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

Percentage Accurate: 73.4% → 82.4%

Time: 19.3s

Alternatives: 19

Speedup: 0.5×

• 58.2% 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: 73.4% 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: 82.4% accurate, 0.5× speedup

Math

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

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 (* (* b c) (- (/ (* a j) b) z)))))

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 = (b * c) * (((a * j) / b) - z);
	}
	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 = (b * c) * (((a * j) / b) - z);
	}
	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 = (b * c) * (((a * j) / b) - z)
	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(Float64(b * c) * Float64(Float64(Float64(a * j) / b) - z));
	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 = (b * c) * (((a * j) / b) - z);
	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[(N[(b * c), $MachinePrecision] * N[(N[(N[(a * j), $MachinePrecision] / b), $MachinePrecision] - z), $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 89.6%

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

   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 b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

      5. associate--l+ N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 18.0%

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

   6. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 54.6%

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

   8. Simplified 54.6%

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

4. Final simplification 81.3%

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

Alternative 2: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7e+141)
   (* z (+ (* x y) (* b (- (/ (* t i) z) c))))
   (if (<= z 2.85e+122)
     (+ (* j (- (* a c) (* y i))) (+ (* x (- (* y z) (* t a))) (* t (* b i))))
     (* z (+ (* x y) (* b (- (* i (/ t z)) 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 (z <= -7e+141) {
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	} else if (z <= 2.85e+122) {
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	} else {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - 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 (z <= (-7d+141)) then
        tmp = z * ((x * y) + (b * (((t * i) / z) - c)))
    else if (z <= 2.85d+122) then
        tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)))
    else
        tmp = z * ((x * y) + (b * ((i * (t / z)) - 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 (z <= -7e+141) {
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	} else if (z <= 2.85e+122) {
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	} else {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7e+141:
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)))
	elif z <= 2.85e+122:
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)))
	else:
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7e+141)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(Float64(t * i) / z) - c))));
	elseif (z <= 2.85e+122)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(t * Float64(b * i))));
	else
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -7e+141)
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	elseif (z <= 2.85e+122)
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	else
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7e+141], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(N[(t * i), $MachinePrecision] / z), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e+122], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999999e141

   1. Initial program 59.7%

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

   3. Taylor expanded in j around 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 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 86.6%

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

   if -6.9999999999999999e141 < z < 2.85000000000000003e122

   1. Initial program 74.1%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. neg-mul-1 N/A

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

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

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

      9. neg-mul-1 N/A

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(b, \left(0 - i\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      11. --lowering--.f64 72.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, i\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 72.6%

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

   if 2.85000000000000003e122 < z

   1. Initial program 50.6%

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

   3. Taylor expanded in j around 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 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 73.2%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

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

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

       4. /-lowering-/.f64 77.8%

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

   13. Applied egg-rr 77.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+208}:\\ \;\;\;\;t\_1 + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.05 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -8e+208)
     (+ t_1 (* y (* x z)))
     (if (<= j 3.05e-231)
       (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
       (if (<= j 3e-95)
         (* z (+ (* x y) (* b (- (* i (/ t z)) c))))
         (+ t_1 (* i (* t 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8e+208) {
		tmp = t_1 + (y * (x * z));
	} else if (j <= 3.05e-231) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (j <= 3e-95) {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	} else {
		tmp = t_1 + (i * (t * b));
	}
	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 <= (-8d+208)) then
        tmp = t_1 + (y * (x * z))
    else if (j <= 3.05d-231) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else if (j <= 3d-95) then
        tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
    else
        tmp = t_1 + (i * (t * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8e+208) {
		tmp = t_1 + (y * (x * z));
	} else if (j <= 3.05e-231) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (j <= 3e-95) {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	} else {
		tmp = t_1 + (i * (t * b));
	}
	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 <= -8e+208:
		tmp = t_1 + (y * (x * z))
	elif j <= 3.05e-231:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	elif j <= 3e-95:
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
	else:
		tmp = t_1 + (i * (t * b))
	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 <= -8e+208)
		tmp = Float64(t_1 + Float64(y * Float64(x * z)));
	elseif (j <= 3.05e-231)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 3e-95)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	else
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	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 <= -8e+208)
		tmp = t_1 + (y * (x * z));
	elseif (j <= 3.05e-231)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	elseif (j <= 3e-95)
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	else
		tmp = t_1 + (i * (t * b));
	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, -8e+208], N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.05e-231], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-95], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.9999999999999999e208

   1. Initial program 47.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 75.1%

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

   5. Simplified 75.1%

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

   if -7.9999999999999999e208 < j < 3.0499999999999998e-231

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

         \[\leadsto \left(a \cdot \left(-1 \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. distribute-lft-in N/A

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

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

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

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

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      17. *-lowering-*.f64 74.3%

