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

Percentage Accurate: 73.2% → 82.1%

Time: 19.8s

Alternatives: 27

Speedup: 0.5×

• 58.0% 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: 73.2% 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: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(x * y) / b) - c) * Float64(z * 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))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (((x * y) / b) - c) * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(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]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $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 92.7%

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

   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 15.3%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 61.4%

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

   8. Simplified 61.4%

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

4. Final simplification 85.5%

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

Alternative 2: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - \frac{x \cdot a}{b}\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-31}:\\ \;\;\;\;\left(t - \frac{y \cdot j}{b}\right) \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot \left(a - \frac{z \cdot b}{j}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= c -1.3e+121)
     (* c (- (* a j) (* z b)))
     (if (<= c -2.5e+38)
       t_1
       (if (<= c -2.55e-83)
         (* (* t b) (- i (/ (* x a) b)))
         (if (<= c 1.7e-123)
           t_1
           (if (<= c 9.5e-31)
             (* (- t (/ (* y j) b)) (* b i))
             (* c (* j (- a (/ (* z b) j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (c <= -1.3e+121) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -2.5e+38) {
		tmp = t_1;
	} else if (c <= -2.55e-83) {
		tmp = (t * b) * (i - ((x * a) / b));
	} else if (c <= 1.7e-123) {
		tmp = t_1;
	} else if (c <= 9.5e-31) {
		tmp = (t - ((y * j) / b)) * (b * i);
	} else {
		tmp = c * (j * (a - ((z * b) / j)));
	}
	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 = y * ((x * z) - (i * j))
    if (c <= (-1.3d+121)) then
        tmp = c * ((a * j) - (z * b))
    else if (c <= (-2.5d+38)) then
        tmp = t_1
    else if (c <= (-2.55d-83)) then
        tmp = (t * b) * (i - ((x * a) / b))
    else if (c <= 1.7d-123) then
        tmp = t_1
    else if (c <= 9.5d-31) then
        tmp = (t - ((y * j) / b)) * (b * i)
    else
        tmp = c * (j * (a - ((z * b) / j)))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (c <= -1.3e+121) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -2.5e+38) {
		tmp = t_1;
	} else if (c <= -2.55e-83) {
		tmp = (t * b) * (i - ((x * a) / b));
	} else if (c <= 1.7e-123) {
		tmp = t_1;
	} else if (c <= 9.5e-31) {
		tmp = (t - ((y * j) / b)) * (b * i);
	} else {
		tmp = c * (j * (a - ((z * b) / j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if c <= -1.3e+121:
		tmp = c * ((a * j) - (z * b))
	elif c <= -2.5e+38:
		tmp = t_1
	elif c <= -2.55e-83:
		tmp = (t * b) * (i - ((x * a) / b))
	elif c <= 1.7e-123:
		tmp = t_1
	elif c <= 9.5e-31:
		tmp = (t - ((y * j) / b)) * (b * i)
	else:
		tmp = c * (j * (a - ((z * b) / j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (c <= -1.3e+121)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (c <= -2.5e+38)
		tmp = t_1;
	elseif (c <= -2.55e-83)
		tmp = Float64(Float64(t * b) * Float64(i - Float64(Float64(x * a) / b)));
	elseif (c <= 1.7e-123)
		tmp = t_1;
	elseif (c <= 9.5e-31)
		tmp = Float64(Float64(t - Float64(Float64(y * j) / b)) * Float64(b * i));
	else
		tmp = Float64(c * Float64(j * Float64(a - Float64(Float64(z * b) / j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (c <= -1.3e+121)
		tmp = c * ((a * j) - (z * b));
	elseif (c <= -2.5e+38)
		tmp = t_1;
	elseif (c <= -2.55e-83)
		tmp = (t * b) * (i - ((x * a) / b));
	elseif (c <= 1.7e-123)
		tmp = t_1;
	elseif (c <= 9.5e-31)
		tmp = (t - ((y * j) / b)) * (b * i);
	else
		tmp = c * (j * (a - ((z * b) / j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e+121], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.5e+38], t$95$1, If[LessEqual[c, -2.55e-83], N[(N[(t * b), $MachinePrecision] * N[(i - N[(N[(x * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-123], t$95$1, If[LessEqual[c, 9.5e-31], N[(N[(t - N[(N[(y * j), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * N[(a - N[(N[(z * b), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.2999999999999999e121

   1. Initial program 41.5%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   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 72.2%

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

   5. Simplified 72.2%

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

   if -1.2999999999999999e121 < c < -2.49999999999999985e38 or -2.55000000000000018e-83 < c < 1.7e-123

   1. Initial program 80.9%

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

   3. Taylor expanded in 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 58.1%

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

   5. Simplified 58.1%

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

   if -2.49999999999999985e38 < c < -2.55000000000000018e-83

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 78.0%

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

   6. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. *-lowering-*.f64 57.3%

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

   8. Simplified 57.3%

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

   if 1.7e-123 < c < 9.5000000000000008e-31

   1. Initial program 94.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 87.9%

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

   6. Taylor expanded in i around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot i\right) \cdot \color{blue}{\left(t + -1 \cdot \frac{j \cdot y}{b}\right)} \]

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

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. *-lowering-*.f64 63.5%

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

   8. Simplified 63.5%

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

   if 9.5000000000000008e-31 < c

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in j around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

      6. *-lowering-*.f64 68.7%

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

   8. Simplified 68.7%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot \left(a - \frac{b \cdot z}{j}\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - \frac{x \cdot a}{b}\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-31}:\\ \;\;\;\;\left(t - \frac{y \cdot j}{b}\right) \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot \left(a - \frac{z \cdot b}{j}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-13}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= a -4.2e+114)
     (+ (* j (- (* a c) (* y i))) (* y (* x z)))
     (if (<= a -1.15e-13)
       (+ t_2 t_1)
       (if (<= a 3.8e-50)
         (+ (* y (- (* x z) (* i j))) t_1)
         (+ t_2 (* c (- (* a j) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (a <= -4.2e+114) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else if (a <= -1.15e-13) {
		tmp = t_2 + t_1;
	} else if (a <= 3.8e-50) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2 + (c * ((a * j) - (z * 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) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (a <= (-4.2d+114)) then
        tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
    else if (a <= (-1.15d-13)) then
        tmp = t_2 + t_1
    else if (a <= 3.8d-50) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_2 + (c * ((a * j) - (z * 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (a <= -4.2e+114) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else if (a <= -1.15e-13) {
		tmp = t_2 + t_1;
	} else if (a <= 3.8e-50) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2 + (c * ((a * j) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if a <= -4.2e+114:
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
	elif a <= -1.15e-13:
		tmp = t_2 + t_1
	elif a <= 3.8e-50:
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_2 + (c * ((a * j) - (z * b)))
	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)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (a <= -4.2e+114)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)));
	elseif (a <= -1.15e-13)
		tmp = Float64(t_2 + t_1);
	elseif (a <= 3.8e-50)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = Float64(t_2 + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (a <= -4.2e+114)
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	elseif (a <= -1.15e-13)
		tmp = t_2 + t_1;
	elseif (a <= 3.8e-50)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_2 + (c * ((a * j) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+114], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-13], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[a, 3.8e-50], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2000000000000001e114

