Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 72.5% → 81.6%

Time: 18.4s

Alternatives: 23

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 52.6%

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

   5. Simplified 52.6%

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

4. Final simplification 83.0%

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

Alternative 2: 30.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0 - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-286}:\\ \;\;\;\;0 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- 0.0 (* j (* y i)))))
   (if (<= y -1.08e+70)
     t_1
     (if (<= y -1.55e-28)
       (* x (- 0.0 (* t a)))
       (if (<= y -3.8e-156)
         (* i (* t b))
         (if (<= y 4.6e-286)
           (- 0.0 (* c (* z b)))
           (if (<= y 9e-17)
             (* t (- 0.0 (* x a)))
             (if (<= y 2e+67) (* x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -1.08e+70) {
		tmp = t_1;
	} else if (y <= -1.55e-28) {
		tmp = x * (0.0 - (t * a));
	} else if (y <= -3.8e-156) {
		tmp = i * (t * b);
	} else if (y <= 4.6e-286) {
		tmp = 0.0 - (c * (z * b));
	} else if (y <= 9e-17) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 2e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0d0 - (j * (y * i))
    if (y <= (-1.08d+70)) then
        tmp = t_1
    else if (y <= (-1.55d-28)) then
        tmp = x * (0.0d0 - (t * a))
    else if (y <= (-3.8d-156)) then
        tmp = i * (t * b)
    else if (y <= 4.6d-286) then
        tmp = 0.0d0 - (c * (z * b))
    else if (y <= 9d-17) then
        tmp = t * (0.0d0 - (x * a))
    else if (y <= 2d+67) then
        tmp = x * (y * z)
    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 j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -1.08e+70) {
		tmp = t_1;
	} else if (y <= -1.55e-28) {
		tmp = x * (0.0 - (t * a));
	} else if (y <= -3.8e-156) {
		tmp = i * (t * b);
	} else if (y <= 4.6e-286) {
		tmp = 0.0 - (c * (z * b));
	} else if (y <= 9e-17) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 2e+67) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = 0.0 - (j * (y * i))
	tmp = 0
	if y <= -1.08e+70:
		tmp = t_1
	elif y <= -1.55e-28:
		tmp = x * (0.0 - (t * a))
	elif y <= -3.8e-156:
		tmp = i * (t * b)
	elif y <= 4.6e-286:
		tmp = 0.0 - (c * (z * b))
	elif y <= 9e-17:
		tmp = t * (0.0 - (x * a))
	elif y <= 2e+67:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(0.0 - Float64(j * Float64(y * i)))
	tmp = 0.0
	if (y <= -1.08e+70)
		tmp = t_1;
	elseif (y <= -1.55e-28)
		tmp = Float64(x * Float64(0.0 - Float64(t * a)));
	elseif (y <= -3.8e-156)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 4.6e-286)
		tmp = Float64(0.0 - Float64(c * Float64(z * b)));
	elseif (y <= 9e-17)
		tmp = Float64(t * Float64(0.0 - Float64(x * a)));
	elseif (y <= 2e+67)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = 0.0 - (j * (y * i));
	tmp = 0.0;
	if (y <= -1.08e+70)
		tmp = t_1;
	elseif (y <= -1.55e-28)
		tmp = x * (0.0 - (t * a));
	elseif (y <= -3.8e-156)
		tmp = i * (t * b);
	elseif (y <= 4.6e-286)
		tmp = 0.0 - (c * (z * b));
	elseif (y <= 9e-17)
		tmp = t * (0.0 - (x * a));
	elseif (y <= 2e+67)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(0.0 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+70], t$95$1, If[LessEqual[y, -1.55e-28], N[(x * N[(0.0 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-156], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-286], N[(0.0 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-17], N[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+67], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.0799999999999999e70 or 1.99999999999999997e67 < y

   1. Initial program 62.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

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

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

      6. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), y\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{0 - \left(i \cdot j\right) \cdot y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot y\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(j \cdot i\right) \cdot y\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(j \cdot \left(i \cdot y\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \left(i \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, y\right)\right)\right) \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{-j \cdot \left(i \cdot y\right)} \]

   if -1.0799999999999999e70 < y < -1.54999999999999996e-28

   1. Initial program 74.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.0%

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

   5. Simplified 66.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a \cdot \left(t \cdot x\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot t\right) \cdot x\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot t\right)\right) \cdot \color{blue}{x} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(a \cdot t\right)\right), \color{blue}{x}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a \cdot t\right)\right), x\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - a \cdot t\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot t\right)\right), x\right) \]

      9. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, t\right)\right), x\right) \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\left(0 - a \cdot t\right) \cdot x} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a \cdot t\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(a \cdot t\right)\right), x\right) \]

      3. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, t\right)\right), x\right) \]

   10. Applied egg-rr 51.6%

       \[\leadsto \color{blue}{\left(-a \cdot t\right)} \cdot x \]

   if -1.54999999999999996e-28 < y < -3.80000000000000008e-156

   1. Initial program 86.5%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 52.9%

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

   5. Simplified 52.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 42.3%

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

   8. Simplified 42.3%

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{i} \]

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 46.6%

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

   10. Applied egg-rr 46.6%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if -3.80000000000000008e-156 < y < 4.6000000000000003e-286

   1. Initial program 80.6%

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

   3. Taylor expanded in j around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. associate--r+ N/A

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

      7. div-sub N/A

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

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

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

   5. Simplified 72.0%

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

   6. Taylor expanded in b around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot j\right) \cdot \color{blue}{\left(\frac{i \cdot t}{j} - \frac{c \cdot z}{j}\right)} \]

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

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

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

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

      4. div-sub N/A

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 46.1%

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

   8. Simplified 46.1%

      \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \frac{t \cdot i - z \cdot c}{j}} \]

   9. Taylor expanded in t around 0

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

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right) \]

       2. neg-sub0 N/A

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

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

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

       4. associate-*r* N/A

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

       5. *-commutative N/A

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

       6. associate-*r* N/A

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

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

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

       8. *-lowering-*.f64 43.1%

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

   11. Simplified 43.1%

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

   if 4.6000000000000003e-286 < y < 8.99999999999999957e-17

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 55.3%

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

   5. Simplified 55.3%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 55.3%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 55.3%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(a \cdot x\right)}, t\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 37.0%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, x\right), t\right)\right) \]