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

   5. Simplified 74.3%

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

   if 3.0499999999999998e-231 < j < 3e-95

   1. Initial program 68.2%

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

   3. Taylor expanded in 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 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 62.8%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

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

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

       4. /-lowering-/.f64 67.6%

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

   13. Applied egg-rr 67.6%

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

   if 3e-95 < j

   1. Initial program 62.9%

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

   3. Taylor expanded in 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 62.4%

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

   5. Simplified 62.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+208}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.05 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -240000000000:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - a \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq 10^{-270}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -240000000000.0)
   (* b (* t (- i (* a (/ x b)))))
   (if (<= t 1e-270)
     (* c (- (* a j) (* z b)))
     (if (<= t 8e-34)
       (* z (+ (* x y) (* b (- (* i (/ t z)) c))))
       (if (<= t 1.9e+196)
         (* a (- (* c j) (* x t)))
         (* t (- (* b i) (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -240000000000.0) {
		tmp = b * (t * (i - (a * (x / b))));
	} else if (t <= 1e-270) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 8e-34) {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	} else if (t <= 1.9e+196) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	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 (t <= (-240000000000.0d0)) then
        tmp = b * (t * (i - (a * (x / b))))
    else if (t <= 1d-270) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 8d-34) then
        tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
    else if (t <= 1.9d+196) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * ((b * i) - (x * a))
    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 (t <= -240000000000.0) {
		tmp = b * (t * (i - (a * (x / b))));
	} else if (t <= 1e-270) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 8e-34) {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	} else if (t <= 1.9e+196) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -240000000000.0:
		tmp = b * (t * (i - (a * (x / b))))
	elif t <= 1e-270:
		tmp = c * ((a * j) - (z * b))
	elif t <= 8e-34:
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
	elif t <= 1.9e+196:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -240000000000.0)
		tmp = Float64(b * Float64(t * Float64(i - Float64(a * Float64(x / b)))));
	elseif (t <= 1e-270)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 8e-34)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	elseif (t <= 1.9e+196)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -240000000000.0)
		tmp = b * (t * (i - (a * (x / b))));
	elseif (t <= 1e-270)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 8e-34)
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	elseif (t <= 1.9e+196)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -240000000000.0], N[(b * N[(t * N[(i - N[(a * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-270], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-34], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+196], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.4e11

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

      5. associate--l+ N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 66.2%

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

   6. Taylor expanded in t around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 68.2%

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

   8. Simplified 68.2%

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

   if -2.4e11 < t < 1e-270

   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 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 57.9%

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

   5. Simplified 57.9%

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

   if 1e-270 < t < 7.99999999999999942e-34

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 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 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 73.9%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

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

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

       4. /-lowering-/.f64 74.0%

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

   13. Applied egg-rr 74.0%

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

   if 7.99999999999999942e-34 < t < 1.9000000000000001e196

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.9%

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

   5. Simplified 58.9%

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

   if 1.9000000000000001e196 < t

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 95.3%

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

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 95.3%

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

   7. Applied egg-rr 95.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -240000000000:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - a \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq 10^{-270}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4800000000000:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - a \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4800000000000.0)
   (* b (* t (- i (* a (/ x b)))))
   (if (<= t 9.5e-271)
     (* c (- (* a j) (* z b)))
     (if (<= t 5.8e-34)
       (* z (- (* x y) (* b c)))
       (if (<= t 1.28e+199)
         (* a (- (* c j) (* x t)))
         (* t (- (* b i) (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4800000000000.0) {
		tmp = b * (t * (i - (a * (x / b))));
	} else if (t <= 9.5e-271) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 5.8e-34) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.28e+199) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	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 (t <= (-4800000000000.0d0)) then
        tmp = b * (t * (i - (a * (x / b))))
    else if (t <= 9.5d-271) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 5.8d-34) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.28d+199) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * ((b * i) - (x * a))
    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 (t <= -4800000000000.0) {
		tmp = b * (t * (i - (a * (x / b))));
	} else if (t <= 9.5e-271) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 5.8e-34) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.28e+199) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4800000000000.0:
		tmp = b * (t * (i - (a * (x / b))))
	elif t <= 9.5e-271:
		tmp = c * ((a * j) - (z * b))
	elif t <= 5.8e-34:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.28e+199:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4800000000000.0)
		tmp = Float64(b * Float64(t * Float64(i - Float64(a * Float64(x / b)))));
	elseif (t <= 9.5e-271)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 5.8e-34)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.28e+199)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4800000000000.0)
		tmp = b * (t * (i - (a * (x / b))));
	elseif (t <= 9.5e-271)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 5.8e-34)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.28e+199)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4800000000000.0], N[(b * N[(t * N[(i - N[(a * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-271], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-34], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.28e+199], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.8e12

