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

Percentage Accurate: 89.8% → 96.3%

Time: 16.6s

Alternatives: 15

Speedup: 0.7×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.1%

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

      1. *-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 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 98.0%

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

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

   1. Initial program 0.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 0.0%

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

   3. Simplified 0.0%

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

   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 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 97.7%

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

Alternative 2: 85.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot -2\right) \cdot \left(i \cdot t\_1\right)\\ t_3 := \left(c \cdot t\_1\right) \cdot i\\ t_4 := 2 \cdot \left(z \cdot t - t\_3\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 0.01:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c)))
        (t_2 (* (* c -2.0) (* i t_1)))
        (t_3 (* (* c t_1) i))
        (t_4 (* 2.0 (- (* z t) t_3))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -5e+70)
       t_4
       (if (<= t_3 0.01)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= t_3 5e+267) t_4 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double t_4 = 2.0 * ((z * t) - t_3);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -5e+70) {
		tmp = t_4;
	} else if (t_3 <= 0.01) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (t_3 <= 5e+267) {
		tmp = t_4;
	} else {
		tmp = 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double t_4 = 2.0 * ((z * t) - t_3);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= -5e+70) {
		tmp = t_4;
	} else if (t_3 <= 0.01) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (t_3 <= 5e+267) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * -2.0) * (i * t_1)
	t_3 = (c * t_1) * i
	t_4 = 2.0 * ((z * t) - t_3)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= -5e+70:
		tmp = t_4
	elif t_3 <= 0.01:
		tmp = ((x * y) + (z * t)) * 2.0
	elif t_3 <= 5e+267:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * -2.0) * Float64(i * t_1))
	t_3 = Float64(Float64(c * t_1) * i)
	t_4 = Float64(2.0 * Float64(Float64(z * t) - t_3))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -5e+70)
		tmp = t_4;
	elseif (t_3 <= 0.01)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (t_3 <= 5e+267)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * -2.0) * (i * t_1);
	t_3 = (c * t_1) * i;
	t_4 = 2.0 * ((z * t) - t_3);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= -5e+70)
		tmp = t_4;
	elseif (t_3 <= 0.01)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (t_3 <= 5e+267)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * -2.0), $MachinePrecision] * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$4 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -5e+70], t$95$4, If[LessEqual[t$95$3, 0.01], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$3, 5e+267], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 4.9999999999999999e267 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 70.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 87.0%

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

   3. Simplified 87.0%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 90.7%

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

   9. Simplified 90.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000002e70 or 0.0100000000000000002 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999999e267

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 77.0%

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

   5. Simplified 77.0%

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

   if -5.0000000000000002e70 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 0.0100000000000000002

   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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 0.01:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+267}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot -2\right) \cdot \left(i \cdot t\_1\right)\\ t_3 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_3\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c)))
        (t_2 (* (* c -2.0) (* i t_1)))
        (t_3 (* (* c t_1) i)))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 5e+267) (* (- (+ (* x y) (* z t)) t_3) 2.0) 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 5e+267) {
		tmp = (((x * y) + (z * t)) - t_3) * 2.0;
	} else {
		tmp = 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= 5e+267) {
		tmp = (((x * y) + (z * t)) - t_3) * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * -2.0) * (i * t_1)
	t_3 = (c * t_1) * i
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= 5e+267:
		tmp = (((x * y) + (z * t)) - t_3) * 2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * -2.0) * Float64(i * t_1))
	t_3 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 5e+267)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_3) * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * -2.0) * (i * t_1);
	t_3 = (c * t_1) * i;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= 5e+267)
		tmp = (((x * y) + (z * t)) - t_3) * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * -2.0), $MachinePrecision] * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 5e+267], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] * 2.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 4.9999999999999999e267 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 70.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 87.0%

