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

Percentage Accurate: 89.7% → 95.5%

Time: 19.1s

Alternatives: 16

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.7% 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: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+234}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - a \cdot \frac{c \cdot i}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) 5e+234)
   (* 2.0 (fma z t (- (* x y) (* (+ a (* c b)) (* c i)))))
   (* 2.0 (* y (- x (* a (/ (* c i) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= 5e+234) {
		tmp = 2.0 * fma(z, t, ((x * y) - ((a + (c * b)) * (c * i))));
	} else {
		tmp = 2.0 * (y * (x - (a * ((c * i) / y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= 5e+234)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(x * y) - Float64(Float64(a + Float64(c * b)) * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(y * Float64(x - Float64(a * Float64(Float64(c * i) / y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], 5e+234], N[(2.0 * N[(z * t + N[(N[(x * y), $MachinePrecision] - N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x - N[(a * N[(N[(c * i), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.0000000000000003e234

   1. Initial program 94.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 94.3%

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

   3. Simplified 94.3%

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

      1. associate--r- N/A

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

      2. fmm-def N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. fma-define N/A

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

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

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

      7. *-commutative N/A

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

      8. fmm-def N/A

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

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

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

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

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-commutative N/A

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

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

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

      18. *-lowering-*.f64 98.3%

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

   6. Applied egg-rr 98.3%

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

   if 5.0000000000000003e234 < (*.f64 x y)

   1. Initial program 71.4%

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

      1. *-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 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in y around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. associate-/l* N/A

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

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

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

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

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

      8. *-lowering-*.f64 95.2%

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

   10. Simplified 95.2%

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

Alternative 2: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ t_2 := i \cdot \left(c \cdot t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+287}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(t\_1 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))) (t_2 (* i (* c t_1))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* z t) (* c (* t_1 i))))
     (if (<= t_2 5e+287)
       (* 2.0 (- (+ (* x y) (* z t)) t_2))
       (* c (* i (* t_1 -2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+287) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = c * (i * (t_1 * -2.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+287) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = c * (i * (t_1 * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	t_2 = i * (c * t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	elif t_2 <= 5e+287:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = c * (i * (t_1 * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	elseif (t_2 <= 5e+287)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(c * Float64(i * Float64(t_1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	elseif (t_2 <= 5e+287)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = c * (i * (t_1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+287], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(t$95$1 * -2.0), $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 84.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 97.4%

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

   7. Simplified 97.4%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e287

   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

   if 5e287 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 73.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

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

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq 5 \cdot 10^{+287}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ t_2 := 2 \cdot \left(z \cdot t - t\_1 \cdot \left(c \cdot i\right)\right)\\ t_3 := i \cdot \left(c \cdot t\_1\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b)))
        (t_2 (* 2.0 (- (* z t) (* t_1 (* c i)))))
        (t_3 (* i (* c t_1))))
   (if (<= t_3 -1e+41)
     t_2
     (if (<= t_3 2e+127) (* 2.0 (+ (* x y) (* z t))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = 2.0 * ((z * t) - (t_1 * (c * i)));
	double t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -1e+41) {
		tmp = t_2;
	} else if (t_3 <= 2e+127) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a + (c * b)
    t_2 = 2.0d0 * ((z * t) - (t_1 * (c * i)))
    t_3 = i * (c * t_1)
    if (t_3 <= (-1d+41)) then
        tmp = t_2
    else if (t_3 <= 2d+127) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = 2.0 * ((z * t) - (t_1 * (c * i)));
	double t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -1e+41) {
		tmp = t_2;
	} else if (t_3 <= 2e+127) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	t_2 = 2.0 * ((z * t) - (t_1 * (c * i)))
	t_3 = i * (c * t_1)
	tmp = 0
	if t_3 <= -1e+41:
		tmp = t_2
	elif t_3 <= 2e+127:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(t_1 * Float64(c * i))))
	t_3 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_3 <= -1e+41)
		tmp = t_2;
	elseif (t_3 <= 2e+127)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	t_2 = 2.0 * ((z * t) - (t_1 * (c * i)));
	t_3 = i * (c * t_1);
	tmp = 0.0;
	if (t_3 <= -1e+41)
		tmp = t_2;
	elseif (t_3 <= 2e+127)
		tmp = 2.0 * ((x * y) + (z * t));
	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[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+41], t$95$2, If[LessEqual[t$95$3, 2e+127], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.00000000000000001e41 or 1.99999999999999991e127 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 84.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 84.6%