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

      5. associate--l+ N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 66.2%

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

   6. Taylor expanded in t around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 68.2%

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

   8. Simplified 68.2%

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

   if -4.8e12 < t < 9.50000000000000103e-271

   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 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 57.9%

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

   5. Simplified 57.9%

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

   if 9.50000000000000103e-271 < t < 5.8000000000000004e-34

   1. Initial program 79.1%

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

   3. Taylor expanded in 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 63.8%

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

   5. Simplified 63.8%

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

   if 5.8000000000000004e-34 < t < 1.2799999999999999e199

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.9%

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

   5. Simplified 58.9%

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

   if 1.2799999999999999e199 < t

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 95.3%

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

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 95.3%

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

   7. Applied egg-rr 95.3%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4800000000000:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - a \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -700000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.7 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -700000000000.0)
     t_1
     (if (<= t 8.7e-271)
       (* c (- (* a j) (* z b)))
       (if (<= t 3.3e-35)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.95e+196) (* a (- (* c j) (* 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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -700000000000.0) {
		tmp = t_1;
	} else if (t <= 8.7e-271) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 3.3e-35) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.95e+196) {
		tmp = a * ((c * j) - (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 = t * ((b * i) - (x * a))
    if (t <= (-700000000000.0d0)) then
        tmp = t_1
    else if (t <= 8.7d-271) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 3.3d-35) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.95d+196) then
        tmp = a * ((c * j) - (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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -700000000000.0) {
		tmp = t_1;
	} else if (t <= 8.7e-271) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 3.3e-35) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.95e+196) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= -700000000000.0:
		tmp = t_1
	elif t <= 8.7e-271:
		tmp = c * ((a * j) - (z * b))
	elif t <= 3.3e-35:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.95e+196:
		tmp = a * ((c * j) - (x * t))
	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 <= -700000000000.0)
		tmp = t_1;
	elseif (t <= 8.7e-271)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 3.3e-35)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.95e+196)
		tmp = Float64(a * Float64(Float64(c * j) - 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 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -700000000000.0)
		tmp = t_1;
	elseif (t <= 8.7e-271)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 3.3e-35)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.95e+196)
		tmp = a * ((c * j) - (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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -700000000000.0], t$95$1, If[LessEqual[t, 8.7e-271], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-35], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+196], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7e11 or 1.95e196 < t

   1. Initial program 65.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 73.9%

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

   5. Simplified 73.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 73.9%

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

   7. Applied egg-rr 73.9%

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

   if -7e11 < t < 8.6999999999999999e-271

   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 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 57.9%

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

   5. Simplified 57.9%

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

   if 8.6999999999999999e-271 < t < 3.3e-35

   1. Initial program 79.1%

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

   3. Taylor expanded in 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 63.8%

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

   5. Simplified 63.8%

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

   if 3.3e-35 < t < 1.95e196

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.9%

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

   5. Simplified 58.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -700000000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 8.7 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -3.8e+69)
     t_1
     (if (<= c -1.2e-99)
       (* b (- (* t i) (* z c)))
       (if (<= c 1.9e-104)
         (* x (- (* y z) (* t a)))
         (if (<= c 6.4e+46) (* j (- (* a c) (* 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.8e+69) {
		tmp = t_1;
	} else if (c <= -1.2e-99) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= 1.9e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 6.4e+46) {
		tmp = j * ((a * c) - (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 = c * ((a * j) - (z * b))
    if (c <= (-3.8d+69)) then
        tmp = t_1
    else if (c <= (-1.2d-99)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= 1.9d-104) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 6.4d+46) then
        tmp = j * ((a * c) - (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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.8e+69) {
		tmp = t_1;
	} else if (c <= -1.2e-99) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= 1.9e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 6.4e+46) {
		tmp = j * ((a * c) - (y * i));
	} 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 <= -3.8e+69:
		tmp = t_1
	elif c <= -1.2e-99:
		tmp = b * ((t * i) - (z * c))
	elif c <= 1.9e-104:
		tmp = x * ((y * z) - (t * a))
	elif c <= 6.4e+46:
		tmp = j * ((a * c) - (y * i))
	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 <= -3.8e+69)
		tmp = t_1;
	elseif (c <= -1.2e-99)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= 1.9e-104)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 6.4e+46)
		tmp = Float64(j * Float64(Float64(a * c) - 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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.8e+69)
		tmp = t_1;
	elseif (c <= -1.2e-99)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= 1.9e-104)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 6.4e+46)
		tmp = j * ((a * c) - (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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+69], t$95$1, If[LessEqual[c, -1.2e-99], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e-104], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e+46], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.80000000000000028e69 or 6.3999999999999996e46 < c

   1. Initial program 56.3%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   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 70.5%

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

   5. Simplified 70.5%

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

   if -3.80000000000000028e69 < c < -1.2e-99

   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 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 50.9%