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

   3. Simplified 87.0%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 90.7%

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

   9. Simplified 90.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999999e267

   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. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot t\_1\\ t_3 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(c \cdot -2\right) \cdot t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i t_1)) (t_3 (* (* c t_1) i)))
   (if (<= t_3 (- INFINITY))
     (* (* c -2.0) t_2)
     (if (<= t_3 2e+157)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) (* c 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 + (b * c);
	double t_2 = i * t_1;
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (c * -2.0) * t_2;
	} else if (t_3 <= 2e+157) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - (c * 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 + (b * c);
	double t_2 = i * t_1;
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (c * -2.0) * t_2;
	} else if (t_3 <= 2e+157) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - (c * t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * t_1
	t_3 = (c * t_1) * i
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (c * -2.0) * t_2
	elif t_3 <= 2e+157:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - (c * t_2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * t_1)
	t_3 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(c * -2.0) * t_2);
	elseif (t_3 <= 2e+157)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * t_1;
	t_3 = (c * t_1) * i;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (c * -2.0) * t_2;
	elseif (t_3 <= 2e+157)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - (c * t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(c * -2.0), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 2e+157], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 93.2%

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

   3. Simplified 93.2%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 95.7%

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

   9. Simplified 95.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.99999999999999997e157

   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 95.5%

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

   5. Simplified 95.5%

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

   if 1.99999999999999997e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 72.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 77.4%

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

   3. Simplified 77.4%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 85.8%

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

   7. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 79.1%

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

   9. Simplified 79.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot -2\right) \cdot \left(i \cdot t\_1\right)\\ t_3 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c)))
        (t_2 (* (* c -2.0) (* i t_1)))
        (t_3 (* (* c t_1) i)))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 5e+267) (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c)))) 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 5e+267) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 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 + (b * c);
	double t_2 = (c * -2.0) * (i * t_1);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= 5e+267) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * -2.0) * (i * t_1)
	t_3 = (c * t_1) * i
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= 5e+267:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * -2.0) * Float64(i * t_1))
	t_3 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 5e+267)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * -2.0) * (i * t_1);
	t_3 = (c * t_1) * i;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= 5e+267)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * -2.0), $MachinePrecision] * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 5e+267], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 4.9999999999999999e267 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 70.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 87.0%

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

   3. Simplified 87.0%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 90.7%

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

   9. Simplified 90.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999999e267

   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 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+267}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-52}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (- (* z t) (* c (* i (+ a (* b c)))))))))
   (if (<= c -1.5e-202)
     t_1
     (if (<= c 5.6e-52) (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (b * c))))));
	double tmp;
	if (c <= -1.5e-202) {
		tmp = t_1;
	} else if (c <= 5.6e-52) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + ((z * t) - (c * (i * (a + (b * c))))))
    if (c <= (-1.5d-202)) then
        tmp = t_1
    else if (c <= 5.6d-52) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + ((z * t) - (c * (i * (a + (b * c))))));
	double tmp;
	if (c <= -1.5e-202) {
		tmp = t_1;
	} else if (c <= 5.6e-52) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} 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 + (b * c))))))
	tmp = 0
	if c <= -1.5e-202:
		tmp = t_1
	elif c <= 5.6e-52:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	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(b * c)))))))
	tmp = 0.0
	if (c <= -1.5e-202)
		tmp = t_1;
	elseif (c <= 5.6e-52)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	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 + (b * c))))));
	tmp = 0.0;
	if (c <= -1.5e-202)
		tmp = t_1;
	elseif (c <= 5.6e-52)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e-202], t$95$1, If[LessEqual[c, 5.6e-52], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.50000000000000005e-202 or 5.59999999999999989e-52 < c