   10. Simplified 37.0%

       \[\leadsto -\color{blue}{\left(a \cdot x\right)} \cdot t \]

   if 8.99999999999999957e-17 < y < 1.99999999999999997e67

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

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

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

      2. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+70}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-286}:\\ \;\;\;\;0 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -85000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -3.7e+139)
     t_1
     (if (<= c -85000000.0)
       (* j (- (* a c) (* y i)))
       (if (<= c -1.9e-209)
         (* x (- (* y z) (* t a)))
         (if (<= c 4.3e-151)
           (* y (- (* x z) (* i j)))
           (if (<= c 4.8e+77) (* t (- (* b i) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.7e+139) {
		tmp = t_1;
	} else if (c <= -85000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -1.9e-209) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 4.3e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 4.8e+77) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-3.7d+139)) then
        tmp = t_1
    else if (c <= (-85000000.0d0)) then
        tmp = j * ((a * c) - (y * i))
    else if (c <= (-1.9d-209)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 4.3d-151) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 4.8d+77) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.7e+139) {
		tmp = t_1;
	} else if (c <= -85000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -1.9e-209) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 4.3e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 4.8e+77) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.7e+139:
		tmp = t_1
	elif c <= -85000000.0:
		tmp = j * ((a * c) - (y * i))
	elif c <= -1.9e-209:
		tmp = x * ((y * z) - (t * a))
	elif c <= 4.3e-151:
		tmp = y * ((x * z) - (i * j))
	elif c <= 4.8e+77:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.7e+139)
		tmp = t_1;
	elseif (c <= -85000000.0)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (c <= -1.9e-209)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 4.3e-151)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 4.8e+77)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.7e+139)
		tmp = t_1;
	elseif (c <= -85000000.0)
		tmp = j * ((a * c) - (y * i));
	elseif (c <= -1.9e-209)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 4.3e-151)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 4.8e+77)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+139], t$95$1, If[LessEqual[c, -85000000.0], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-209], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.3e-151], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+77], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.69999999999999992e139 or 4.7999999999999997e77 < c

   1. Initial program 49.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 71.8%

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

   5. Simplified 71.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if -3.69999999999999992e139 < c < -8.5e7

   1. Initial program 57.3%

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

   3. Taylor expanded in j around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 57.7%

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

   5. Simplified 57.7%

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

   if -8.5e7 < c < -1.8999999999999999e-209

   1. Initial program 82.6%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 52.0%

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

   5. Simplified 52.0%

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

   if -1.8999999999999999e-209 < c < 4.30000000000000018e-151

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \left(\mathsf{neg}\left(i \cdot j\right)\right)\right)\right) \]

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 67.8%

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

   5. Simplified 67.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   if 4.30000000000000018e-151 < c < 4.7999999999999997e77

   1. Initial program 85.3%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. *-lowering-*.f64 64.3%

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

   8. Simplified 64.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -85000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-27}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.05e+123)
     t_2
     (if (<= t 8e-27)
       (+ t_1 (* z (- (* x y) (* b c))))
       (if (<= t 2.7e+134) (- t_1 (* b (- (* z c) (* t i)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.05e+123) {
		tmp = t_2;
	} else if (t <= 8e-27) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (t <= 2.7e+134) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.05d+123)) then
        tmp = t_2
    else if (t <= 8d-27) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else if (t <= 2.7d+134) then
        tmp = t_1 - (b * ((z * c) - (t * i)))
    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 j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.05e+123) {
		tmp = t_2;
	} else if (t <= 8e-27) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (t <= 2.7e+134) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.05e+123:
		tmp = t_2
	elif t <= 8e-27:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	elif t <= 2.7e+134:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.05e+123)
		tmp = t_2;
	elseif (t <= 8e-27)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (t <= 2.7e+134)
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.05e+123)
		tmp = t_2;
	elseif (t <= 8e-27)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	elseif (t <= 2.7e+134)
		tmp = t_1 - (b * ((z * c) - (t * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+123], t$95$2, If[LessEqual[t, 8e-27], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+134], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.04999999999999995e123 or 2.7e134 < t

   1. Initial program 61.5%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. *-lowering-*.f64 73.0%

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

   8. Simplified 73.0%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -2.04999999999999995e123 < t < 8.0000000000000003e-27

   1. Initial program 78.2%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 71.5%

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

   5. Simplified 71.5%

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

   if 8.0000000000000003e-27 < t < 2.7e134

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 69.7%

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

   5. Simplified 69.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-27}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0 - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-149}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- 0.0 (* j (* y i)))))
   (if (<= y -6.2e+67)
     t_1
     (if (<= y -2.8e-29)
       (* x (- 0.0 (* t a)))
       (if (<= y 2e-149)
         (* i (* t b))
         (if (<= y 8.2e-21)
           (* t (- 0.0 (* x a)))
           (if (<= y 4e+62) (* x (* y z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -6.2e+67) {
		tmp = t_1;
	} else if (y <= -2.8e-29) {
		tmp = x * (0.0 - (t * a));
	} else if (y <= 2e-149) {
		tmp = i * (t * b);
	} else if (y <= 8.2e-21) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 4e+62) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0d0 - (j * (y * i))
    if (y <= (-6.2d+67)) then
        tmp = t_1
    else if (y <= (-2.8d-29)) then
        tmp = x * (0.0d0 - (t * a))
    else if (y <= 2d-149) then
        tmp = i * (t * b)
    else if (y <= 8.2d-21) then
        tmp = t * (0.0d0 - (x * a))
    else if (y <= 4d+62) then
        tmp = x * (y * z)
    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 j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -6.2e+67) {
		tmp = t_1;
	} else if (y <= -2.8e-29) {
		tmp = x * (0.0 - (t * a));
	} else if (y <= 2e-149) {
		tmp = i * (t * b);
	} else if (y <= 8.2e-21) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 4e+62) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = 0.0 - (j * (y * i))
	tmp = 0
	if y <= -6.2e+67:
		tmp = t_1
	elif y <= -2.8e-29:
		tmp = x * (0.0 - (t * a))
	elif y <= 2e-149:
		tmp = i * (t * b)
	elif y <= 8.2e-21:
		tmp = t * (0.0 - (x * a))
	elif y <= 4e+62:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(0.0 - Float64(j * Float64(y * i)))
	tmp = 0.0
	if (y <= -6.2e+67)
		tmp = t_1;
	elseif (y <= -2.8e-29)
		tmp = Float64(x * Float64(0.0 - Float64(t * a)));
	elseif (y <= 2e-149)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 8.2e-21)
		tmp = Float64(t * Float64(0.0 - Float64(x * a)));
	elseif (y <= 4e+62)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = 0.0 - (j * (y * i));
	tmp = 0.0;
	if (y <= -6.2e+67)
		tmp = t_1;
	elseif (y <= -2.8e-29)
		tmp = x * (0.0 - (t * a));
	elseif (y <= 2e-149)
		tmp = i * (t * b);
	elseif (y <= 8.2e-21)
		tmp = t * (0.0 - (x * a));
	elseif (y <= 4e+62)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(0.0 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+67], t$95$1, If[LessEqual[y, -2.8e-29], N[(x * N[(0.0 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-149], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-21], N[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+62], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.19999999999999992e67 or 4.00000000000000014e62 < y