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

   5. Simplified 50.9%

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

   if -1.2e-99 < c < 1.9e-104

   1. Initial program 76.2%

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

   3. Taylor expanded in 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%

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

   if 1.9e-104 < c < 6.3999999999999996e46

   1. Initial program 74.2%

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

   3. Taylor expanded in 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 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -1.5e+84)
     (* i (* t b))
     (if (<= t 1.65e-270)
       t_1
       (if (<= t 8.2e-55)
         (* z (* x y))
         (if (<= t 8.5e+207) t_1 (* b (* 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 = a * (c * j);
	double tmp;
	if (t <= -1.5e+84) {
		tmp = i * (t * b);
	} else if (t <= 1.65e-270) {
		tmp = t_1;
	} else if (t <= 8.2e-55) {
		tmp = z * (x * y);
	} else if (t <= 8.5e+207) {
		tmp = t_1;
	} else {
		tmp = b * (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 = a * (c * j)
    if (t <= (-1.5d+84)) then
        tmp = i * (t * b)
    else if (t <= 1.65d-270) then
        tmp = t_1
    else if (t <= 8.2d-55) then
        tmp = z * (x * y)
    else if (t <= 8.5d+207) then
        tmp = t_1
    else
        tmp = b * (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 = a * (c * j);
	double tmp;
	if (t <= -1.5e+84) {
		tmp = i * (t * b);
	} else if (t <= 1.65e-270) {
		tmp = t_1;
	} else if (t <= 8.2e-55) {
		tmp = z * (x * y);
	} else if (t <= 8.5e+207) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -1.5e+84:
		tmp = i * (t * b)
	elif t <= 1.65e-270:
		tmp = t_1
	elif t <= 8.2e-55:
		tmp = z * (x * y)
	elif t <= 8.5e+207:
		tmp = t_1
	else:
		tmp = b * (t * i)
	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 (t <= -1.5e+84)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 1.65e-270)
		tmp = t_1;
	elseif (t <= 8.2e-55)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 8.5e+207)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	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 (t <= -1.5e+84)
		tmp = i * (t * b);
	elseif (t <= 1.65e-270)
		tmp = t_1;
	elseif (t <= 8.2e-55)
		tmp = z * (x * y);
	elseif (t <= 8.5e+207)
		tmp = t_1;
	else
		tmp = b * (t * i);
	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[t, -1.5e+84], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-270], t$95$1, If[LessEqual[t, 8.2e-55], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+207], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.49999999999999998e84

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 67.5%

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

   5. Simplified 67.5%

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

   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. *-lowering-*.f64 42.3%

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

   8. Simplified 42.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 46.2%

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

   10. Applied egg-rr 46.2%

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

   if -1.49999999999999998e84 < t < 1.65000000000000009e-270 or 8.1999999999999996e-55 < t < 8.4999999999999996e207

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.9%

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

   8. Simplified 38.9%

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

   if 1.65000000000000009e-270 < t < 8.1999999999999996e-55

   1. Initial program 81.9%

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

   3. Taylor expanded in 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 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 42.6%

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

   8. Simplified 42.6%

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

   if 8.4999999999999996e207 < t

   1. Initial program 59.6%

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

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

   5. Simplified 94.8%

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

   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. *-lowering-*.f64 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -4.8e+85)
     t_2
     (if (<= t 1.45e-270)
       t_1
       (if (<= t 4.2e-46) (* z (* x y)) (if (<= t 7e+207) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -4.8e+85) {
		tmp = t_2;
	} else if (t <= 1.45e-270) {
		tmp = t_1;
	} else if (t <= 4.2e-46) {
		tmp = z * (x * y);
	} else if (t <= 7e+207) {
		tmp = 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 = a * (c * j)
    t_2 = b * (t * i)
    if (t <= (-4.8d+85)) then
        tmp = t_2
    else if (t <= 1.45d-270) then
        tmp = t_1
    else if (t <= 4.2d-46) then
        tmp = z * (x * y)
    else if (t <= 7d+207) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -4.8e+85) {
		tmp = t_2;
	} else if (t <= 1.45e-270) {
		tmp = t_1;
	} else if (t <= 4.2e-46) {
		tmp = z * (x * y);
	} else if (t <= 7e+207) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -4.8e+85:
		tmp = t_2
	elif t <= 1.45e-270:
		tmp = t_1
	elif t <= 4.2e-46:
		tmp = z * (x * y)
	elif t <= 7e+207:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -4.8e+85)
		tmp = t_2;
	elseif (t <= 1.45e-270)
		tmp = t_1;
	elseif (t <= 4.2e-46)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 7e+207)
		tmp = 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 = a * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -4.8e+85)
		tmp = t_2;
	elseif (t <= 1.45e-270)
		tmp = t_1;
	elseif (t <= 4.2e-46)
		tmp = z * (x * y);
	elseif (t <= 7e+207)
		tmp = 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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+85], t$95$2, If[LessEqual[t, 1.45e-270], t$95$1, If[LessEqual[t, 4.2e-46], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+207], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999993e85 or 7.00000000000000056e207 < t