   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 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 68.7%

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

   5. Simplified 68.7%

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

   if -4.2000000000000001e114 < a < -1.1499999999999999e-13

   1. Initial program 56.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 72.6%

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

   5. Simplified 72.6%

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

   if -1.1499999999999999e-13 < a < 3.7999999999999999e-50

   1. Initial program 83.8%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-in N/A

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

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

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

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

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

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

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

      14. *-commutative N/A

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

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

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

      16. *-commutative N/A

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

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

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

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

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

   5. Simplified 78.7%

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

   if 3.7999999999999999e-50 < a

   1. Initial program 70.6%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 69.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -1.42e+187)
     t_1
     (if (<= a -6.2e+146)
       (* x (- 0.0 (* t a)))
       (if (<= a 2e-40)
         (* c (* z (- 0.0 b)))
         (if (<= a 1.15e+73)
           (* z (* x y))
           (if (<= a 4.4e+230) (* t (- 0.0 (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.42e+187) {
		tmp = t_1;
	} else if (a <= -6.2e+146) {
		tmp = x * (0.0 - (t * a));
	} else if (a <= 2e-40) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 1.15e+73) {
		tmp = z * (x * y);
	} else if (a <= 4.4e+230) {
		tmp = t * (0.0 - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-1.42d+187)) then
        tmp = t_1
    else if (a <= (-6.2d+146)) then
        tmp = x * (0.0d0 - (t * a))
    else if (a <= 2d-40) then
        tmp = c * (z * (0.0d0 - b))
    else if (a <= 1.15d+73) then
        tmp = z * (x * y)
    else if (a <= 4.4d+230) then
        tmp = t * (0.0d0 - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.42e+187) {
		tmp = t_1;
	} else if (a <= -6.2e+146) {
		tmp = x * (0.0 - (t * a));
	} else if (a <= 2e-40) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 1.15e+73) {
		tmp = z * (x * y);
	} else if (a <= 4.4e+230) {
		tmp = t * (0.0 - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -1.42e+187:
		tmp = t_1
	elif a <= -6.2e+146:
		tmp = x * (0.0 - (t * a))
	elif a <= 2e-40:
		tmp = c * (z * (0.0 - b))
	elif a <= 1.15e+73:
		tmp = z * (x * y)
	elif a <= 4.4e+230:
		tmp = t * (0.0 - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -1.42e+187)
		tmp = t_1;
	elseif (a <= -6.2e+146)
		tmp = Float64(x * Float64(0.0 - Float64(t * a)));
	elseif (a <= 2e-40)
		tmp = Float64(c * Float64(z * Float64(0.0 - b)));
	elseif (a <= 1.15e+73)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 4.4e+230)
		tmp = Float64(t * Float64(0.0 - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -1.42e+187)
		tmp = t_1;
	elseif (a <= -6.2e+146)
		tmp = x * (0.0 - (t * a));
	elseif (a <= 2e-40)
		tmp = c * (z * (0.0 - b));
	elseif (a <= 1.15e+73)
		tmp = z * (x * y);
	elseif (a <= 4.4e+230)
		tmp = t * (0.0 - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.42e+187], t$95$1, If[LessEqual[a, -6.2e+146], N[(x * N[(0.0 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-40], N[(c * N[(z * N[(0.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+73], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+230], N[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.41999999999999991e187 or 4.4000000000000002e230 < a

   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 a around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in j around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.6%

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

   8. Simplified 52.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 61.3%

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

   10. Applied egg-rr 61.3%

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

   if -1.41999999999999991e187 < a < -6.2000000000000004e146

   1. Initial program 40.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

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

      7. --lowering--.f64 86.3%

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

   8. Simplified 86.3%

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

   if -6.2000000000000004e146 < a < 1.9999999999999999e-40

   1. Initial program 77.6%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 53.1%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 34.3%

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

   8. Simplified 34.3%

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

      1. sub0-neg N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 34.3%

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

   10. Applied egg-rr 34.3%

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

   if 1.9999999999999999e-40 < a < 1.15e73

   1. Initial program 76.9%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 76.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 41.1%

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

   8. Simplified 41.1%

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

   if 1.15e73 < a < 4.4000000000000002e230

   1. Initial program 69.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

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

      12. --lowering--.f64 57.9%

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

   5. Simplified 57.9%

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

      1. sub0-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 57.9%

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

   7. Applied egg-rr 57.9%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.5%

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

   10. Simplified 49.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+187}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(0 - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{+147}:\\ \;\;\;\;0 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -1.05e+186)
     t_1
     (if (<= a -6.3e+147)
       (- 0.0 (* a (* x t)))
       (if (<= a 2.05e-41)
         (* c (* z (- 0.0 b)))
         (if (<= a 9.6e+79)
           (* z (* x y))
           (if (<= a 1.75e+231) (* t (- 0.0 (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.05e+186) {
		tmp = t_1;
	} else if (a <= -6.3e+147) {
		tmp = 0.0 - (a * (x * t));
	} else if (a <= 2.05e-41) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 9.6e+79) {
		tmp = z * (x * y);
	} else if (a <= 1.75e+231) {
		tmp = t * (0.0 - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-1.05d+186)) then
        tmp = t_1
    else if (a <= (-6.3d+147)) then
        tmp = 0.0d0 - (a * (x * t))
    else if (a <= 2.05d-41) then
        tmp = c * (z * (0.0d0 - b))
    else if (a <= 9.6d+79) then
        tmp = z * (x * y)
    else if (a <= 1.75d+231) then
        tmp = t * (0.0d0 - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.05e+186) {
		tmp = t_1;
	} else if (a <= -6.3e+147) {
		tmp = 0.0 - (a * (x * t));
	} else if (a <= 2.05e-41) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 9.6e+79) {
		tmp = z * (x * y);
	} else if (a <= 1.75e+231) {
		tmp = t * (0.0 - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -1.05e+186:
		tmp = t_1
	elif a <= -6.3e+147:
		tmp = 0.0 - (a * (x * t))
	elif a <= 2.05e-41:
		tmp = c * (z * (0.0 - b))
	elif a <= 9.6e+79:
		tmp = z * (x * y)
	elif a <= 1.75e+231:
		tmp = t * (0.0 - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -1.05e+186)
		tmp = t_1;
	elseif (a <= -6.3e+147)
		tmp = Float64(0.0 - Float64(a * Float64(x * t)));
	elseif (a <= 2.05e-41)
		tmp = Float64(c * Float64(z * Float64(0.0 - b)));
	elseif (a <= 9.6e+79)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.75e+231)
		tmp = Float64(t * Float64(0.0 - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -1.05e+186)
		tmp = t_1;
	elseif (a <= -6.3e+147)
		tmp = 0.0 - (a * (x * t));
	elseif (a <= 2.05e-41)
		tmp = c * (z * (0.0 - b));
	elseif (a <= 9.6e+79)
		tmp = z * (x * y);
	elseif (a <= 1.75e+231)
		tmp = t * (0.0 - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+186], t$95$1, If[LessEqual[a, -6.3e+147], N[(0.0 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-41], N[(c * N[(z * N[(0.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+79], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e+231], N[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.05e186 or 1.7499999999999999e231 < a