   1. Initial program 85.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 91.8%

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

   3. Simplified 91.8%

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

   if -1.50000000000000005e-202 < c < 5.59999999999999989e-52

   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 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-52}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -6.6 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -6.5e-78)
     t_1
     (if (<= (* x y) -6.6e-200)
       (* a (* c (* i -2.0)))
       (if (<= (* x y) 1.6e-51) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -6.5e-78) {
		tmp = t_1;
	} else if ((x * y) <= -6.6e-200) {
		tmp = a * (c * (i * -2.0));
	} else if ((x * y) <= 1.6e-51) {
		tmp = 2.0 * (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 = (x * y) * 2.0d0
    if ((x * y) <= (-6.5d-78)) then
        tmp = t_1
    else if ((x * y) <= (-6.6d-200)) then
        tmp = a * (c * (i * (-2.0d0)))
    else if ((x * y) <= 1.6d-51) then
        tmp = 2.0d0 * (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 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -6.5e-78) {
		tmp = t_1;
	} else if ((x * y) <= -6.6e-200) {
		tmp = a * (c * (i * -2.0));
	} else if ((x * y) <= 1.6e-51) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -6.5e-78:
		tmp = t_1
	elif (x * y) <= -6.6e-200:
		tmp = a * (c * (i * -2.0))
	elif (x * y) <= 1.6e-51:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -6.5e-78)
		tmp = t_1;
	elseif (Float64(x * y) <= -6.6e-200)
		tmp = Float64(a * Float64(c * Float64(i * -2.0)));
	elseif (Float64(x * y) <= 1.6e-51)
		tmp = Float64(2.0 * 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 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -6.5e-78)
		tmp = t_1;
	elseif ((x * y) <= -6.6e-200)
		tmp = a * (c * (i * -2.0));
	elseif ((x * y) <= 1.6e-51)
		tmp = 2.0 * (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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.5e-78], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -6.6e-200], N[(a * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.6e-51], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.5000000000000003e-78 or 1.6e-51 < (*.f64 x y)

   1. Initial program 88.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 87.4%

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

   3. Simplified 87.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 51.4%

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

   7. Simplified 51.4%

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

   if -6.5000000000000003e-78 < (*.f64 x y) < -6.5999999999999995e-200

   1. Initial program 95.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 85.5%

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

   3. Simplified 85.5%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 56.1%

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

   7. Simplified 56.1%

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

   if -6.5999999999999995e-200 < (*.f64 x y) < 1.6e-51

   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 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 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -6.6 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+68}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c -2.0) (* i (+ a (* b c))))))
   (if (<= c -7.2e+74)
     t_1
     (if (<= c 8.4e+68) (* (+ (* x y) (* z t)) 2.0) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * -2.0) * (i * (a + (b * c)));
	double tmp;
	if (c <= -7.2e+74) {
		tmp = t_1;
	} else if (c <= 8.4e+68) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * (-2.0d0)) * (i * (a + (b * c)))
    if (c <= (-7.2d+74)) then
        tmp = t_1
    else if (c <= 8.4d+68) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * -2.0) * (i * (a + (b * c)));
	double tmp;
	if (c <= -7.2e+74) {
		tmp = t_1;
	} else if (c <= 8.4e+68) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * -2.0) * (i * (a + (b * c)))
	tmp = 0
	if c <= -7.2e+74:
		tmp = t_1
	elif c <= 8.4e+68:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * -2.0) * Float64(i * Float64(a + Float64(b * c))))
	tmp = 0.0
	if (c <= -7.2e+74)
		tmp = t_1;
	elseif (c <= 8.4e+68)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * -2.0) * (i * (a + (b * c)));
	tmp = 0.0;
	if (c <= -7.2e+74)
		tmp = t_1;
	elseif (c <= 8.4e+68)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * -2.0), $MachinePrecision] * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.2e+74], t$95$1, If[LessEqual[c, 8.4e+68], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -7.19999999999999975e74 or 8.40000000000000003e68 < c

   1. Initial program 77.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 93.0%

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

   3. Simplified 93.0%

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

      1. *-commutative N/A

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

      2. associate--r- N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. fmm-def N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 84.6%

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

   9. Simplified 84.6%

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

   if -7.19999999999999975e74 < c < 8.40000000000000003e68

   1. Initial program 96.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 86.8%

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

   3. Simplified 86.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+74}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+68}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(a + b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1e+75)
   (* c (* -2.0 (* b (* c i))))
   (if (<= c 1.7e+70)
     (* (+ (* x y) (* z t)) 2.0)
     (* i (* (+ a (* b c)) (* c -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1e+75) {
		tmp = c * (-2.0 * (b * (c * i)));
	} else if (c <= 1.7e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = i * ((a + (b * c)) * (c * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1d+75)) then
        tmp = c * ((-2.0d0) * (b * (c * i)))
    else if (c <= 1.7d+70) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = i * ((a + (b * c)) * (c * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1e+75) {
		tmp = c * (-2.0 * (b * (c * i)));
	} else if (c <= 1.7e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = i * ((a + (b * c)) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1e+75:
		tmp = c * (-2.0 * (b * (c * i)))
	elif c <= 1.7e+70:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = i * ((a + (b * c)) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1e+75)
		tmp = Float64(c * Float64(-2.0 * Float64(b * Float64(c * i))));
	elseif (c <= 1.7e+70)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(i * Float64(Float64(a + Float64(b * c)) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1e+75)
		tmp = c * (-2.0 * (b * (c * i)));
	elseif (c <= 1.7e+70)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = i * ((a + (b * c)) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1e+75], N[(c * N[(-2.0 * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+70], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(i * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.99999999999999927e74