   1. Initial program 62.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

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

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

      6. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), y\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{0 - \left(i \cdot j\right) \cdot y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot y\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(j \cdot i\right) \cdot y\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(j \cdot \left(i \cdot y\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \left(i \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, y\right)\right)\right) \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{-j \cdot \left(i \cdot y\right)} \]

   if -6.19999999999999992e67 < y < -2.8000000000000002e-29

   1. Initial program 74.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.0%

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

   5. Simplified 66.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a \cdot \left(t \cdot x\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot t\right) \cdot x\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot t\right)\right) \cdot \color{blue}{x} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(a \cdot t\right)\right), \color{blue}{x}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a \cdot t\right)\right), x\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - a \cdot t\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot t\right)\right), x\right) \]

      9. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, t\right)\right), x\right) \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\left(0 - a \cdot t\right) \cdot x} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a \cdot t\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(a \cdot t\right)\right), x\right) \]

      3. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, t\right)\right), x\right) \]

   10. Applied egg-rr 51.6%

       \[\leadsto \color{blue}{\left(-a \cdot t\right)} \cdot x \]

   if -2.8000000000000002e-29 < y < 1.99999999999999996e-149

   1. Initial program 80.7%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 48.6%

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

   5. Simplified 48.6%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 30.3%

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

   8. Simplified 30.3%

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{i} \]

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 34.4%

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

   10. Applied egg-rr 34.4%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if 1.99999999999999996e-149 < y < 8.19999999999999988e-21

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 55.6%

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

   5. Simplified 55.6%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 55.6%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(a \cdot x\right)}, t\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, x\right), t\right)\right) \]

   10. Simplified 45.0%

       \[\leadsto -\color{blue}{\left(a \cdot x\right)} \cdot t \]

   if 8.19999999999999988e-21 < y < 4.00000000000000014e62

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

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

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

      2. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+67}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-149}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0 - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- 0.0 (* j (* y i)))))
   (if (<= y -4.6e+67)
     t_1
     (if (<= y -5.5e-115)
       (* a (- 0.0 (* x t)))
       (if (<= y 2.9e-151)
         (* i (* t b))
         (if (<= y 4.8e-24)
           (* t (- 0.0 (* x a)))
           (if (<= y 4.5e+64) (* x (* y z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -4.6e+67) {
		tmp = t_1;
	} else if (y <= -5.5e-115) {
		tmp = a * (0.0 - (x * t));
	} else if (y <= 2.9e-151) {
		tmp = i * (t * b);
	} else if (y <= 4.8e-24) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 4.5e+64) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0d0 - (j * (y * i))
    if (y <= (-4.6d+67)) then
        tmp = t_1
    else if (y <= (-5.5d-115)) then
        tmp = a * (0.0d0 - (x * t))
    else if (y <= 2.9d-151) then
        tmp = i * (t * b)
    else if (y <= 4.8d-24) then
        tmp = t * (0.0d0 - (x * a))
    else if (y <= 4.5d+64) then
        tmp = x * (y * z)
    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 j) {
	double t_1 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -4.6e+67) {
		tmp = t_1;
	} else if (y <= -5.5e-115) {
		tmp = a * (0.0 - (x * t));
	} else if (y <= 2.9e-151) {
		tmp = i * (t * b);
	} else if (y <= 4.8e-24) {
		tmp = t * (0.0 - (x * a));
	} else if (y <= 4.5e+64) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = 0.0 - (j * (y * i))
	tmp = 0
	if y <= -4.6e+67:
		tmp = t_1
	elif y <= -5.5e-115:
		tmp = a * (0.0 - (x * t))
	elif y <= 2.9e-151:
		tmp = i * (t * b)
	elif y <= 4.8e-24:
		tmp = t * (0.0 - (x * a))
	elif y <= 4.5e+64:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(0.0 - Float64(j * Float64(y * i)))
	tmp = 0.0
	if (y <= -4.6e+67)
		tmp = t_1;
	elseif (y <= -5.5e-115)
		tmp = Float64(a * Float64(0.0 - Float64(x * t)));
	elseif (y <= 2.9e-151)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 4.8e-24)
		tmp = Float64(t * Float64(0.0 - Float64(x * a)));
	elseif (y <= 4.5e+64)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = 0.0 - (j * (y * i));
	tmp = 0.0;
	if (y <= -4.6e+67)
		tmp = t_1;
	elseif (y <= -5.5e-115)
		tmp = a * (0.0 - (x * t));
	elseif (y <= 2.9e-151)
		tmp = i * (t * b);
	elseif (y <= 4.8e-24)
		tmp = t * (0.0 - (x * a));
	elseif (y <= 4.5e+64)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(0.0 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+67], t$95$1, If[LessEqual[y, -5.5e-115], N[(a * N[(0.0 - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-151], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-24], N[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+64], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.5999999999999997e67 or 4.49999999999999973e64 < y