   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 a around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in j around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.6%

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

   8. Simplified 52.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 61.3%

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

   10. Applied egg-rr 61.3%

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

   if -1.05e186 < a < -6.29999999999999983e147

   1. Initial program 40.2%

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

   3. Taylor expanded in 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 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in j around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

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

      12. --lowering--.f64 77.3%

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

   8. Simplified 77.3%

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

   if -6.29999999999999983e147 < a < 2.05000000000000007e-41

   1. Initial program 77.6%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 53.1%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 34.3%

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

   8. Simplified 34.3%

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

      1. sub0-neg N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 34.3%

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

   10. Applied egg-rr 34.3%

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

   if 2.05000000000000007e-41 < a < 9.59999999999999942e79

   1. Initial program 76.9%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 76.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 41.1%

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

   8. Simplified 41.1%

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

   if 9.59999999999999942e79 < a < 1.7499999999999999e231

   1. Initial program 69.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

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

      12. --lowering--.f64 57.9%

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

   5. Simplified 57.9%

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

      1. sub0-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 57.9%

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

   7. Applied egg-rr 57.9%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.5%

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

   10. Simplified 49.5%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{+147}:\\ \;\;\;\;0 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(0 - x \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- 0.0 (* x a)))) (t_2 (* j (* a c))))
   (if (<= a -6.6e+187)
     t_2
     (if (<= a -1.3e+147)
       t_1
       (if (<= a 1.5e-46)
         (* c (* z (- 0.0 b)))
         (if (<= a 1.05e+85) (* z (* x y)) (if (<= a 2.9e+230) 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 = t * (0.0 - (x * a));
	double t_2 = j * (a * c);
	double tmp;
	if (a <= -6.6e+187) {
		tmp = t_2;
	} else if (a <= -1.3e+147) {
		tmp = t_1;
	} else if (a <= 1.5e-46) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 1.05e+85) {
		tmp = z * (x * y);
	} else if (a <= 2.9e+230) {
		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 = t * (0.0d0 - (x * a))
    t_2 = j * (a * c)
    if (a <= (-6.6d+187)) then
        tmp = t_2
    else if (a <= (-1.3d+147)) then
        tmp = t_1
    else if (a <= 1.5d-46) then
        tmp = c * (z * (0.0d0 - b))
    else if (a <= 1.05d+85) then
        tmp = z * (x * y)
    else if (a <= 2.9d+230) 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 = t * (0.0 - (x * a));
	double t_2 = j * (a * c);
	double tmp;
	if (a <= -6.6e+187) {
		tmp = t_2;
	} else if (a <= -1.3e+147) {
		tmp = t_1;
	} else if (a <= 1.5e-46) {
		tmp = c * (z * (0.0 - b));
	} else if (a <= 1.05e+85) {
		tmp = z * (x * y);
	} else if (a <= 2.9e+230) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (0.0 - (x * a))
	t_2 = j * (a * c)
	tmp = 0
	if a <= -6.6e+187:
		tmp = t_2
	elif a <= -1.3e+147:
		tmp = t_1
	elif a <= 1.5e-46:
		tmp = c * (z * (0.0 - b))
	elif a <= 1.05e+85:
		tmp = z * (x * y)
	elif a <= 2.9e+230:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(0.0 - Float64(x * a)))
	t_2 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -6.6e+187)
		tmp = t_2;
	elseif (a <= -1.3e+147)
		tmp = t_1;
	elseif (a <= 1.5e-46)
		tmp = Float64(c * Float64(z * Float64(0.0 - b)));
	elseif (a <= 1.05e+85)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 2.9e+230)
		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 = t * (0.0 - (x * a));
	t_2 = j * (a * c);
	tmp = 0.0;
	if (a <= -6.6e+187)
		tmp = t_2;
	elseif (a <= -1.3e+147)
		tmp = t_1;
	elseif (a <= 1.5e-46)
		tmp = c * (z * (0.0 - b));
	elseif (a <= 1.05e+85)
		tmp = z * (x * y);
	elseif (a <= 2.9e+230)
		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[(t * N[(0.0 - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e+187], t$95$2, If[LessEqual[a, -1.3e+147], t$95$1, If[LessEqual[a, 1.5e-46], N[(c * N[(z * N[(0.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+85], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+230], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6000000000000003e187 or 2.8999999999999999e230 < a

   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 a around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in j around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.6%

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

   8. Simplified 52.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 61.3%

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

   10. Applied egg-rr 61.3%

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

   if -6.6000000000000003e187 < a < -1.2999999999999999e147 or 1.05000000000000005e85 < a < 2.8999999999999999e230

   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 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 62.2%

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

   5. Simplified 62.2%

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

      1. sub0-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 62.2%

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

   7. Applied egg-rr 62.2%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 55.7%

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

   10. Simplified 55.7%

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

   if -1.2999999999999999e147 < a < 1.49999999999999994e-46

   1. Initial program 77.6%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 53.1%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 34.3%

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

   8. Simplified 34.3%

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

      1. sub0-neg N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 34.3%

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

   10. Applied egg-rr 34.3%

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

   if 1.49999999999999994e-46 < a < 1.05000000000000005e85

   1. Initial program 76.9%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 76.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 41.1%

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

   8. Simplified 41.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+187}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(0 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+254}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.05e-22)
   (* (- (/ (* x y) b) c) (* z b))
   (if (<= z 1.25e-55)
     (+ (* j (- (* a c) (* y i))) (* i (* t b)))
     (if (<= z 2e+254)
       (- (* x (- (* y z) (* t a))) (* c (* z b)))
       (* z (- (* x y) (* b 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 <= -2.05e-22) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 1.25e-55) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 2e+254) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = z * ((x * y) - (b * 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 <= (-2.05d-22)) then
        tmp = (((x * y) / b) - c) * (z * b)
    else if (z <= 1.25d-55) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else if (z <= 2d+254) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else
        tmp = z * ((x * y) - (b * 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 <= -2.05e-22) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 1.25e-55) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 2e+254) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.05e-22:
		tmp = (((x * y) / b) - c) * (z * b)
	elif z <= 1.25e-55:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	elif z <= 2e+254:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.05e-22)
		tmp = Float64(Float64(Float64(Float64(x * y) / b) - c) * Float64(z * b));
	elseif (z <= 1.25e-55)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	elseif (z <= 2e+254)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.05e-22)
		tmp = (((x * y) / b) - c) * (z * b);
	elseif (z <= 1.25e-55)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	elseif (z <= 2e+254)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.05e-22], N[(N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-55], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+254], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05e-22

   1. Initial program 56.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(i \cdot t + \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)\right) - c \cdot z\right)} \]
   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 57.2%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 66.6%