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

   3. Simplified 84.6%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   4. Add Preprocessing
   5. 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 92.5%

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

   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 84.0%

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

   9. Simplified 84.0%

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

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

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

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

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

       6. *-lowering-*.f64 91.0%

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

   11. Applied egg-rr 91.0%

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

   if -1.00000000000000001e41 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.99999999999999991e127

   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 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in c around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq -1 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq 2 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ t_2 := i \cdot \left(c \cdot t\_1\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+189}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))) (t_2 (* i (* c t_1))))
   (if (<= t_2 -1e+41)
     (* 2.0 (- (* z t) (* c (* t_1 i))))
     (if (<= t_2 1e+189)
       (* 2.0 (+ (* x y) (* z t)))
       (* (* t_1 (* c i)) -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 + (c * b);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 1e+189) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (t_1 * (c * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (c * b)
    t_2 = i * (c * t_1)
    if (t_2 <= (-1d+41)) then
        tmp = 2.0d0 * ((z * t) - (c * (t_1 * i)))
    else if (t_2 <= 1d+189) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (t_1 * (c * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= -1e+41) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 1e+189) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (t_1 * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	t_2 = i * (c * t_1)
	tmp = 0
	if t_2 <= -1e+41:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	elif t_2 <= 1e+189:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (t_1 * (c * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_2 <= -1e+41)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	elseif (t_2 <= 1e+189)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(t_1 * Float64(c * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= -1e+41)
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	elseif (t_2 <= 1e+189)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (t_1 * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+41], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+189], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.00000000000000001e41

   1. Initial program 89.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 89.8%

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

   7. Simplified 89.8%

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

   if -1.00000000000000001e41 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e189

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in 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 90.1%

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

   7. Simplified 90.1%

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

   if 1e189 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 78.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 76.6%

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

   3. Simplified 76.6%

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

   6. Applied egg-rr 86.1%

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

   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. *-lowering-*.f64 N/A

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

      3. associate-*r* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 88.3%

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

   9. Simplified 88.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq -1 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq 10^{+189}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;i \cdot \left(c \cdot t\_1\right) \leq 5 \cdot 10^{+287}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - t\_1 \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(t\_1 \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= (* i (* c t_1)) 5e+287)
     (* 2.0 (+ (* x y) (- (* z t) (* t_1 (* c i)))))
     (* c (* i (* t_1 -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if ((i * (c * t_1)) <= 5e+287) {
		tmp = 2.0 * ((x * y) + ((z * t) - (t_1 * (c * i))));
	} else {
		tmp = c * (i * (t_1 * -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) :: t_1
    real(8) :: tmp
    t_1 = a + (c * b)
    if ((i * (c * t_1)) <= 5d+287) then
        tmp = 2.0d0 * ((x * y) + ((z * t) - (t_1 * (c * i))))
    else
        tmp = c * (i * (t_1 * (-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 t_1 = a + (c * b);
	double tmp;
	if ((i * (c * t_1)) <= 5e+287) {
		tmp = 2.0 * ((x * y) + ((z * t) - (t_1 * (c * i))));
	} else {
		tmp = c * (i * (t_1 * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	tmp = 0
	if (i * (c * t_1)) <= 5e+287:
		tmp = 2.0 * ((x * y) + ((z * t) - (t_1 * (c * i))))
	else:
		tmp = c * (i * (t_1 * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (Float64(i * Float64(c * t_1)) <= 5e+287)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(t_1 * Float64(c * i)))));
	else
		tmp = Float64(c * Float64(i * Float64(t_1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	tmp = 0.0;
	if ((i * (c * t_1)) <= 5e+287)
		tmp = 2.0 * ((x * y) + ((z * t) - (t_1 * (c * i))));
	else
		tmp = c * (i * (t_1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision], 5e+287], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(t$95$1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e287