   1. Initial program 76.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 74.3%

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

   7. Simplified 74.3%

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

      1. *-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. *-lowering-*.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

   if -9.99999999999999927e74 < c < 1.7e70

   1. Initial program 96.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 86.8%

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

   3. Simplified 86.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

   if 1.7e70 < c

   1. Initial program 78.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 94.7%

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

   3. Simplified 94.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 71.2%

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

   7. Simplified 71.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(a + b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -3.4e+74)
   (* c (* -2.0 (* b (* c i))))
   (if (<= c 2.4e+70)
     (* (+ (* x y) (* z t)) 2.0)
     (* (* c i) (* c (* b -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.4e+74) {
		tmp = c * (-2.0 * (b * (c * i)));
	} else if (c <= 2.4e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * i) * (c * (b * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-3.4d+74)) then
        tmp = c * ((-2.0d0) * (b * (c * i)))
    else if (c <= 2.4d+70) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (c * i) * (c * (b * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.4e+74) {
		tmp = c * (-2.0 * (b * (c * i)));
	} else if (c <= 2.4e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (c * i) * (c * (b * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -3.4e+74:
		tmp = c * (-2.0 * (b * (c * i)))
	elif c <= 2.4e+70:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (c * i) * (c * (b * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -3.4e+74)
		tmp = Float64(c * Float64(-2.0 * Float64(b * Float64(c * i))));
	elseif (c <= 2.4e+70)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(c * i) * Float64(c * Float64(b * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -3.4e+74)
		tmp = c * (-2.0 * (b * (c * i)));
	elseif (c <= 2.4e+70)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (c * i) * (c * (b * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -3.4e+74], N[(c * N[(-2.0 * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e+70], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(c * i), $MachinePrecision] * N[(c * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.3999999999999999e74

   1. Initial program 76.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 74.3%

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

   7. Simplified 74.3%

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

      1. *-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. *-lowering-*.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

   if -3.3999999999999999e74 < c < 2.39999999999999987e70

   1. Initial program 96.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 86.8%

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

   3. Simplified 86.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

   if 2.39999999999999987e70 < c

   1. Initial program 78.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 67.3%

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

   7. Simplified 67.3%

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

      1. associate-*l* N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 67.5%

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

   9. Applied egg-rr 67.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -1.02 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* c (* b -2.0)))))
   (if (<= c -1.02e+75)
     t_1
     (if (<= c 9.5e+70) (* (+ (* x y) (* z t)) 2.0) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (c * (b * -2.0));
	double tmp;
	if (c <= -1.02e+75) {
		tmp = t_1;
	} else if (c <= 9.5e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) * (c * (b * (-2.0d0)))
    if (c <= (-1.02d+75)) then
        tmp = t_1
    else if (c <= 9.5d+70) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (c * (b * -2.0));
	double tmp;
	if (c <= -1.02e+75) {
		tmp = t_1;
	} else if (c <= 9.5e+70) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (c * (b * -2.0))
	tmp = 0
	if c <= -1.02e+75:
		tmp = t_1
	elif c <= 9.5e+70:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(c * Float64(b * -2.0)))
	tmp = 0.0
	if (c <= -1.02e+75)
		tmp = t_1;
	elseif (c <= 9.5e+70)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (c * (b * -2.0));
	tmp = 0.0;
	if (c <= -1.02e+75)
		tmp = t_1;
	elseif (c <= 9.5e+70)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(c * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.02e+75], t$95$1, If[LessEqual[c, 9.5e+70], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.0200000000000001e75 or 9.5000000000000002e70 < c