   1. Initial program 62.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

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

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

      6. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), y\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{0 - \left(i \cdot j\right) \cdot y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot y\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(j \cdot i\right) \cdot y\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(j \cdot \left(i \cdot y\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \left(i \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, y\right)\right)\right) \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{-j \cdot \left(i \cdot y\right)} \]

   if -4.5999999999999997e67 < y < -5.50000000000000028e-115

   1. Initial program 81.6%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 49.9%

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

   5. Simplified 49.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 49.9%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(a \cdot \left(t \cdot x\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot x\right)\right)\right) \]

      2. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, x\right)\right)\right) \]

   10. Simplified 43.2%

       \[\leadsto -\color{blue}{a \cdot \left(t \cdot x\right)} \]

   if -5.50000000000000028e-115 < y < 2.90000000000000013e-151

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 50.8%

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

   5. Simplified 50.8%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 29.4%

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

   8. Simplified 29.4%

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{i} \]

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 34.4%

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

   10. Applied egg-rr 34.4%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if 2.90000000000000013e-151 < y < 4.7999999999999996e-24

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 55.6%

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

   5. Simplified 55.6%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 55.6%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(a \cdot x\right)}, t\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, x\right), t\right)\right) \]

   10. Simplified 45.0%

       \[\leadsto -\color{blue}{\left(a \cdot x\right)} \cdot t \]

   if 4.7999999999999996e-24 < y < 4.49999999999999973e64

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

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

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

      2. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+67}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(0 - x \cdot t\right)\\ t_2 := 0 - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- 0.0 (* x t)))) (t_2 (- 0.0 (* j (* y i)))))
   (if (<= y -5.9e+67)
     t_2
     (if (<= y -1.9e-114)
       t_1
       (if (<= y 3.8e-150)
         (* i (* t b))
         (if (<= y 5.8e-17) t_1 (if (<= y 2e+61) (* x (* y z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (0.0 - (x * t));
	double t_2 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -5.9e+67) {
		tmp = t_2;
	} else if (y <= -1.9e-114) {
		tmp = t_1;
	} else if (y <= 3.8e-150) {
		tmp = i * (t * b);
	} else if (y <= 5.8e-17) {
		tmp = t_1;
	} else if (y <= 2e+61) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (0.0d0 - (x * t))
    t_2 = 0.0d0 - (j * (y * i))
    if (y <= (-5.9d+67)) then
        tmp = t_2
    else if (y <= (-1.9d-114)) then
        tmp = t_1
    else if (y <= 3.8d-150) then
        tmp = i * (t * b)
    else if (y <= 5.8d-17) then
        tmp = t_1
    else if (y <= 2d+61) then
        tmp = x * (y * z)
    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 j) {
	double t_1 = a * (0.0 - (x * t));
	double t_2 = 0.0 - (j * (y * i));
	double tmp;
	if (y <= -5.9e+67) {
		tmp = t_2;
	} else if (y <= -1.9e-114) {
		tmp = t_1;
	} else if (y <= 3.8e-150) {
		tmp = i * (t * b);
	} else if (y <= 5.8e-17) {
		tmp = t_1;
	} else if (y <= 2e+61) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (0.0 - (x * t))
	t_2 = 0.0 - (j * (y * i))
	tmp = 0
	if y <= -5.9e+67:
		tmp = t_2
	elif y <= -1.9e-114:
		tmp = t_1
	elif y <= 3.8e-150:
		tmp = i * (t * b)
	elif y <= 5.8e-17:
		tmp = t_1
	elif y <= 2e+61:
		tmp = x * (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(0.0 - Float64(x * t)))
	t_2 = Float64(0.0 - Float64(j * Float64(y * i)))
	tmp = 0.0
	if (y <= -5.9e+67)
		tmp = t_2;
	elseif (y <= -1.9e-114)
		tmp = t_1;
	elseif (y <= 3.8e-150)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 5.8e-17)
		tmp = t_1;
	elseif (y <= 2e+61)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (0.0 - (x * t));
	t_2 = 0.0 - (j * (y * i));
	tmp = 0.0;
	if (y <= -5.9e+67)
		tmp = t_2;
	elseif (y <= -1.9e-114)
		tmp = t_1;
	elseif (y <= 3.8e-150)
		tmp = i * (t * b);
	elseif (y <= 5.8e-17)
		tmp = t_1;
	elseif (y <= 2e+61)
		tmp = x * (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(0.0 - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.9e+67], t$95$2, If[LessEqual[y, -1.9e-114], t$95$1, If[LessEqual[y, 3.8e-150], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-17], t$95$1, If[LessEqual[y, 2e+61], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.9000000000000003e67 or 1.9999999999999999e61 < y

   1. Initial program 62.7%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

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

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

      6. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), y\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{0 - \left(i \cdot j\right) \cdot y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot y\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(j \cdot i\right) \cdot y\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(j \cdot \left(i \cdot y\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \left(i \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, y\right)\right)\right) \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{-j \cdot \left(i \cdot y\right)} \]

   if -5.9000000000000003e67 < y < -1.8999999999999999e-114 or 3.7999999999999998e-150 < y < 5.8000000000000006e-17

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 52.5%

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

   5. Simplified 52.5%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 52.5%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 52.5%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(a \cdot \left(t \cdot x\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot x\right)\right)\right) \]

      2. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, x\right)\right)\right) \]

   10. Simplified 44.0%

       \[\leadsto -\color{blue}{a \cdot \left(t \cdot x\right)} \]

   if -1.8999999999999999e-114 < y < 3.7999999999999998e-150

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 50.8%

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

   5. Simplified 50.8%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 29.4%

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

   8. Simplified 29.4%

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{i} \]

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 34.4%

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

   10. Applied egg-rr 34.4%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if 5.8000000000000006e-17 < y < 1.9999999999999999e61

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf

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

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

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

      2. *-lowering-*.f64 50.9%

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

   8. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+67}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.75e-40)
     (+ t_1 (* i (* t b)))
     (if (<= j 3.3e-5)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
       (- t_1 (* b (- (* z c) (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.75e-40) {
		tmp = t_1 + (i * (t * b));
	} else if (j <= 3.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.75d-40)) then
        tmp = t_1 + (i * (t * b))
    else if (j <= 3.3d-5) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1 - (b * ((z * c) - (t * 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 j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.75e-40) {
		tmp = t_1 + (i * (t * b));
	} else if (j <= 3.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.75e-40:
		tmp = t_1 + (i * (t * b))
	elif j <= 3.3e-5:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.75e-40)
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	elseif (j <= 3.3e-5)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.75e-40)
		tmp = t_1 + (i * (t * b));
	elseif (j <= 3.3e-5)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1 - (b * ((z * c) - (t * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e-40], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e-5], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.7500000000000001e-40