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

   8. Simplified 66.6%

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

   if -2.05e-22 < z < 1.25e-55

   1. Initial program 80.4%

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

   3. Taylor expanded in 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 66.7%

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

   5. Simplified 66.7%

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

   if 1.25e-55 < z < 1.9999999999999999e254

   1. Initial program 78.8%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 73.5%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

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

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

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

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

      14. *-lowering-*.f64 68.6%

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

   8. Simplified 68.6%

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

   if 1.9999999999999999e254 < z

   1. Initial program 46.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+254}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-61}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.15e-22)
   (* (- (/ (* x y) b) c) (* z b))
   (if (<= z 3e-61)
     (+ (* j (- (* a c) (* y i))) (* i (* t b)))
     (if (<= z 1.95e+116)
       (+ (* x (- (* y z) (* t a))) (* c (* a j)))
       (* z (- (* x y) (* b 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 <= -2.15e-22) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 3e-61) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 1.95e+116) {
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	} else {
		tmp = z * ((x * y) - (b * 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 <= (-2.15d-22)) then
        tmp = (((x * y) / b) - c) * (z * b)
    else if (z <= 3d-61) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else if (z <= 1.95d+116) then
        tmp = (x * ((y * z) - (t * a))) + (c * (a * j))
    else
        tmp = z * ((x * y) - (b * 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 <= -2.15e-22) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 3e-61) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (z <= 1.95e+116) {
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.15e-22:
		tmp = (((x * y) / b) - c) * (z * b)
	elif z <= 3e-61:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	elif z <= 1.95e+116:
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.15e-22)
		tmp = Float64(Float64(Float64(Float64(x * y) / b) - c) * Float64(z * b));
	elseif (z <= 3e-61)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	elseif (z <= 1.95e+116)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(a * j)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.15e-22)
		tmp = (((x * y) / b) - c) * (z * b);
	elseif (z <= 3e-61)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	elseif (z <= 1.95e+116)
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.15e-22], N[(N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-61], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+116], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15000000000000019e-22

   1. Initial program 56.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(i \cdot t + \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)\right) - c \cdot z\right)} \]
   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 57.2%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 66.6%

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

   8. Simplified 66.6%

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

   if -2.15000000000000019e-22 < z < 3.00000000000000012e-61

   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 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 66.1%

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

   5. Simplified 66.1%

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

   if 3.00000000000000012e-61 < z < 1.95000000000000016e116

   1. Initial program 83.2%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 76.7%

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

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 68.8%

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

   8. Simplified 68.8%

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

   if 1.95000000000000016e116 < z

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 71.1%

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

   5. Simplified 71.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-22}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-61}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.04 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.3e+121)
     t_2
     (if (<= c -1.7e+41)
       t_1
       (if (<= c -4e-83)
         (* t (- (* b i) (* x a)))
         (if (<= c 1.04e-47) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.3e+121) {
		tmp = t_2;
	} else if (c <= -1.7e+41) {
		tmp = t_1;
	} else if (c <= -4e-83) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.04e-47) {
		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 = y * ((x * z) - (i * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.3d+121)) then
        tmp = t_2
    else if (c <= (-1.7d+41)) then
        tmp = t_1
    else if (c <= (-4d-83)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 1.04d-47) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.3e+121) {
		tmp = t_2;
	} else if (c <= -1.7e+41) {
		tmp = t_1;
	} else if (c <= -4e-83) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.04e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.3e+121:
		tmp = t_2
	elif c <= -1.7e+41:
		tmp = t_1
	elif c <= -4e-83:
		tmp = t * ((b * i) - (x * a))
	elif c <= 1.04e-47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.3e+121)
		tmp = t_2;
	elseif (c <= -1.7e+41)
		tmp = t_1;
	elseif (c <= -4e-83)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 1.04e-47)
		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 = y * ((x * z) - (i * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.3e+121)
		tmp = t_2;
	elseif (c <= -1.7e+41)
		tmp = t_1;
	elseif (c <= -4e-83)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 1.04e-47)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e+121], t$95$2, If[LessEqual[c, -1.7e+41], t$95$1, If[LessEqual[c, -4e-83], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.04e-47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2999999999999999e121 or 1.03999999999999995e-47 < c

   1. Initial program 57.9%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   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 67.0%

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

   5. Simplified 67.0%

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

   if -1.2999999999999999e121 < c < -1.69999999999999999e41 or -4.0000000000000001e-83 < c < 1.03999999999999995e-47

   1. Initial program 82.4%

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

   3. Taylor expanded in 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 55.6%

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

   5. Simplified 55.6%

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

   if -1.69999999999999999e41 < c < -4.0000000000000001e-83

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 57.0%

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

   5. Simplified 57.0%

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

      1. sub0-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 57.0%

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

   7. Applied egg-rr 57.0%

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

   8. Taylor expanded in a around 0

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

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

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(x \cdot t\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

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

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

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

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 57.0%

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

   10. Simplified 57.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.04 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-101}:\\ \;\;\;\;0 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.2e-44)
     t_1
     (if (<= a -2.8e-101)
       (- 0.0 (* i (* y j)))
       (if (<= a -1.12e-251)
         (* t (* b i))
         (if (<= a 7.5e-14) (* c (* z (- 0.0 b))) 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 <= -1.2e-44) {
		tmp = t_1;
	} else if (a <= -2.8e-101) {
		tmp = 0.0 - (i * (y * j));
	} else if (a <= -1.12e-251) {
		tmp = t * (b * i);
	} else if (a <= 7.5e-14) {
		tmp = c * (z * (0.0 - b));
	} 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 <= (-1.2d-44)) then
        tmp = t_1
    else if (a <= (-2.8d-101)) then
        tmp = 0.0d0 - (i * (y * j))
    else if (a <= (-1.12d-251)) then
        tmp = t * (b * i)
    else if (a <= 7.5d-14) then
        tmp = c * (z * (0.0d0 - b))
    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 <= -1.2e-44) {
		tmp = t_1;
	} else if (a <= -2.8e-101) {
		tmp = 0.0 - (i * (y * j));
	} else if (a <= -1.12e-251) {
		tmp = t * (b * i);
	} else if (a <= 7.5e-14) {
		tmp = c * (z * (0.0 - b));
	} 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 <= -1.2e-44:
		tmp = t_1
	elif a <= -2.8e-101:
		tmp = 0.0 - (i * (y * j))
	elif a <= -1.12e-251:
		tmp = t * (b * i)
	elif a <= 7.5e-14:
		tmp = c * (z * (0.0 - b))
	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 <= -1.2e-44)
		tmp = t_1;
	elseif (a <= -2.8e-101)
		tmp = Float64(0.0 - Float64(i * Float64(y * j)));
	elseif (a <= -1.12e-251)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 7.5e-14)
		tmp = Float64(c * Float64(z * Float64(0.0 - b)));
	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 <= -1.2e-44)
		tmp = t_1;
	elseif (a <= -2.8e-101)
		tmp = 0.0 - (i * (y * j));
	elseif (a <= -1.12e-251)
		tmp = t * (b * i);
	elseif (a <= 7.5e-14)
		tmp = c * (z * (0.0 - b));
	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, -1.2e-44], t$95$1, If[LessEqual[a, -2.8e-101], N[(0.0 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e-251], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-14], N[(c * N[(z * N[(0.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.20000000000000004e-44 or 7.4999999999999996e-14 < a