   1. Initial program 97.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 94.0%

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

   3. Simplified 94.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 98.5%

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

   if 5e287 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 73.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

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

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq 5 \cdot 10^{+287}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;i \cdot \left(c \cdot t\_1\right) \leq 2 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1 \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= (* i (* c t_1)) 2e+127)
     (* 2.0 (+ (* x y) (- (* z t) (* c (* t_1 i)))))
     (* 2.0 (- (* z t) (* t_1 (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if ((i * (c * t_1)) <= 2e+127) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	} else {
		tmp = 2.0 * ((z * t) - (t_1 * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (c * b)
    if ((i * (c * t_1)) <= 2d+127) then
        tmp = 2.0d0 * ((x * y) + ((z * t) - (c * (t_1 * i))))
    else
        tmp = 2.0d0 * ((z * t) - (t_1 * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if ((i * (c * t_1)) <= 2e+127) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	} else {
		tmp = 2.0 * ((z * t) - (t_1 * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	tmp = 0
	if (i * (c * t_1)) <= 2e+127:
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))))
	else:
		tmp = 2.0 * ((z * t) - (t_1 * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (Float64(i * Float64(c * t_1)) <= 2e+127)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(t_1 * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(t_1 * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	tmp = 0.0;
	if ((i * (c * t_1)) <= 2e+127)
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	else
		tmp = 2.0 * ((z * t) - (t_1 * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.99999999999999991e127

   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 97.4%

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

   3. Simplified 97.4%

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

   if 1.99999999999999991e127 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 75.4%

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

   3. Simplified 75.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 87.3%

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

   7. Taylor expanded in 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 78.7%

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

   9. Simplified 78.7%

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

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

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

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

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

       6. *-lowering-*.f64 89.0%

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

   11. Applied egg-rr 89.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + c \cdot b\right)\right) \leq 2 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+212}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(c \cdot b\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (* (+ a (* c b)) -2.0)))))
   (if (<= c -6.5e+100)
     t_1
     (if (<= c 5e+70)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 6.2e+212) (* 2.0 (- (* z t) (* c (* (* c b) i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * ((a + (c * b)) * -2.0));
	double tmp;
	if (c <= -6.5e+100) {
		tmp = t_1;
	} else if (c <= 5e+70) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.2e+212) {
		tmp = 2.0 * ((z * t) - (c * ((c * b) * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * ((a + (c * b)) * (-2.0d0)))
    if (c <= (-6.5d+100)) then
        tmp = t_1
    else if (c <= 5d+70) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 6.2d+212) then
        tmp = 2.0d0 * ((z * t) - (c * ((c * b) * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * ((a + (c * b)) * -2.0));
	double tmp;
	if (c <= -6.5e+100) {
		tmp = t_1;
	} else if (c <= 5e+70) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.2e+212) {
		tmp = 2.0 * ((z * t) - (c * ((c * b) * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * ((a + (c * b)) * -2.0))
	tmp = 0
	if c <= -6.5e+100:
		tmp = t_1
	elif c <= 5e+70:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 6.2e+212:
		tmp = 2.0 * ((z * t) - (c * ((c * b) * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(Float64(a + Float64(c * b)) * -2.0)))
	tmp = 0.0
	if (c <= -6.5e+100)
		tmp = t_1;
	elseif (c <= 5e+70)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 6.2e+212)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(c * b) * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * ((a + (c * b)) * -2.0));
	tmp = 0.0;
	if (c <= -6.5e+100)
		tmp = t_1;
	elseif (c <= 5e+70)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 6.2e+212)
		tmp = 2.0 * ((z * t) - (c * ((c * b) * i)));
	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[(i * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e+100], t$95$1, If[LessEqual[c, 5e+70], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e+212], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(c * b), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.50000000000000001e100 or 6.19999999999999996e212 < c

   1. Initial program 83.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 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 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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