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 75.1%

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

   5. Simplified 75.1%

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

   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. *-lowering-*.f64 45.5%

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

   8. Simplified 45.5%

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

   if -4.79999999999999993e85 < t < 1.44999999999999991e-270 or 4.19999999999999975e-46 < t < 7.00000000000000056e207

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.9%

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

   8. Simplified 38.9%

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

   if 1.44999999999999991e-270 < t < 4.19999999999999975e-46

   1. Initial program 81.9%

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

   3. Taylor expanded in 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 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 42.6%

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

   8. Simplified 42.6%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -1.9e+85)
     t_2
     (if (<= t 1.8e-270)
       t_1
       (if (<= t 1.02e-47) (* y (* x z)) (if (<= t 5.4e+207) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.9e+85) {
		tmp = t_2;
	} else if (t <= 1.8e-270) {
		tmp = t_1;
	} else if (t <= 1.02e-47) {
		tmp = y * (x * z);
	} else if (t <= 5.4e+207) {
		tmp = 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 = a * (c * j)
    t_2 = b * (t * i)
    if (t <= (-1.9d+85)) then
        tmp = t_2
    else if (t <= 1.8d-270) then
        tmp = t_1
    else if (t <= 1.02d-47) then
        tmp = y * (x * z)
    else if (t <= 5.4d+207) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.9e+85) {
		tmp = t_2;
	} else if (t <= 1.8e-270) {
		tmp = t_1;
	} else if (t <= 1.02e-47) {
		tmp = y * (x * z);
	} else if (t <= 5.4e+207) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -1.9e+85:
		tmp = t_2
	elif t <= 1.8e-270:
		tmp = t_1
	elif t <= 1.02e-47:
		tmp = y * (x * z)
	elif t <= 5.4e+207:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1.9e+85)
		tmp = t_2;
	elseif (t <= 1.8e-270)
		tmp = t_1;
	elseif (t <= 1.02e-47)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 5.4e+207)
		tmp = 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 = a * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -1.9e+85)
		tmp = t_2;
	elseif (t <= 1.8e-270)
		tmp = t_1;
	elseif (t <= 1.02e-47)
		tmp = y * (x * z);
	elseif (t <= 5.4e+207)
		tmp = 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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+85], t$95$2, If[LessEqual[t, 1.8e-270], t$95$1, If[LessEqual[t, 1.02e-47], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+207], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.89999999999999996e85 or 5.4000000000000005e207 < t

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 75.1%

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

   5. Simplified 75.1%

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

   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. *-lowering-*.f64 45.5%

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

   8. Simplified 45.5%

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

   if -1.89999999999999996e85 < t < 1.7999999999999999e-270 or 1.02000000000000002e-47 < t < 5.4000000000000005e207

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.9%

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

   8. Simplified 38.9%

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

   if 1.7999999999999999e-270 < t < 1.02000000000000002e-47

   1. Initial program 81.9%

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

   3. Taylor expanded in 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 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -3.5e+83)
     t_2
     (if (<= t 1.6e-270)
       t_1
       (if (<= t 6.6e-52) (* x (* y z)) (if (<= t 5.4e+207) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -3.5e+83) {
		tmp = t_2;
	} else if (t <= 1.6e-270) {
		tmp = t_1;
	} else if (t <= 6.6e-52) {
		tmp = x * (y * z);
	} else if (t <= 5.4e+207) {
		tmp = 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 = a * (c * j)
    t_2 = b * (t * i)
    if (t <= (-3.5d+83)) then
        tmp = t_2
    else if (t <= 1.6d-270) then
        tmp = t_1
    else if (t <= 6.6d-52) then
        tmp = x * (y * z)
    else if (t <= 5.4d+207) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -3.5e+83) {
		tmp = t_2;
	} else if (t <= 1.6e-270) {
		tmp = t_1;
	} else if (t <= 6.6e-52) {
		tmp = x * (y * z);
	} else if (t <= 5.4e+207) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -3.5e+83:
		tmp = t_2
	elif t <= 1.6e-270:
		tmp = t_1
	elif t <= 6.6e-52:
		tmp = x * (y * z)
	elif t <= 5.4e+207:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -3.5e+83)
		tmp = t_2;
	elseif (t <= 1.6e-270)
		tmp = t_1;
	elseif (t <= 6.6e-52)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 5.4e+207)
		tmp = 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 = a * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -3.5e+83)
		tmp = t_2;
	elseif (t <= 1.6e-270)
		tmp = t_1;
	elseif (t <= 6.6e-52)
		tmp = x * (y * z);
	elseif (t <= 5.4e+207)
		tmp = 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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+83], t$95$2, If[LessEqual[t, 1.6e-270], t$95$1, If[LessEqual[t, 6.6e-52], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+207], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999977e83 or 5.4000000000000005e207 < t