   1. Initial program 63.6%

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

   3. Taylor expanded in a around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 57.0%

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

   5. Simplified 57.0%

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

   if -1.20000000000000004e-44 < a < -2.79999999999999989e-101

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. neg-sub0 N/A

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

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

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

      7. *-lowering-*.f64 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

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

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

      5. *-lowering-*.f64 51.2%

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

   8. Simplified 51.2%

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

   if -2.79999999999999989e-101 < a < -1.12000000000000007e-251

   1. Initial program 92.4%

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

   3. Taylor expanded in 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 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in a around 0

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

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

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

      2. *-lowering-*.f64 35.2%

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

   8. Simplified 35.2%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 42.1%

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

   10. Applied egg-rr 42.1%

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

   if -1.12000000000000007e-251 < a < 7.4999999999999996e-14

   1. Initial program 76.7%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

   5. Simplified 57.1%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 37.9%

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

   8. Simplified 37.9%

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

      1. sub0-neg N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 37.9%

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

   10. Applied egg-rr 37.9%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-101}:\\ \;\;\;\;0 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -5.8e+46)
     (- t_1 (* c (* z b)))
     (if (<= j 2.6e+89)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* 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 <= -5.8e+46) {
		tmp = t_1 - (c * (z * b));
	} else if (j <= 2.6e+89) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (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 <= (-5.8d+46)) then
        tmp = t_1 - (c * (z * b))
    else if (j <= 2.6d+89) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (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 <= -5.8e+46) {
		tmp = t_1 - (c * (z * b));
	} else if (j <= 2.6e+89) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (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 <= -5.8e+46:
		tmp = t_1 - (c * (z * b))
	elif j <= 2.6e+89:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (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 <= -5.8e+46)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (j <= 2.6e+89)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 + Float64(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 <= -5.8e+46)
		tmp = t_1 - (c * (z * b));
	elseif (j <= 2.6e+89)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (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, -5.8e+46], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+89], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.8000000000000004e46

   1. Initial program 80.3%

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

   3. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 80.8%

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

   5. Simplified 80.8%

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

   if -5.8000000000000004e46 < j < 2.6000000000000001e89

   1. Initial program 71.4%

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

   3. Taylor expanded in j around 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 67.5%

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

   5. Simplified 67.5%

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

   if 2.6000000000000001e89 < j

   1. Initial program 64.2%

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

   3. Taylor expanded in 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 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+87}:\\ \;\;\;\;t\_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -8e+87)
     (- t_1 (* c (* z b)))
     (if (<= j 4.9e+88)
       (+ (* x (- (* y z) (* t a))) (* c (- (* a j) (* z b))))
       (+ 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+87) {
		tmp = t_1 - (c * (z * b));
	} else if (j <= 4.9e+88) {
		tmp = (x * ((y * z) - (t * a))) + (c * ((a * j) - (z * b)));
	} 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+87)) then
        tmp = t_1 - (c * (z * b))
    else if (j <= 4.9d+88) then
        tmp = (x * ((y * z) - (t * a))) + (c * ((a * j) - (z * b)))
    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+87) {
		tmp = t_1 - (c * (z * b));
	} else if (j <= 4.9e+88) {
		tmp = (x * ((y * z) - (t * a))) + (c * ((a * j) - (z * b)));
	} 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+87:
		tmp = t_1 - (c * (z * b))
	elif j <= 4.9e+88:
		tmp = (x * ((y * z) - (t * a))) + (c * ((a * j) - (z * b)))
	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+87)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (j <= 4.9e+88)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	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+87)
		tmp = t_1 - (c * (z * b));
	elseif (j <= 4.9e+88)
		tmp = (x * ((y * z) - (t * a))) + (c * ((a * j) - (z * b)));
	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+87], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.9e+88], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.9999999999999997e87

   1. Initial program 77.0%

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

   3. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 83.1%

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

   5. Simplified 83.1%

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

   if -7.9999999999999997e87 < j < 4.9000000000000002e88

   1. Initial program 72.4%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if 4.9000000000000002e88 < j

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 74.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(b, t\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+233}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- 0.0 b)))))
   (if (<= c -1.95e+28)
     t_1
     (if (<= c -1.65e-83)
       (* i (* t b))
       (if (<= c 2.2e-148)
         (* z (* x y))
         (if (<= c 5.6e+233) (* j (* a 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 = c * (z * (0.0 - b));
	double tmp;
	if (c <= -1.95e+28) {
		tmp = t_1;
	} else if (c <= -1.65e-83) {
		tmp = i * (t * b);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else if (c <= 5.6e+233) {
		tmp = j * (a * 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 = c * (z * (0.0d0 - b))
    if (c <= (-1.95d+28)) then
        tmp = t_1
    else if (c <= (-1.65d-83)) then
        tmp = i * (t * b)
    else if (c <= 2.2d-148) then
        tmp = z * (x * y)
    else if (c <= 5.6d+233) then
        tmp = j * (a * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * (0.0 - b));
	double tmp;
	if (c <= -1.95e+28) {
		tmp = t_1;
	} else if (c <= -1.65e-83) {
		tmp = i * (t * b);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else if (c <= 5.6e+233) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * (0.0 - b))
	tmp = 0
	if c <= -1.95e+28:
		tmp = t_1
	elif c <= -1.65e-83:
		tmp = i * (t * b)
	elif c <= 2.2e-148:
		tmp = z * (x * y)
	elif c <= 5.6e+233:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(0.0 - b)))
	tmp = 0.0
	if (c <= -1.95e+28)
		tmp = t_1;
	elseif (c <= -1.65e-83)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 2.2e-148)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 5.6e+233)
		tmp = Float64(j * Float64(a * 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 = c * (z * (0.0 - b));
	tmp = 0.0;
	if (c <= -1.95e+28)
		tmp = t_1;
	elseif (c <= -1.65e-83)
		tmp = i * (t * b);
	elseif (c <= 2.2e-148)
		tmp = z * (x * y);
	elseif (c <= 5.6e+233)
		tmp = j * (a * 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[(c * N[(z * N[(0.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.95e+28], t$95$1, If[LessEqual[c, -1.65e-83], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-148], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e+233], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.9499999999999999e28 or 5.60000000000000021e233 < c

   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 i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{b \cdot \left(c \cdot z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(b \cdot c\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(c \cdot b\right) \cdot z\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{0 - c \cdot \left(b \cdot z\right)} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(c \cdot \left(b \cdot z\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(c \cdot \left(b \cdot z\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \left(b \cdot z\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \left(z \cdot b\right)\right)\right) \]

      5. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(z, b\right)\right)\right) \]

   10. Applied egg-rr 42.4%

       \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

   if -1.9499999999999999e28 < c < -1.65e-83

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 57.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   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 33.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   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. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot b\right), i\right) \]

      5. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), i\right) \]

   10. Applied egg-rr 37.5%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if -1.65e-83 < c < 2.20000000000000017e-148

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      4. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if 2.20000000000000017e-148 < c < 5.60000000000000021e233