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

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 84.5%

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

   7. Simplified 84.5%

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

   if -6.50000000000000001e100 < c < 5.0000000000000002e70

   1. Initial program 97.6%

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

      1. *-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. Taylor expanded in c around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 76.3%

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

   7. Simplified 76.3%

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

   if 5.0000000000000002e70 < c < 6.19999999999999996e212

   1. Initial program 85.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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. 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 99.9%

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

   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 93.3%

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

   9. Simplified 93.3%

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

   10. Taylor expanded in a around 0

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 82.3%

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

   12. Simplified 82.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+212}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(c \cdot b\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(i \cdot \left(t\_1 \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= c -1.1e+101)
     (* c (* i (* t_1 -2.0)))
     (if (<= c 3.7e+68)
       (* 2.0 (+ (* x y) (* z t)))
       (* (* t_1 (* c i)) -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 + (c * b);
	double tmp;
	if (c <= -1.1e+101) {
		tmp = c * (i * (t_1 * -2.0));
	} else if (c <= 3.7e+68) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (t_1 * (c * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (c * b)
    if (c <= (-1.1d+101)) then
        tmp = c * (i * (t_1 * (-2.0d0)))
    else if (c <= 3.7d+68) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (t_1 * (c * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if (c <= -1.1e+101) {
		tmp = c * (i * (t_1 * -2.0));
	} else if (c <= 3.7e+68) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (t_1 * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	tmp = 0
	if c <= -1.1e+101:
		tmp = c * (i * (t_1 * -2.0))
	elif c <= 3.7e+68:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (t_1 * (c * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (c <= -1.1e+101)
		tmp = Float64(c * Float64(i * Float64(t_1 * -2.0)));
	elseif (c <= 3.7e+68)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(t_1 * Float64(c * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	tmp = 0.0;
	if (c <= -1.1e+101)
		tmp = c * (i * (t_1 * -2.0));
	elseif (c <= 3.7e+68)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (t_1 * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e+101], N[(c * N[(i * N[(t$95$1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+68], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.1e101

   1. Initial program 84.7%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in 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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

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

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 82.4%

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

   7. Simplified 82.4%

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

   if -1.1e101 < c < 3.69999999999999998e68

   1. Initial program 97.5%

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

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

   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. Taylor expanded in c around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 76.8%

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

   7. Simplified 76.8%

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

   if 3.69999999999999998e68 < c

   1. Initial program 83.5%

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

   6. Applied egg-rr 92.7%

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

   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. *-lowering-*.f64 N/A

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

      3. associate-*r* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (* (+ a (* c b)) -2.0)))))
   (if (<= c -6.2e+100)
     t_1
     (if (<= c 6.6e+66) (* 2.0 (+ (* x y) (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * ((a + (c * b)) * -2.0));
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= 6.6e+66) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * ((a + (c * b)) * (-2.0d0)))
    if (c <= (-6.2d+100)) then
        tmp = t_1
    else if (c <= 6.6d+66) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * ((a + (c * b)) * -2.0));
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= 6.6e+66) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * ((a + (c * b)) * -2.0))
	tmp = 0
	if c <= -6.2e+100:
		tmp = t_1
	elif c <= 6.6e+66:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(Float64(a + Float64(c * b)) * -2.0)))
	tmp = 0.0
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= 6.6e+66)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * ((a + (c * b)) * -2.0));
	tmp = 0.0;
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= 6.6e+66)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(i * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+100], t$95$1, If[LessEqual[c, 6.6e+66], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -6.20000000000000014e100 or 6.6000000000000003e66 < c

   1. Initial program 84.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in 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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