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 75.1%

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

   5. Simplified 75.1%

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

   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. *-lowering-*.f64 45.5%

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

   8. Simplified 45.5%

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

   if -3.49999999999999977e83 < t < 1.59999999999999994e-270 or 6.5999999999999999e-52 < t < 5.4000000000000005e207

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.9%

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

   8. Simplified 38.9%

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

   if 1.59999999999999994e-270 < t < 6.5999999999999999e-52

   1. Initial program 81.9%

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

   3. Taylor expanded in 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 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 36.7%

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

   8. Simplified 36.7%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -4e-86)
   (* z (+ (* x y) (* b (- (/ (* t i) z) c))))
   (if (<= z 4e+74)
     (+ (* j (- (* a c) (* y i))) (* i (* t b)))
     (* z (+ (* x y) (* b (- (* i (/ t z)) 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 (z <= -4e-86) {
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	} else if (z <= 4e+74) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - 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 (z <= (-4d-86)) then
        tmp = z * ((x * y) + (b * (((t * i) / z) - c)))
    else if (z <= 4d+74) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else
        tmp = z * ((x * y) + (b * ((i * (t / z)) - 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 (z <= -4e-86) {
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	} else if (z <= 4e+74) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -4e-86:
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)))
	elif z <= 4e+74:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	else:
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -4e-86)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(Float64(t * i) / z) - c))));
	elseif (z <= 4e+74)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	else
		tmp = Float64(z * Float64(Float64(x * y) + Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -4e-86)
		tmp = z * ((x * y) + (b * (((t * i) / z) - c)));
	elseif (z <= 4e+74)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	else
		tmp = z * ((x * y) + (b * ((i * (t / z)) - c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -4e-86], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(N[(t * i), $MachinePrecision] / z), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+74], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] + N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000034e-86

   1. Initial program 70.0%

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

   3. Taylor expanded in 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 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 69.9%

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

   if -4.00000000000000034e-86 < z < 3.99999999999999981e74

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 62.4%

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

   5. Simplified 62.4%

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

   if 3.99999999999999981e74 < z

   1. Initial program 54.9%

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

   3. Taylor expanded in j around 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 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around inf

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

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

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

       2. associate--l+ N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. +-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. +-commutative N/A

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

       10. mul-1-neg N/A

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

       11. sub-neg N/A

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

       12. associate-/l* N/A

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

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

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

       14. unsub-neg N/A

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

       15. mul-1-neg N/A

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

       16. +-commutative N/A

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

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

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

       18. +-commutative N/A

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

       19. mul-1-neg N/A

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

       20. unsub-neg N/A

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

       21. --lowering--.f64 N/A

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

   11. Simplified 67.1%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

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

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

       4. /-lowering-/.f64 72.5%

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

   13. Applied egg-rr 72.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y + b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -7.5e+69)
     t_1
     (if (<= c -9e-106)
       (* b (- (* t i) (* z c)))
       (if (<= c 1.85e+43) (* y (- (* x z) (* i 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e+69) {
		tmp = t_1;
	} else if (c <= -9e-106) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= 1.85e+43) {
		tmp = y * ((x * z) - (i * 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 = c * ((a * j) - (z * b))
    if (c <= (-7.5d+69)) then
        tmp = t_1
    else if (c <= (-9d-106)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= 1.85d+43) then
        tmp = y * ((x * z) - (i * 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e+69) {
		tmp = t_1;
	} else if (c <= -9e-106) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= 1.85e+43) {
		tmp = y * ((x * z) - (i * j));
	} 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 <= -7.5e+69:
		tmp = t_1
	elif c <= -9e-106:
		tmp = b * ((t * i) - (z * c))
	elif c <= 1.85e+43:
		tmp = y * ((x * z) - (i * j))
	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 <= -7.5e+69)
		tmp = t_1;
	elseif (c <= -9e-106)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= 1.85e+43)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * 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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -7.5e+69)
		tmp = t_1;
	elseif (c <= -9e-106)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= 1.85e+43)
		tmp = y * ((x * z) - (i * 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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e+69], t$95$1, If[LessEqual[c, -9e-106], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+43], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.49999999999999939e69 or 1.85e43 < c

   1. Initial program 56.3%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   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 70.5%

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

   5. Simplified 70.5%

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

   if -7.49999999999999939e69 < c < -8.99999999999999911e-106

   1. Initial program 78.3%

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

   3. Taylor expanded in 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 48.8%

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

   5. Simplified 48.8%

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

   if -8.99999999999999911e-106 < c < 1.85e43

   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 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 57.8%