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 44.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 30.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 30.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 39.4%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+233}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-50}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6e-50)
   (* (- (/ (* x y) b) c) (* z b))
   (if (<= z 3.2e-173)
     (* j (- (* a c) (* y i)))
     (if (<= z 3.6e+94)
       (* a (* t (- (/ (* c j) t) x)))
       (* z (- (* x y) (* b 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 <= -6e-50) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 3.2e-173) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.6e+94) {
		tmp = a * (t * (((c * j) / t) - x));
	} else {
		tmp = z * ((x * y) - (b * 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 <= (-6d-50)) then
        tmp = (((x * y) / b) - c) * (z * b)
    else if (z <= 3.2d-173) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 3.6d+94) then
        tmp = a * (t * (((c * j) / t) - x))
    else
        tmp = z * ((x * y) - (b * 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 <= -6e-50) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 3.2e-173) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 3.6e+94) {
		tmp = a * (t * (((c * j) / t) - x));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6e-50:
		tmp = (((x * y) / b) - c) * (z * b)
	elif z <= 3.2e-173:
		tmp = j * ((a * c) - (y * i))
	elif z <= 3.6e+94:
		tmp = a * (t * (((c * j) / t) - x))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6e-50)
		tmp = Float64(Float64(Float64(Float64(x * y) / b) - c) * Float64(z * b));
	elseif (z <= 3.2e-173)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 3.6e+94)
		tmp = Float64(a * Float64(t * Float64(Float64(Float64(c * j) / t) - x)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6e-50)
		tmp = (((x * y) / b) - c) * (z * b);
	elseif (z <= 3.2e-173)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 3.6e+94)
		tmp = a * (t * (((c * j) / t) - x));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6e-50], N[(N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-173], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+94], N[(a * N[(t * N[(N[(N[(c * j), $MachinePrecision] / t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.99999999999999981e-50

   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 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 58.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(\left(a \cdot c - i \cdot y\right) \cdot \frac{j}{b} + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - c \cdot z\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{x \cdot y}{b} - c\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\left(\frac{x \cdot y}{b} - c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot z\right), \color{blue}{\left(\frac{x \cdot y}{b} - c\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot b\right), \left(\color{blue}{\frac{x \cdot y}{b}} - c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \left(\color{blue}{\frac{x \cdot y}{b}} - c\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{b}\right), \color{blue}{c}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), b\right), c\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(y \cdot x\right), b\right), c\right)\right) \]

      8. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), b\right), c\right)\right) \]

   8. Simplified 64.5%

      \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot \left(\frac{y \cdot x}{b} - c\right)} \]

   if -5.99999999999999981e-50 < z < 3.2e-173

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.4%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if 3.2e-173 < z < 3.59999999999999992e94

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 52.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{c \cdot j}{t} - x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{c \cdot j}{t}\right), \color{blue}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(c \cdot j\right), t\right), x\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(j \cdot c\right), t\right), x\right)\right)\right) \]

      5. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(j, c\right), t\right), x\right)\right)\right) \]

   8. Simplified 58.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(\frac{j \cdot c}{t} - x\right)\right)} \]

   if 3.59999999999999992e94 < z

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 70.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-50}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.95e-49)
     t_1
     (if (<= z 1.25e-173)
       (* j (- (* a c) (* y i)))
       (if (<= z 1.45e+94) (* a (* t (- (/ (* c j) t) x))) 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.95e-49) {
		tmp = t_1;
	} else if (z <= 1.25e-173) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.45e+94) {
		tmp = a * (t * (((c * j) / t) - x));
	} 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 = z * ((x * y) - (b * c))
    if (z <= (-1.95d-49)) then
        tmp = t_1
    else if (z <= 1.25d-173) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 1.45d+94) then
        tmp = a * (t * (((c * j) / t) - x))
    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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.95e-49) {
		tmp = t_1;
	} else if (z <= 1.25e-173) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.45e+94) {
		tmp = a * (t * (((c * j) / t) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.95e-49:
		tmp = t_1
	elif z <= 1.25e-173:
		tmp = j * ((a * c) - (y * i))
	elif z <= 1.45e+94:
		tmp = a * (t * (((c * j) / t) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.95e-49)
		tmp = t_1;
	elseif (z <= 1.25e-173)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 1.45e+94)
		tmp = Float64(a * Float64(t * Float64(Float64(Float64(c * j) / t) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.95e-49)
		tmp = t_1;
	elseif (z <= 1.25e-173)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 1.45e+94)
		tmp = a * (t * (((c * j) / t) - x));
	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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-49], t$95$1, If[LessEqual[z, 1.25e-173], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+94], N[(a * N[(t * N[(N[(N[(c * j), $MachinePrecision] / t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000006e-49 or 1.4499999999999999e94 < z

   1. Initial program 59.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 62.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 62.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   if -1.95000000000000006e-49 < z < 1.2500000000000001e-173

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.4%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if 1.2500000000000001e-173 < z < 1.4499999999999999e94

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 52.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{c \cdot j}{t} - x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{c \cdot j}{t}\right), \color{blue}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(c \cdot j\right), t\right), x\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(j \cdot c\right), t\right), x\right)\right)\right) \]

      5. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(j, c\right), t\right), x\right)\right)\right) \]

   8. Simplified 58.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(\frac{j \cdot c}{t} - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(t \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -4.9e-26)
   (* (- (/ (* x y) b) c) (* z b))
   (if (<= z 2.95e+95)
     (+ (* j (- (* a c) (* y i))) (* i (* t b)))
     (* z (- (* x y) (* b 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 <= -4.9e-26) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 2.95e+95) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * ((x * y) - (b * 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 <= (-4.9d-26)) then
        tmp = (((x * y) / b) - c) * (z * b)
    else if (z <= 2.95d+95) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else
        tmp = z * ((x * y) - (b * 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 <= -4.9e-26) {
		tmp = (((x * y) / b) - c) * (z * b);
	} else if (z <= 2.95e+95) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -4.9e-26:
		tmp = (((x * y) / b) - c) * (z * b)
	elif z <= 2.95e+95:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -4.9e-26)
		tmp = Float64(Float64(Float64(Float64(x * y) / b) - c) * Float64(z * b));
	elseif (z <= 2.95e+95)
		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 * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -4.9e-26)
		tmp = (((x * y) / b) - c) * (z * b);
	elseif (z <= 2.95e+95)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -4.9e-26], N[(N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+95], 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 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8999999999999999e-26

   1. Initial program 56.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(i \cdot t + \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)\right) - c \cdot z\right)} \]
   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 57.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t + \left(\left(a \cdot c - i \cdot y\right) \cdot \frac{j}{b} + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - c \cdot z\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{x \cdot y}{b} - c\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\left(\frac{x \cdot y}{b} - c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot z\right), \color{blue}{\left(\frac{x \cdot y}{b} - c\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot b\right), \left(\color{blue}{\frac{x \cdot y}{b}} - c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \left(\color{blue}{\frac{x \cdot y}{b}} - c\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{b}\right), \color{blue}{c}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), b\right), c\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(y \cdot x\right), b\right), c\right)\right) \]