   1. Initial program 74.3%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 73.4%

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

   5. Simplified 73.4%

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

   if -1.7500000000000001e-40 < j < 3.3000000000000003e-5

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 75.2%

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

   5. Simplified 75.2%

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

   if 3.3000000000000003e-5 < j

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -1.2e+123)
     t_1
     (if (<= t 3.15e+66)
       (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.2e+123) {
		tmp = t_1;
	} else if (t <= 3.15e+66) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-1.2d+123)) then
        tmp = t_1
    else if (t <= 3.15d+66) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.2e+123) {
		tmp = t_1;
	} else if (t <= 3.15e+66) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.2e+123:
		tmp = t_1
	elif t <= 3.15e+66:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.2e+123)
		tmp = t_1;
	elseif (t <= 3.15e+66)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.2e+123)
		tmp = t_1;
	elseif (t <= 3.15e+66)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+123], t$95$1, If[LessEqual[t, 3.15e+66], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999994e123 or 3.1499999999999999e66 < t

   1. Initial program 65.8%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. *-lowering-*.f64 70.0%

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

   8. Simplified 70.0%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -1.19999999999999994e123 < t < 3.1499999999999999e66

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 69.5%

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

   5. Simplified 69.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* i (* t b)))))
   (if (<= j -1.1e-40)
     t_1
     (if (<= j 3.5e-25) (- (* b (- (* t i) (* z c))) (* a (* x t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (i * (t * b));
	double tmp;
	if (j <= -1.1e-40) {
		tmp = t_1;
	} else if (j <= 3.5e-25) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (i * (t * b))
    if (j <= (-1.1d-40)) then
        tmp = t_1
    else if (j <= 3.5d-25) then
        tmp = (b * ((t * i) - (z * c))) - (a * (x * 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 j) {
	double t_1 = (j * ((a * c) - (y * i))) + (i * (t * b));
	double tmp;
	if (j <= -1.1e-40) {
		tmp = t_1;
	} else if (j <= 3.5e-25) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (i * (t * b))
	tmp = 0
	if j <= -1.1e-40:
		tmp = t_1
	elif j <= 3.5e-25:
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)))
	tmp = 0.0
	if (j <= -1.1e-40)
		tmp = t_1;
	elseif (j <= 3.5e-25)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (i * (t * b));
	tmp = 0.0;
	if (j <= -1.1e-40)
		tmp = t_1;
	elseif (j <= 3.5e-25)
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.1e-40], t$95$1, If[LessEqual[j, 3.5e-25], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.10000000000000004e-40 or 3.5000000000000002e-25 < j

   1. Initial program 72.5%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 72.9%

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

   5. Simplified 72.9%

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

   if -1.10000000000000004e-40 < j < 3.5000000000000002e-25

   1. Initial program 72.1%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 72.9%

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

   5. Simplified 72.9%

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

      1. +-commutative N/A

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

      2. associate-+r- N/A

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

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

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

   7. Applied egg-rr 68.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)}, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - a \cdot \left(t \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{b}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right) \]

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 60.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, t\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right) \]

   10. Simplified 60.3%

       \[\leadsto \color{blue}{\left(0 - a \cdot \left(x \cdot t\right)\right)} - b \cdot \left(z \cdot c - t \cdot i\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - b \cdot c\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{t\_1}{j}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x y) (* b c))))
   (if (<= z -2.6e+163)
     (* (* z j) (/ t_1 j))
     (if (<= z 8.2e+21)
       (+ (* j (- (* a c) (* y i))) (* i (* t b)))
       (* z t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * y) - (b * c);
	double tmp;
	if (z <= -2.6e+163) {
		tmp = (z * j) * (t_1 / j);
	} else if (z <= 8.2e+21) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (b * c)
    if (z <= (-2.6d+163)) then
        tmp = (z * j) * (t_1 / j)
    else if (z <= 8.2d+21) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else
        tmp = z * 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 j) {
	double t_1 = (x * y) - (b * c);
	double tmp;
	if (z <= -2.6e+163) {
		tmp = (z * j) * (t_1 / j);
	} else if (z <= 8.2e+21) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * y) - (b * c)
	tmp = 0
	if z <= -2.6e+163:
		tmp = (z * j) * (t_1 / j)
	elif z <= 8.2e+21:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	else:
		tmp = z * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * y) - Float64(b * c))
	tmp = 0.0
	if (z <= -2.6e+163)
		tmp = Float64(Float64(z * j) * Float64(t_1 / j));
	elseif (z <= 8.2e+21)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	else
		tmp = Float64(z * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * y) - (b * c);
	tmp = 0.0;
	if (z <= -2.6e+163)
		tmp = (z * j) * (t_1 / j);
	elseif (z <= 8.2e+21)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	else
		tmp = z * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+163], N[(N[(z * j), $MachinePrecision] * N[(t$95$1 / j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+21], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000002e163

   1. Initial program 58.6%

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

   3. Taylor expanded in j around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. associate--r+ N/A

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

      7. div-sub N/A

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

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

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{j \cdot \left(z \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(j \cdot z\right) \cdot \color{blue}{\left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot z\right), \color{blue}{\left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot j\right), \left(\color{blue}{\frac{x \cdot y}{j}} - \frac{b \cdot c}{j}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \left(\color{blue}{\frac{x \cdot y}{j}} - \frac{b \cdot c}{j}\right)\right) \]

      5. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \left(\frac{x \cdot y - b \cdot c}{\color{blue}{j}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \mathsf{/.f64}\left(\left(x \cdot y - b \cdot c\right), \color{blue}{j}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right), j\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(b \cdot c\right)\right), j\right)\right) \]

      9. *-lowering-*.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, j\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, c\right)\right), j\right)\right) \]