   1. Initial program 77.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 71.2%

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

   7. Simplified 71.2%

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

      1. associate-*l* N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 73.4%

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

   9. Applied egg-rr 73.4%

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

   if -1.0200000000000001e75 < c < 9.5000000000000002e70

   1. Initial program 96.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 86.8%

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

   3. Simplified 86.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+75}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(c \cdot \left(i \cdot \left(b \cdot -2\right)\right)\right)\\ \mathbf{if}\;c \leq -5.9 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* c (* i (* b -2.0))))))
   (if (<= c -5.9e+75)
     t_1
     (if (<= c 5.6e+69) (* (+ (* x y) (* z t)) 2.0) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (c * (i * (b * -2.0)));
	double tmp;
	if (c <= -5.9e+75) {
		tmp = t_1;
	} else if (c <= 5.6e+69) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (c * (i * (b * (-2.0d0))))
    if (c <= (-5.9d+75)) then
        tmp = t_1
    else if (c <= 5.6d+69) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (c * (i * (b * -2.0)));
	double tmp;
	if (c <= -5.9e+75) {
		tmp = t_1;
	} else if (c <= 5.6e+69) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (c * (i * (b * -2.0)))
	tmp = 0
	if c <= -5.9e+75:
		tmp = t_1
	elif c <= 5.6e+69:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(c * Float64(i * Float64(b * -2.0))))
	tmp = 0.0
	if (c <= -5.9e+75)
		tmp = t_1;
	elseif (c <= 5.6e+69)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (c * (i * (b * -2.0)));
	tmp = 0.0;
	if (c <= -5.9e+75)
		tmp = t_1;
	elseif (c <= 5.6e+69)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(c * N[(i * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.9e+75], t$95$1, If[LessEqual[c, 5.6e+69], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -5.89999999999999983e75 or 5.59999999999999964e69 < c

   1. Initial program 77.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

      17. *-commutative N/A

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

      18. *-lowering-*.f64 71.2%

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

   7. Simplified 71.2%

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

   if -5.89999999999999983e75 < c < 5.59999999999999964e69

   1. Initial program 96.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 86.8%

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

   3. Simplified 86.8%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.9 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(c \cdot \left(i \cdot \left(b \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(c \cdot \left(i \cdot \left(b \cdot -2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -1.1e-72)
     t_1
     (if (<= (* x y) 1.15e-51) (* 2.0 (* z t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.1e-72) {
		tmp = t_1;
	} else if ((x * y) <= 1.15e-51) {
		tmp = 2.0 * (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 = (x * y) * 2.0d0
    if ((x * y) <= (-1.1d-72)) then
        tmp = t_1
    else if ((x * y) <= 1.15d-51) then
        tmp = 2.0d0 * (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 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.1e-72) {
		tmp = t_1;
	} else if ((x * y) <= 1.15e-51) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.1e-72:
		tmp = t_1
	elif (x * y) <= 1.15e-51:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.1e-72)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.15e-51)
		tmp = Float64(2.0 * 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 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.1e-72)
		tmp = t_1;
	elseif ((x * y) <= 1.15e-51)
		tmp = 2.0 * (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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.1e-72], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.15e-51], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.10000000000000001e-72 or 1.15000000000000001e-51 < (*.f64 x y)

   1. Initial program 88.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in 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 52.0%

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

   7. Simplified 52.0%

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

   if -1.10000000000000001e-72 < (*.f64 x y) < 1.15000000000000001e-51

   1. Initial program 92.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in 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 44.0%

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

   7. Simplified 44.0%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{-72}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -3.3e+187) (* a (* c (* i -2.0))) (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.3e+187) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-3.3d+187)) then
        tmp = a * (c * (i * (-2.0d0)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.3e+187) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -3.3e+187:
		tmp = a * (c * (i * -2.0))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -3.3e+187)
		tmp = Float64(a * Float64(c * Float64(i * -2.0)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -3.3e+187)
		tmp = a * (c * (i * -2.0));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -3.3e+187], N[(a * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3000000000000001e187

   1. Initial program 87.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 74.0%

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

   3. Simplified 74.0%

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

   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 66.5%

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

   7. Simplified 66.5%

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

   if -3.3000000000000001e187 < a

   1. Initial program 90.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 90.9%

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

   3. Simplified 90.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% 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 90.2%

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

   1. *-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 89.0%

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

3. Simplified 89.0%

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

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 28.0%

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

7. Simplified 28.0%

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

8. Final simplification 28.0%

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

Developer Target 1: 94.3% 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 2024138 
(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))))