      8. *-lowering-*.f64 66.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, b\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), b\right), c\right)\right) \]

   8. Simplified 66.6%

      \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot \left(\frac{y \cdot x}{b} - c\right)} \]

   if -4.8999999999999999e-26 < z < 2.95000000000000002e95

   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 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 61.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(b, t\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 2.95000000000000002e95 < z

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 70.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;\left(\frac{x \cdot y}{b} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.65e-15)
   (* a (- (* c j) (* x t)))
   (if (<= t -3.45e-217)
     (* c (- (* a j) (* z b)))
     (if (<= t 1.6e+108)
       (* z (- (* x y) (* b c)))
       (* 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 <= -1.65e-15) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= -3.45e-217) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.6e+108) {
		tmp = z * ((x * y) - (b * c));
	} 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 <= (-1.65d-15)) then
        tmp = a * ((c * j) - (x * t))
    else if (t <= (-3.45d-217)) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.6d+108) then
        tmp = z * ((x * y) - (b * c))
    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 <= -1.65e-15) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= -3.45e-217) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.6e+108) {
		tmp = z * ((x * y) - (b * c));
	} 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 <= -1.65e-15:
		tmp = a * ((c * j) - (x * t))
	elif t <= -3.45e-217:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.6e+108:
		tmp = z * ((x * y) - (b * c))
	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 <= -1.65e-15)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (t <= -3.45e-217)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.6e+108)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	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 <= -1.65e-15)
		tmp = a * ((c * j) - (x * t));
	elseif (t <= -3.45e-217)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.6e+108)
		tmp = z * ((x * y) - (b * c));
	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, -1.65e-15], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.45e-217], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+108], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65e-15

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 60.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 60.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -1.65e-15 < t < -3.44999999999999987e-217

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(a \cdot j - b \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 57.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if -3.44999999999999987e-217 < t < 1.6e108

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 54.5%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 54.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   if 1.6e108 < t

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 76.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(x \cdot t\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x\right) \cdot t + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + 1 \cdot \left(\color{blue}{b} \cdot \left(i \cdot t\right)\right) \]

      8. *-lft-identity N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + b \cdot \color{blue}{\left(i \cdot t\right)} \]

      9. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + \left(b \cdot i\right) \cdot \color{blue}{t} \]

      10. distribute-rgt-in N/A

          \[\leadsto t \cdot \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + b \cdot i\right)} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + b \cdot i\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{\left(\mathsf{neg}\left(a \cdot x\right)\right)}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \left(x \cdot \color{blue}{a}\right)\right)\right) \]

      17. *-lowering-*.f64 76.9%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 76.9%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.8e-18)
     t_1
     (if (<= x 1.1e-179)
       (* c (- (* a j) (* z b)))
       (if (<= x 1.85e+33) (* 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.8e-18) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 1.85e+33) {
		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 = x * ((y * z) - (t * a))
    if (x <= (-1.8d-18)) then
        tmp = t_1
    else if (x <= 1.1d-179) then
        tmp = c * ((a * j) - (z * b))
    else if (x <= 1.85d+33) 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.8e-18) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 1.85e+33) {
		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 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.8e-18:
		tmp = t_1
	elif x <= 1.1e-179:
		tmp = c * ((a * j) - (z * b))
	elif x <= 1.85e+33:
		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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.8e-18)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (x <= 1.85e+33)
		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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.8e-18)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = c * ((a * j) - (z * b));
	elseif (x <= 1.85e+33)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-18], t$95$1, If[LessEqual[x, 1.1e-179], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+33], 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 x < -1.80000000000000005e-18 or 1.8499999999999999e33 < x

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 60.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -1.80000000000000005e-18 < x < 1.10000000000000002e-179

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 51.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if 1.10000000000000002e-179 < x < 1.8499999999999999e33

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 75.3%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 75.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-83}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -1.15e+27)
     t_1
     (if (<= c -3.5e-83)
       (* i (* t b))
       (if (<= c 2.2e-148) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -1.15e+27) {
		tmp = t_1;
	} else if (c <= -3.5e-83) {
		tmp = i * (t * b);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (c <= (-1.15d+27)) then
        tmp = t_1
    else if (c <= (-3.5d-83)) then
        tmp = i * (t * b)
    else if (c <= 2.2d-148) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -1.15e+27) {
		tmp = t_1;
	} else if (c <= -3.5e-83) {
		tmp = i * (t * b);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -1.15e+27:
		tmp = t_1
	elif c <= -3.5e-83:
		tmp = i * (t * b)
	elif c <= 2.2e-148:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (c <= -1.15e+27)
		tmp = t_1;
	elseif (c <= -3.5e-83)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 2.2e-148)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (c <= -1.15e+27)
		tmp = t_1;
	elseif (c <= -3.5e-83)
		tmp = i * (t * b);
	elseif (c <= 2.2e-148)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+27], t$95$1, If[LessEqual[c, -3.5e-83], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-148], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.15e27 or 2.20000000000000017e-148 < c

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 41.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 41.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 31.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 31.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 36.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 36.1%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -1.15e27 < c < -3.5000000000000003e-83

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 59.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 59.4%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   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 35.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   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. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot b\right), i\right) \]

      5. *-lowering-*.f64 38.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, b\right), i\right) \]

   10. Applied egg-rr 38.9%

       \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

   if -3.5000000000000003e-83 < c < 2.20000000000000017e-148

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      4. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-83}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -1.9e-48)
     t_1
     (if (<= c -1.65e-83)
       (* t (* b i))
       (if (<= c 2.2e-148) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -1.9e-48) {
		tmp = t_1;
	} else if (c <= -1.65e-83) {
		tmp = t * (b * i);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (c <= (-1.9d-48)) then
        tmp = t_1
    else if (c <= (-1.65d-83)) then
        tmp = t * (b * i)
    else if (c <= 2.2d-148) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -1.9e-48) {
		tmp = t_1;
	} else if (c <= -1.65e-83) {
		tmp = t * (b * i);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -1.9e-48:
		tmp = t_1
	elif c <= -1.65e-83:
		tmp = t * (b * i)
	elif c <= 2.2e-148:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (c <= -1.9e-48)
		tmp = t_1;
	elseif (c <= -1.65e-83)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 2.2e-148)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (c <= -1.9e-48)
		tmp = t_1;
	elseif (c <= -1.65e-83)
		tmp = t * (b * i);
	elseif (c <= 2.2e-148)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e-48], t$95$1, If[LessEqual[c, -1.65e-83], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-148], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.90000000000000001e-48 or 2.20000000000000017e-148 < c

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 31.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 35.6%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -1.90000000000000001e-48 < c < -1.65e-83

   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 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 69.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 47.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot i\right) \cdot \color{blue}{t} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot i\right), \color{blue}{t}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(i \cdot b\right), t\right) \]

      4. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, b\right), t\right) \]