   8. Simplified 74.1%

      \[\leadsto \color{blue}{\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}} \]

   if -2.6000000000000002e163 < z < 8.2e21

   1. Initial program 75.6%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 62.0%

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

   5. Simplified 62.0%

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

   if 8.2e21 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(j \cdot \left(a - i \cdot \frac{y}{c}\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 510:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -3.8e-5)
   (* c (* j (- a (* i (/ y c)))))
   (if (<= j -1.22e-289)
     (* t (- (* b i) (* x a)))
     (if (<= j 510.0) (* z (- (* x y) (* b c))) (* j (- (* a c) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -3.8e-5) {
		tmp = c * (j * (a - (i * (y / c))));
	} else if (j <= -1.22e-289) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 510.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: tmp
    if (j <= (-3.8d-5)) then
        tmp = c * (j * (a - (i * (y / c))))
    else if (j <= (-1.22d-289)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 510.0d0) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = j * ((a * c) - (y * 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 j) {
	double tmp;
	if (j <= -3.8e-5) {
		tmp = c * (j * (a - (i * (y / c))));
	} else if (j <= -1.22e-289) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 510.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -3.8e-5:
		tmp = c * (j * (a - (i * (y / c))))
	elif j <= -1.22e-289:
		tmp = t * ((b * i) - (x * a))
	elif j <= 510.0:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -3.8e-5)
		tmp = Float64(c * Float64(j * Float64(a - Float64(i * Float64(y / c)))));
	elseif (j <= -1.22e-289)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 510.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -3.8e-5)
		tmp = c * (j * (a - (i * (y / c))));
	elseif (j <= -1.22e-289)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 510.0)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -3.8e-5], N[(c * N[(j * N[(a - N[(i * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.22e-289], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 510.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.8000000000000002e-5

   1. Initial program 74.5%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot \left(a - \frac{i \cdot y}{c}\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

      4. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 69.8%

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

   8. Simplified 69.8%

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

   if -3.8000000000000002e-5 < j < -1.22e-289

   1. Initial program 67.3%

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

   3. Taylor expanded in c around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. associate-/l* N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. /-lowering-/.f64 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. *-lowering-*.f64 59.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 59.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -1.22e-289 < j < 510

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   if 510 < j

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 66.1%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(j \cdot \left(a - i \cdot \frac{y}{c}\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 510:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.000105:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 270:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -0.000105)
     t_1
     (if (<= j -5.5e-290)
       (* t (- (* b i) (* x a)))
       (if (<= j 270.0) (* z (- (* x y) (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.000105) {
		tmp = t_1;
	} else if (j <= -5.5e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 270.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-0.000105d0)) then
        tmp = t_1
    else if (j <= (-5.5d-290)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 270.0d0) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.000105) {
		tmp = t_1;
	} else if (j <= -5.5e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 270.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -0.000105:
		tmp = t_1
	elif j <= -5.5e-290:
		tmp = t * ((b * i) - (x * a))
	elif j <= 270.0:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -0.000105)
		tmp = t_1;
	elseif (j <= -5.5e-290)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 270.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -0.000105)
		tmp = t_1;
	elseif (j <= -5.5e-290)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 270.0)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -0.000105], t$95$1, If[LessEqual[j, -5.5e-290], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 270.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.05e-4 or 270 < j

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 65.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.05e-4 < j < -5.5e-290

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \color{blue}{\left(c \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \color{blue}{-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j - \color{blue}{\frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\left(i \cdot j\right) \cdot y}{c}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\left(i \cdot j\right) \cdot \color{blue}{\frac{y}{c}}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(i \cdot j\right), \color{blue}{\left(\frac{y}{c}\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(j \cdot i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      13. /-lowering-/.f64 71.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \mathsf{/.f64}\left(y, \color{blue}{c}\right)\right)\right)\right)\right) \]

   5. Simplified 71.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a - \left(j \cdot i\right) \cdot \frac{y}{c}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 59.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 59.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -5.5e-290 < j < 270

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.000105:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 270:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.7e-10)
     t_1
     (if (<= j -3.3e-234)
       (* t (- (* b i) (* x a)))
       (if (<= j 2.25e-5) (* x (- (* y z) (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e-10) {
		tmp = t_1;
	} else if (j <= -3.3e-234) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.25e-5) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.7d-10)) then
        tmp = t_1
    else if (j <= (-3.3d-234)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.25d-5) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e-10) {
		tmp = t_1;
	} else if (j <= -3.3e-234) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.25e-5) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.7e-10:
		tmp = t_1
	elif j <= -3.3e-234:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.25e-5:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.7e-10)
		tmp = t_1;
	elseif (j <= -3.3e-234)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.25e-5)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.7e-10)
		tmp = t_1;
	elseif (j <= -3.3e-234)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.25e-5)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e-10], t$95$1, If[LessEqual[j, -3.3e-234], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-5], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.7e-10 or 2.25000000000000014e-5 < j

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 64.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -2.7e-10 < j < -3.30000000000000014e-234

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \color{blue}{\left(c \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \color{blue}{-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j - \color{blue}{\frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\left(i \cdot j\right) \cdot y}{c}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\left(i \cdot j\right) \cdot \color{blue}{\frac{y}{c}}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(i \cdot j\right), \color{blue}{\left(\frac{y}{c}\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(j \cdot i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      13. /-lowering-/.f64 75.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \mathsf{/.f64}\left(y, \color{blue}{c}\right)\right)\right)\right)\right) \]

   5. Simplified 75.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a - \left(j \cdot i\right) \cdot \frac{y}{c}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 61.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 61.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -3.30000000000000014e-234 < j < 2.25000000000000014e-5

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 340:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -3.8)
     t_1
     (if (<= j -1.65e-293)
       (* t (- (* b i) (* x a)))
       (if (<= j 340.0) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8) {
		tmp = t_1;
	} else if (j <= -1.65e-293) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 340.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-3.8d0)) then
        tmp = t_1
    else if (j <= (-1.65d-293)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 340.0d0) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8) {
		tmp = t_1;
	} else if (j <= -1.65e-293) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 340.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.8:
		tmp = t_1
	elif j <= -1.65e-293:
		tmp = t * ((b * i) - (x * a))
	elif j <= 340.0:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.8)
		tmp = t_1;
	elseif (j <= -1.65e-293)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 340.0)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.8)
		tmp = t_1;
	elseif (j <= -1.65e-293)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 340.0)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8], t$95$1, If[LessEqual[j, -1.65e-293], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 340.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.7999999999999998 or 340 < j