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

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 77.8%

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

   7. Simplified 77.8%

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

   if -6.20000000000000014e100 < c < 6.6000000000000003e66

   1. Initial program 97.5%

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

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

   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. Taylor expanded in c around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(\left(a + c \cdot b\right) \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.2e+110)
   (* b (* (* c i) (* c -2.0)))
   (if (<= c 3.5e+71)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* i (* c (* c b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.2e+110) {
		tmp = b * ((c * i) * (c * -2.0));
	} else if (c <= 3.5e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (i * (c * (c * b)));
	}
	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 <= (-1.2d+110)) then
        tmp = b * ((c * i) * (c * (-2.0d0)))
    else if (c <= 3.5d+71) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * (i * (c * (c * b)))
    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 <= -1.2e+110) {
		tmp = b * ((c * i) * (c * -2.0));
	} else if (c <= 3.5e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (i * (c * (c * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.2e+110:
		tmp = b * ((c * i) * (c * -2.0))
	elif c <= 3.5e+71:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * (i * (c * (c * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.2e+110)
		tmp = Float64(b * Float64(Float64(c * i) * Float64(c * -2.0)));
	elseif (c <= 3.5e+71)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(i * Float64(c * Float64(c * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.2e+110)
		tmp = b * ((c * i) * (c * -2.0));
	elseif (c <= 3.5e+71)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * (i * (c * (c * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.2e+110], N[(b * N[(N[(c * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+71], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(i * N[(c * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.20000000000000006e110

   1. Initial program 83.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 70.2%

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

   7. Simplified 70.2%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

   if -1.20000000000000006e110 < c < 3.4999999999999999e71

   1. Initial program 97.6%

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

      1. *-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 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in c around 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 75.7%

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

   7. Simplified 75.7%

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

   if 3.4999999999999999e71 < c

   1. Initial program 83.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 57.2%

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

   9. Applied egg-rr 57.2%

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

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

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

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

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

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

       5. *-lowering-*.f64 59.5%

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

   11. Applied egg-rr 59.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.9e+110)
   (* b (* (* c i) (* c -2.0)))
   (if (<= c 1.6e+71)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* c (* b (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.9e+110) {
		tmp = b * ((c * i) * (c * -2.0));
	} else if (c <= 1.6e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.9d+110)) then
        tmp = b * ((c * i) * (c * (-2.0d0)))
    else if (c <= 1.6d+71) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * (c * (b * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.9e+110) {
		tmp = b * ((c * i) * (c * -2.0));
	} else if (c <= 1.6e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.9e+110:
		tmp = b * ((c * i) * (c * -2.0))
	elif c <= 1.6e+71:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * (c * (b * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.9e+110)
		tmp = Float64(b * Float64(Float64(c * i) * Float64(c * -2.0)));
	elseif (c <= 1.6e+71)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.9e+110)
		tmp = b * ((c * i) * (c * -2.0));
	elseif (c <= 1.6e+71)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * (c * (b * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.9e+110], N[(b * N[(N[(c * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+71], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.89999999999999994e110

   1. Initial program 83.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 70.2%

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

   7. Simplified 70.2%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-lowering-*.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

   if -1.89999999999999994e110 < c < 1.60000000000000012e71

   1. Initial program 97.6%

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

      1. *-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 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in c around 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 75.7%

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

   7. Simplified 75.7%

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

   if 1.60000000000000012e71 < c

   1. Initial program 83.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 57.2%

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

   9. Applied egg-rr 57.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* b (* c i))))))
   (if (<= c -2e+114)
     t_1
     (if (<= c 9.2e+70) (* 2.0 (+ (* x y) (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2e+114) {
		tmp = t_1;
	} else if (c <= 9.2e+70) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * (b * (c * i)))
    if (c <= (-2d+114)) then
        tmp = t_1
    else if (c <= 9.2d+70) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2e+114) {
		tmp = t_1;
	} else if (c <= 9.2e+70) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * (b * (c * i)))
	tmp = 0
	if c <= -2e+114:
		tmp = t_1
	elif c <= 9.2e+70:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	tmp = 0.0
	if (c <= -2e+114)
		tmp = t_1;
	elseif (c <= 9.2e+70)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * (b * (c * i)));
	tmp = 0.0;
	if (c <= -2e+114)
		tmp = t_1;
	elseif (c <= 9.2e+70)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+114], t$95$1, If[LessEqual[c, 9.2e+70], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -2e114 or 9.19999999999999975e70 < c

   1. Initial program 82.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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. 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 64.3%