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

   5. Simplified 57.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.65 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1.7e-52)
     t_1
     (if (<= b 5.3e-79)
       (* a (- (* c j) (* x t)))
       (if (<= b 3.65e+106) (* j (- (* a c) (* 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.7e-52) {
		tmp = t_1;
	} else if (b <= 5.3e-79) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.65e+106) {
		tmp = j * ((a * c) - (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 = b * ((t * i) - (z * c))
    if (b <= (-1.7d-52)) then
        tmp = t_1
    else if (b <= 5.3d-79) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 3.65d+106) then
        tmp = j * ((a * c) - (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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.7e-52) {
		tmp = t_1;
	} else if (b <= 5.3e-79) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.65e+106) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.7e-52:
		tmp = t_1
	elif b <= 5.3e-79:
		tmp = a * ((c * j) - (x * t))
	elif b <= 3.65e+106:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.7e-52)
		tmp = t_1;
	elseif (b <= 5.3e-79)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 3.65e+106)
		tmp = Float64(j * Float64(Float64(a * c) - 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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.7e-52)
		tmp = t_1;
	elseif (b <= 5.3e-79)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 3.65e+106)
		tmp = j * ((a * c) - (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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e-52], t$95$1, If[LessEqual[b, 5.3e-79], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.65e+106], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.70000000000000009e-52 or 3.65000000000000002e106 < b

   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 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 59.7%

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

   5. Simplified 59.7%

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

   if -1.70000000000000009e-52 < b < 5.2999999999999998e-79

   1. Initial program 60.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 52.9%

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

   5. Simplified 52.9%

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

   if 5.2999999999999998e-79 < b < 3.65000000000000002e106

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 55.5%

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

   5. Simplified 55.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.65 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-136}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(0 - z\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.05e-100)
     t_1
     (if (<= a 2.2e-136)
       (* (* b c) (- 0.0 z))
       (if (<= a 3.8e-64) (* y (* x 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.05e-100) {
		tmp = t_1;
	} else if (a <= 2.2e-136) {
		tmp = (b * c) * (0.0 - z);
	} else if (a <= 3.8e-64) {
		tmp = y * (x * 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 = a * ((c * j) - (x * t))
    if (a <= (-2.05d-100)) then
        tmp = t_1
    else if (a <= 2.2d-136) then
        tmp = (b * c) * (0.0d0 - z)
    else if (a <= 3.8d-64) then
        tmp = y * (x * 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.05e-100) {
		tmp = t_1;
	} else if (a <= 2.2e-136) {
		tmp = (b * c) * (0.0 - z);
	} else if (a <= 3.8e-64) {
		tmp = y * (x * z);
	} 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 <= -2.05e-100:
		tmp = t_1
	elif a <= 2.2e-136:
		tmp = (b * c) * (0.0 - z)
	elif a <= 3.8e-64:
		tmp = y * (x * z)
	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 <= -2.05e-100)
		tmp = t_1;
	elseif (a <= 2.2e-136)
		tmp = Float64(Float64(b * c) * Float64(0.0 - z));
	elseif (a <= 3.8e-64)
		tmp = Float64(y * Float64(x * 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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.05e-100)
		tmp = t_1;
	elseif (a <= 2.2e-136)
		tmp = (b * c) * (0.0 - z);
	elseif (a <= 3.8e-64)
		tmp = y * (x * 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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-100], t$95$1, If[LessEqual[a, 2.2e-136], N[(N[(b * c), $MachinePrecision] * N[(0.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-64], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0499999999999999e-100 or 3.8000000000000002e-64 < a

   1. Initial program 62.4%

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

   3. Taylor expanded in 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 55.7%

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

   5. Simplified 55.7%

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

   if -2.0499999999999999e-100 < a < 2.2000000000000001e-136

   1. Initial program 77.5%

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

   3. Taylor expanded in 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 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 61.0%

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

   8. Simplified 61.0%

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

   9. Taylor expanded in c around inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   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. *-lowering-*.f64 N/A

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

       5. *-lowering-*.f64 32.5%

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

   11. Simplified 32.5%

       \[\leadsto \color{blue}{0 - b \cdot \left(c \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 34.3%