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 65.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -3.7999999999999998 < j < -1.6499999999999999e-293

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \color{blue}{\left(c \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + a \cdot j\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \color{blue}{-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j + \left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \left(a \cdot j - \color{blue}{\frac{i \cdot \left(j \cdot y\right)}{c}}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(\frac{i \cdot \left(j \cdot y\right)}{c}\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\color{blue}{i \cdot \left(j \cdot y\right)}}{c}\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\frac{\left(i \cdot j\right) \cdot y}{c}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\left(i \cdot j\right) \cdot \color{blue}{\frac{y}{c}}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(i \cdot j\right), \color{blue}{\left(\frac{y}{c}\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\left(j \cdot i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \left(\frac{\color{blue}{y}}{c}\right)\right)\right)\right)\right) \]

      13. /-lowering-/.f64 70.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), \mathsf{/.f64}\left(y, \color{blue}{c}\right)\right)\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a - \left(j \cdot i\right) \cdot \frac{y}{c}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 58.4%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 58.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -1.6499999999999999e-293 < j < 340

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t - c \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 340:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.28 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+51}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.28e-58)
     t_1
     (if (<= a 2.35e-242)
       (* x (* y z))
       (if (<= a 1.85e+51) (- 0.0 (* j (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.28e-58) {
		tmp = t_1;
	} else if (a <= 2.35e-242) {
		tmp = x * (y * z);
	} else if (a <= 1.85e+51) {
		tmp = 0.0 - (j * (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.28d-58)) then
        tmp = t_1
    else if (a <= 2.35d-242) then
        tmp = x * (y * z)
    else if (a <= 1.85d+51) then
        tmp = 0.0d0 - (j * (y * 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 j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.28e-58) {
		tmp = t_1;
	} else if (a <= 2.35e-242) {
		tmp = x * (y * z);
	} else if (a <= 1.85e+51) {
		tmp = 0.0 - (j * (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.28e-58:
		tmp = t_1
	elif a <= 2.35e-242:
		tmp = x * (y * z)
	elif a <= 1.85e+51:
		tmp = 0.0 - (j * (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.28e-58)
		tmp = t_1;
	elseif (a <= 2.35e-242)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.85e+51)
		tmp = Float64(0.0 - Float64(j * Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.28e-58)
		tmp = t_1;
	elseif (a <= 2.35e-242)
		tmp = x * (y * z);
	elseif (a <= 1.85e+51)
		tmp = 0.0 - (j * (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.28e-58], t$95$1, If[LessEqual[a, 2.35e-242], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+51], N[(0.0 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.28e-58 or 1.8500000000000001e51 < a

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 56.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -1.28e-58 < a < 2.35000000000000018e-242

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 39.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 38.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 2.35000000000000018e-242 < a < 1.8500000000000001e51

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(j \cdot \left(a \cdot c - i \cdot y\right)\right), \color{blue}{\left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \left(a \cdot c - i \cdot y\right)\right), \left(\color{blue}{b} \cdot \left(c \cdot z - i \cdot t\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \left(i \cdot y\right)\right)\right), \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(i \cdot y\right)\right)\right), \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, y\right)\right)\right), \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, y\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(c \cdot z - i \cdot t\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, y\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(c \cdot z\right), \color{blue}{\left(i \cdot t\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, y\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \left(\color{blue}{i} \cdot t\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, y\right)\right)\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(i \cdot j\right), \color{blue}{y}\right)\right) \]

      6. *-lowering-*.f64 34.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), y\right)\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{0 - \left(i \cdot j\right) \cdot y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot y\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(j \cdot i\right) \cdot y\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(j \cdot \left(i \cdot y\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \left(i \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 40.3%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, y\right)\right)\right) \]

   10. Applied egg-rr 40.3%

       \[\leadsto \color{blue}{-j \cdot \left(i \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+51}:\\ \;\;\;\;0 - j \cdot \left(y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.2e+118)
   (* i (* t b))
   (if (<= i -1.7e-214)
     (* j (* a c))
     (if (<= i 1.4e+67) (* a (- 0.0 (* x t))) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.2e+118) {
		tmp = i * (t * b);
	} else if (i <= -1.7e-214) {
		tmp = j * (a * c);
	} else if (i <= 1.4e+67) {
		tmp = a * (0.0 - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: tmp
    if (i <= (-5.2d+118)) then
        tmp = i * (t * b)
    else if (i <= (-1.7d-214)) then
        tmp = j * (a * c)
    else if (i <= 1.4d+67) then
        tmp = a * (0.0d0 - (x * t))
    else
        tmp = t * (b * 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 j) {
	double tmp;
	if (i <= -5.2e+118) {
		tmp = i * (t * b);
	} else if (i <= -1.7e-214) {
		tmp = j * (a * c);
	} else if (i <= 1.4e+67) {
		tmp = a * (0.0 - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.2e+118:
		tmp = i * (t * b)
	elif i <= -1.7e-214:
		tmp = j * (a * c)
	elif i <= 1.4e+67:
		tmp = a * (0.0 - (x * t))
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.2e+118)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -1.7e-214)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.4e+67)
		tmp = Float64(a * Float64(0.0 - Float64(x * t)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.2e+118)
		tmp = i * (t * b);
	elseif (i <= -1.7e-214)
		tmp = j * (a * c);
	elseif (i <= 1.4e+67)
		tmp = a * (0.0 - (x * t));
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.2e+118], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.7e-214], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+67], N[(a * N[(0.0 - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.20000000000000032e118

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 54.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 45.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 45.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{i} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot t\right), \color{blue}{i}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot b\right), i\right) \]

      4. *-lowering-*.f64 48.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), i\right) \]

   10. Applied egg-rr 48.6%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if -5.20000000000000032e118 < i < -1.7e-214

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 52.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-lowering-*.f64 40.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      3. *-lowering-*.f64 41.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 41.4%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -1.7e-214 < i < 1.3999999999999999e67

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 37.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 37.8%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 37.8%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 37.8%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(a \cdot \left(t \cdot x\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot x\right)\right)\right) \]

