)\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(\left(c \cdot i\right) \cdot \color{blue}{-2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot \color{blue}{\left(i \cdot -2\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{\left(i \cdot -2\right)}\right)\right) \]

      8. *-lowering-*.f64 87.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(i, \color{blue}{-2}\right)\right)\right) \]

   7. Simplified 87.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.55 \cdot 10^{+255}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.4% 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 93.9%

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)}\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + \color{blue}{\left(x \cdot y + z \cdot t\right)}\right)\right) \]

   4. associate-+r+ N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(\left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right) + \color{blue}{z \cdot t}\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right) + \color{blue}{z} \cdot t\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(\left(x \cdot y - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + \color{blue}{z} \cdot t\right)\right) \]

   7. associate-+l- N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot y - \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - z \cdot t\right)}\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i} - z \cdot t\right)\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

   13. associate-*l* N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(i \cdot \left(a + b \cdot c\right)\right)\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(\left(a + b \cdot c\right) \cdot i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(a + b \cdot c\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

   17. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \left(b \cdot c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \left(z \cdot t\right)\right)\right)\right) \]

   19. *-lowering-*.f64 92.8%

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, c\right)\right), i\right)\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

3. Simplified 92.8%

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

5. Taylor expanded in z around inf

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right) \]

   2. *-lowering-*.f64 30.3%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

7. Simplified 30.3%

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

8. Final simplification 30.3%

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

Developer Target 1: 93.9% 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 2024145 
(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
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

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