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

   13. Applied egg-rr 34.3%

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

   if 2.2000000000000001e-136 < a < 3.8000000000000002e-64

   1. Initial program 93.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.2%

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

   8. Simplified 51.2%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-136}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(0 - z\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+84)
   (* i (* t b))
   (if (<= t 1.15e-270)
     (* a (* c j))
     (if (<= t 1.35e-42) (* z (* x y)) (* a (- 0.0 (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4e+84) {
		tmp = i * (t * b);
	} else if (t <= 1.15e-270) {
		tmp = a * (c * j);
	} else if (t <= 1.35e-42) {
		tmp = z * (x * y);
	} else {
		tmp = a * (0.0 - (x * t));
	}
	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 (t <= (-4d+84)) then
        tmp = i * (t * b)
    else if (t <= 1.15d-270) then
        tmp = a * (c * j)
    else if (t <= 1.35d-42) then
        tmp = z * (x * y)
    else
        tmp = a * (0.0d0 - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4e+84) {
		tmp = i * (t * b);
	} else if (t <= 1.15e-270) {
		tmp = a * (c * j);
	} else if (t <= 1.35e-42) {
		tmp = z * (x * y);
	} else {
		tmp = a * (0.0 - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4e+84:
		tmp = i * (t * b)
	elif t <= 1.15e-270:
		tmp = a * (c * j)
	elif t <= 1.35e-42:
		tmp = z * (x * y)
	else:
		tmp = a * (0.0 - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+84)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 1.15e-270)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 1.35e-42)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(a * Float64(0.0 - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4e+84)
		tmp = i * (t * b);
	elseif (t <= 1.15e-270)
		tmp = a * (c * j);
	elseif (t <= 1.35e-42)
		tmp = z * (x * y);
	else
		tmp = a * (0.0 - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+84], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-270], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-42], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(a * N[(0.0 - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.00000000000000023e84

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 67.5%

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

   5. Simplified 67.5%

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

   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. *-lowering-*.f64 42.3%

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

   8. Simplified 42.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 46.2%

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

   10. Applied egg-rr 46.2%

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

   if -4.00000000000000023e84 < t < 1.1500000000000001e-270

   1. Initial program 70.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 41.7%

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

   8. Simplified 41.7%

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

   if 1.1500000000000001e-270 < t < 1.35e-42

   1. Initial program 81.9%

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

   3. Taylor expanded in 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 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 42.6%

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

   8. Simplified 42.6%

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

   if 1.35e-42 < t

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(a \cdot x\right)}, \mathsf{\_.f64}\left(0, t\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 40.8%

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

   8. Simplified 40.8%

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

      1. sub0-neg N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. *-lowering-*.f64 46.0%

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

   10. Applied egg-rr 46.0%

       \[\leadsto \color{blue}{\left(-x \cdot t\right) \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.42e+41)
     t_1
     (if (<= a 1.28e+73) (* 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 <= -1.42e+41) {
		tmp = t_1;
	} else if (a <= 1.28e+73) {
		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 <= (-1.42d+41)) then
        tmp = t_1
    else if (a <= 1.28d+73) 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 <= -1.42e+41) {
		tmp = t_1;
	} else if (a <= 1.28e+73) {
		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 <= -1.42e+41:
		tmp = t_1
	elif a <= 1.28e+73:
		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 <= -1.42e+41)
		tmp = t_1;
	elseif (a <= 1.28e+73)
		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 <= -1.42e+41)
		tmp = t_1;
	elseif (a <= 1.28e+73)
		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, -1.42e+41], t$95$1, If[LessEqual[a, 1.28e+73], 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 < -1.42000000000000007e41 or 1.2800000000000001e73 < a

   1. Initial program 57.7%

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

   3. Taylor expanded in 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 65.5%

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

   5. Simplified 65.5%

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

   if -1.42000000000000007e41 < a < 1.2800000000000001e73

   1. Initial program 76.8%

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

   3. Taylor expanded in 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 44.8%

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

   5. Simplified 44.8%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -2.8e+82) t_1 (if (<= t 8.5e+207) (* 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 (t <= -2.8e+82) {
		tmp = t_1;
	} else if (t <= 8.5e+207) {
		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 (t <= (-2.8d+82)) then
        tmp = t_1
    else if (t <= 8.5d+207) 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 (t <= -2.8e+82) {
		tmp = t_1;
	} else if (t <= 8.5e+207) {
		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 t <= -2.8e+82:
		tmp = t_1
	elif t <= 8.5e+207:
		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 (t <= -2.8e+82)
		tmp = t_1;
	elseif (t <= 8.5e+207)
		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 (t <= -2.8e+82)
		tmp = t_1;
	elseif (t <= 8.5e+207)
		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[t, -2.8e+82], t$95$1, If[LessEqual[t, 8.5e+207], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e82 or 8.4999999999999996e207 < t

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 75.1%

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

   5. Simplified 75.1%

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

   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. *-lowering-*.f64 45.5%

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

   8. Simplified 45.5%

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

   if -2.8e82 < t < 8.4999999999999996e207

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 31.5%

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

   8. Simplified 31.5%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+207}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.1% 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 68.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
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 42.7%

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

5. Simplified 42.7%

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

6. Taylor expanded in j around inf

   \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
7. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 26.0%

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

8. Simplified 26.0%

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

9. Final simplification 26.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 60.2% 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 2024160 
(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)))))