      2. *-lowering-*.f64 33.1%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, x\right)\right)\right) \]

   10. Simplified 33.1%

       \[\leadsto -\color{blue}{a \cdot \left(t \cdot x\right)} \]

   if 1.3999999999999999e67 < i

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 42.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 38.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto b \cdot \left(i \cdot \color{blue}{t}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(b \cdot i\right) \cdot \color{blue}{t} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot i\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 40.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, i\right), t\right) \]

   10. Applied egg-rr 40.0%

       \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.6)
   (* a (* c j))
   (if (<= c 7e-161)
     (* x (* y z))
     (if (<= c 1.9e+29) (* b (* t i)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.6) {
		tmp = a * (c * j);
	} else if (c <= 7e-161) {
		tmp = x * (y * z);
	} else if (c <= 1.9e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.6d0)) then
        tmp = a * (c * j)
    else if (c <= 7d-161) then
        tmp = x * (y * z)
    else if (c <= 1.9d+29) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.6) {
		tmp = a * (c * j);
	} else if (c <= 7e-161) {
		tmp = x * (y * z);
	} else if (c <= 1.9e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.6:
		tmp = a * (c * j)
	elif c <= 7e-161:
		tmp = x * (y * z)
	elif c <= 1.9e+29:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.6)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= 7e-161)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.9e+29)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.6)
		tmp = a * (c * j);
	elseif (c <= 7e-161)
		tmp = x * (y * z);
	elseif (c <= 1.9e+29)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.6], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-161], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.6000000000000001

   1. Initial program 53.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 38.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-lowering-*.f64 31.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 31.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.6000000000000001 < c < 7.00000000000000039e-161

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 32.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 7.00000000000000039e-161 < c < 1.89999999999999985e29

   1. Initial program 89.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 64.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.89999999999999985e29 < c

   1. Initial program 54.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 59.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-lowering-*.f64 40.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      3. *-lowering-*.f64 48.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 48.4%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -38:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -38.0)
     t_1
     (if (<= c 1.42e-161)
       (* x (* y z))
       (if (<= c 1.5e+29) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -38.0) {
		tmp = t_1;
	} else if (c <= 1.42e-161) {
		tmp = x * (y * z);
	} else if (c <= 1.5e+29) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-38.0d0)) then
        tmp = t_1
    else if (c <= 1.42d-161) then
        tmp = x * (y * z)
    else if (c <= 1.5d+29) then
        tmp = b * (t * 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 j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -38.0) {
		tmp = t_1;
	} else if (c <= 1.42e-161) {
		tmp = x * (y * z);
	} else if (c <= 1.5e+29) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -38.0:
		tmp = t_1
	elif c <= 1.42e-161:
		tmp = x * (y * z)
	elif c <= 1.5e+29:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -38.0)
		tmp = t_1;
	elseif (c <= 1.42e-161)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.5e+29)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -38.0)
		tmp = t_1;
	elseif (c <= 1.42e-161)
		tmp = x * (y * z);
	elseif (c <= 1.5e+29)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -38.0], t$95$1, If[LessEqual[c, 1.42e-161], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -38 or 1.5e29 < c

   1. Initial program 53.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 48.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -38 < c < 1.42000000000000004e-161

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 32.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.42000000000000004e-161 < c < 1.5e29

   1. Initial program 89.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 64.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 52.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.85 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 320:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.85e-26) t_1 (if (<= j 320.0) (* b (- (* t i) (* z c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.85e-26) {
		tmp = t_1;
	} else if (j <= 320.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.85d-26)) then
        tmp = t_1
    else if (j <= 320.0d0) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.85e-26) {
		tmp = t_1;
	} else if (j <= 320.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.85e-26:
		tmp = t_1
	elif j <= 320.0:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.85e-26)
		tmp = t_1;
	elseif (j <= 320.0)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.85e-26)
		tmp = t_1;
	elseif (j <= 320.0)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.85e-26], t$95$1, If[LessEqual[j, 320.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.8499999999999999e-26 or 320 < j

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 64.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.8499999999999999e-26 < j < 320

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t - c \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 43.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 320:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.06e+168)
     t_1
     (if (<= a 4.2e+121) (* b (- (* t i) (* z c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.06e+168) {
		tmp = t_1;
	} else if (a <= 4.2e+121) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.06d+168)) then
        tmp = t_1
    else if (a <= 4.2d+121) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.06e+168) {
		tmp = t_1;
	} else if (a <= 4.2e+121) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.06e+168:
		tmp = t_1
	elif a <= 4.2e+121:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.06e+168)
		tmp = t_1;
	elseif (a <= 4.2e+121)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.06e+168)
		tmp = t_1;
	elseif (a <= 4.2e+121)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.06e+168], t$95$1, If[LessEqual[a, 4.2e+121], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0599999999999999e168 or 4.2000000000000003e121 < a

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -1.0599999999999999e168 < a < 4.2000000000000003e121

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t - c \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 41.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 41.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= i -5.5e+118) t_1 (if (<= i 2.4e-22) (* a (* c j)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -5.5e+118) {
		tmp = t_1;
	} else if (i <= 2.4e-22) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (i <= (-5.5d+118)) then
        tmp = t_1
    else if (i <= 2.4d-22) then
        tmp = a * (c * j)
    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 j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -5.5e+118) {
		tmp = t_1;
	} else if (i <= 2.4e-22) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if i <= -5.5e+118:
		tmp = t_1
	elif i <= 2.4e-22:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (i <= -5.5e+118)
		tmp = t_1;
	elseif (i <= 2.4e-22)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (i <= -5.5e+118)
		tmp = t_1;
	elseif (i <= 2.4e-22)
		tmp = a * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e+118], t$95$1, If[LessEqual[i, 2.4e-22], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -5.5000000000000003e118 or 2.40000000000000002e-22 < i

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 46.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 36.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -5.5000000000000003e118 < i < 2.40000000000000002e-22

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-lowering-*.f64 29.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 29.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   8. *-lowering-*.f64 39.5%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

5. Simplified 39.5%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

   2. *-lowering-*.f64 22.3%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

8. Simplified 22.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
9. Add Preprocessing

Developer Target 1: 58.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))