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

   7. Simplified 64.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.7%

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

   9. Applied egg-rr 66.7%

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

   if -2e114 < c < 9.19999999999999975e70

   1. Initial program 97.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in 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 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+114}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* -2.0 (* c (* b i))))))
   (if (<= c -3.5e+114)
     t_1
     (if (<= c 2.05e+71) (* 2.0 (+ (* x y) (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (-2.0 * (c * (b * i)));
	double tmp;
	if (c <= -3.5e+114) {
		tmp = t_1;
	} else if (c <= 2.05e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((-2.0d0) * (c * (b * i)))
    if (c <= (-3.5d+114)) then
        tmp = t_1
    else if (c <= 2.05d+71) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (-2.0 * (c * (b * i)));
	double tmp;
	if (c <= -3.5e+114) {
		tmp = t_1;
	} else if (c <= 2.05e+71) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (-2.0 * (c * (b * i)))
	tmp = 0
	if c <= -3.5e+114:
		tmp = t_1
	elif c <= 2.05e+71:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(-2.0 * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -3.5e+114)
		tmp = t_1;
	elseif (c <= 2.05e+71)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (-2.0 * (c * (b * i)));
	tmp = 0.0;
	if (c <= -3.5e+114)
		tmp = t_1;
	elseif (c <= 2.05e+71)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(-2.0 * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+114], t$95$1, If[LessEqual[c, 2.05e+71], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -3.5000000000000001e114 or 2.0500000000000001e71 < c

   1. Initial program 82.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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. 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 64.3%

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

   7. Simplified 64.3%

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

   if -3.5000000000000001e114 < c < 2.0500000000000001e71

   1. Initial program 97.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in 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 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -1.75e+75)
     t_1
     (if (<= (* x y) 6.2e+36) (* 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) <= -1.75e+75) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e+36) {
		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) <= (-1.75d+75)) then
        tmp = t_1
    else if ((x * y) <= 6.2d+36) 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) <= -1.75e+75) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e+36) {
		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) <= -1.75e+75:
		tmp = t_1
	elif (x * y) <= 6.2e+36:
		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) <= -1.75e+75)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.2e+36)
		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) <= -1.75e+75)
		tmp = t_1;
	elseif ((x * y) <= 6.2e+36)
		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], -1.75e+75], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.2e+36], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.7499999999999999e75 or 6.1999999999999999e36 < (*.f64 x y)

   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 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 60.2%

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

   7. Simplified 60.2%

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

   if -1.7499999999999999e75 < (*.f64 x y) < 6.1999999999999999e36

   1. Initial program 93.9%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 94.0%

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

   3. Simplified 94.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
   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 47.7%

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

   7. Simplified 47.7%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.95e+152) (* a (* c (* i -2.0))) (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.95e+152) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.95d+152)) then
        tmp = a * (c * (i * (-2.0d0)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.95e+152) {
		tmp = a * (c * (i * -2.0));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.95e+152:
		tmp = a * (c * (i * -2.0))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.95e+152)
		tmp = Float64(a * Float64(c * Float64(i * -2.0)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.95e+152)
		tmp = a * (c * (i * -2.0));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.95e+152], N[(a * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.95000000000000006e152

   1. Initial program 81.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. associate-+l- N/A

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

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

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

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

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

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

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

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

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

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

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

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

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

      19. *-lowering-*.f64 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. 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 54.8%

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

   7. Simplified 54.8%

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

   if -1.95000000000000006e152 < c

   1. Initial program 94.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in c around 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 66.9%

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

   7. Simplified 66.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.0% 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 92.7%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. associate-+r+ N/A

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

   5. +-commutative N/A

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

   6. sub-neg N/A

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

   7. associate-+l- N/A

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

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

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

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

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

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

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

   11. associate-*l* N/A

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

   12. *-commutative N/A

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

   13. associate-*l* N/A

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

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

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

   15. *-commutative N/A

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

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

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

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

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

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

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

   19. *-lowering-*.f64 92.0%

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

3. Simplified 92.0%

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot y - \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right) - z \cdot t\right)\right)} \]
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 37.1%

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

7. Simplified 37.1%

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

8. Final simplification 37.1%

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

Developer Target 1: 94.0% 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 2024150 
(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))))