   10. Applied egg-rr 47.4%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} \]

   if -1.65e-83 < c < 2.20000000000000017e-148

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      4. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -3e-48)
     t_1
     (if (<= c -2.55e-83)
       (* b (* t i))
       (if (<= c 2.2e-148) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -3e-48) {
		tmp = t_1;
	} else if (c <= -2.55e-83) {
		tmp = b * (t * i);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (c <= (-3d-48)) then
        tmp = t_1
    else if (c <= (-2.55d-83)) then
        tmp = b * (t * i)
    else if (c <= 2.2d-148) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (c <= -3e-48) {
		tmp = t_1;
	} else if (c <= -2.55e-83) {
		tmp = b * (t * i);
	} else if (c <= 2.2e-148) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -3e-48:
		tmp = t_1
	elif c <= -2.55e-83:
		tmp = b * (t * i)
	elif c <= 2.2e-148:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (c <= -3e-48)
		tmp = t_1;
	elseif (c <= -2.55e-83)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 2.2e-148)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (c <= -3e-48)
		tmp = t_1;
	elseif (c <= -2.55e-83)
		tmp = b * (t * i);
	elseif (c <= 2.2e-148)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e-48], t$95$1, If[LessEqual[c, -2.55e-83], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-148], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9999999999999999e-48 or 2.20000000000000017e-148 < c

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 31.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \left(c \cdot \color{blue}{j}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(a \cdot c\right) \cdot \color{blue}{j} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot c\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, c\right), j\right) \]

   10. Applied egg-rr 35.6%

       \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -2.9999999999999999e-48 < c < -2.55000000000000018e-83

   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 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 69.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 47.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -2.55000000000000018e-83 < c < 2.20000000000000017e-148

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      4. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -1.52e+184)
     t_1
     (if (<= t -1.8e-258)
       (* a (* c j))
       (if (<= t 1.1e+169) (* z (* x y)) 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 <= -1.52e+184) {
		tmp = t_1;
	} else if (t <= -1.8e-258) {
		tmp = a * (c * j);
	} else if (t <= 1.1e+169) {
		tmp = z * (x * y);
	} 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 <= (-1.52d+184)) then
        tmp = t_1
    else if (t <= (-1.8d-258)) then
        tmp = a * (c * j)
    else if (t <= 1.1d+169) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -1.52e+184) {
		tmp = t_1;
	} else if (t <= -1.8e-258) {
		tmp = a * (c * j);
	} else if (t <= 1.1e+169) {
		tmp = z * (x * y);
	} 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 <= -1.52e+184:
		tmp = t_1
	elif t <= -1.8e-258:
		tmp = a * (c * j)
	elif t <= 1.1e+169:
		tmp = z * (x * y)
	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 <= -1.52e+184)
		tmp = t_1;
	elseif (t <= -1.8e-258)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 1.1e+169)
		tmp = Float64(z * Float64(x * y));
	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 <= -1.52e+184)
		tmp = t_1;
	elseif (t <= -1.8e-258)
		tmp = a * (c * j);
	elseif (t <= 1.1e+169)
		tmp = z * (x * y);
	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, -1.52e+184], t$95$1, If[LessEqual[t, -1.8e-258], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+169], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.52e184 or 1.1e169 < t

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 78.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   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 48.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.52e184 < t < -1.79999999999999989e-258

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 46.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -1.79999999999999989e-258 < t < 1.1e169

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right) + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(j \cdot c\right) + \left(\mathsf{neg}\left(b \cdot \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\mathsf{neg}\left(\color{blue}{b \cdot \left(c \cdot z\right)}\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot b\right) \cdot \left(z \cdot \color{blue}{c}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(\left(-1 \cdot b\right) \cdot z\right) \cdot \color{blue}{c}\right) \]

      10. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j - \color{blue}{b \cdot z}\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(y \cdot z - a \cdot t\right)\right), \color{blue}{\left(c \cdot \left(a \cdot j - b \cdot z\right)\right)}\right) \]

   5. Simplified 64.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(j \cdot a - b \cdot z\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      4. *-lowering-*.f64 31.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 31.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -2.85e+184)
     t_1
     (if (<= t -8e-255) (* a (* c j)) (if (<= t 9.5e-15) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -2.85e+184) {
		tmp = t_1;
	} else if (t <= -8e-255) {
		tmp = a * (c * j);
	} else if (t <= 9.5e-15) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (t <= (-2.85d+184)) then
        tmp = t_1
    else if (t <= (-8d-255)) then
        tmp = a * (c * j)
    else if (t <= 9.5d-15) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -2.85e+184) {
		tmp = t_1;
	} else if (t <= -8e-255) {
		tmp = a * (c * j);
	} else if (t <= 9.5e-15) {
		tmp = x * (y * z);
	} 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 <= -2.85e+184:
		tmp = t_1
	elif t <= -8e-255:
		tmp = a * (c * j)
	elif t <= 9.5e-15:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -2.85e+184)
		tmp = t_1;
	elseif (t <= -8e-255)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 9.5e-15)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (t <= -2.85e+184)
		tmp = t_1;
	elseif (t <= -8e-255)
		tmp = a * (c * j);
	elseif (t <= 9.5e-15)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.85e+184], t$95$1, If[LessEqual[t, -8e-255], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-15], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.85000000000000008e184 or 9.5000000000000005e-15 < t

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 63.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 39.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 39.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -2.85000000000000008e184 < t < -8.0000000000000001e-255

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 46.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -8.0000000000000001e-255 < t < 9.5000000000000005e-15

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 37.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 33.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 33.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 48.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.2e-15)
   (* a (- (* c j) (* x t)))
   (if (<= t 4.6e+18) (* c (- (* a j) (* z b))) (* 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 <= -4.2e-15) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= 4.6e+18) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= (-4.2d-15)) then
        tmp = a * ((c * j) - (x * t))
    else if (t <= 4.6d+18) then
        tmp = c * ((a * j) - (z * b))
    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 <= -4.2e-15) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= 4.6e+18) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= -4.2e-15:
		tmp = a * ((c * j) - (x * t))
	elif t <= 4.6e+18:
		tmp = c * ((a * j) - (z * b))
	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 <= -4.2e-15)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (t <= 4.6e+18)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 <= -4.2e-15)
		tmp = a * ((c * j) - (x * t));
	elseif (t <= 4.6e+18)
		tmp = c * ((a * j) - (z * b));
	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, -4.2e-15], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+18], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999962e-15

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 60.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 60.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -4.19999999999999962e-15 < t < 4.6e18

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   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 50.2%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if 4.6e18 < t

   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 t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot -1\right) \cdot \color{blue}{\left(a \cdot x - b \cdot i\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{a \cdot x} - b \cdot i\right) \]

      4. *-commutative N/A

         \[\leadsto \left(a \cdot x - b \cdot i\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 64.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 64.5%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \left(a \cdot x - i \cdot b\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot x - i \cdot b\right) \cdot t\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot x - i \cdot b\right) \cdot t\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot x - i \cdot b\right), t\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), t\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), t\right)\right) \]

      8. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(b, i\right)\right), t\right)\right) \]

   7. Applied egg-rr 64.5%

      \[\leadsto \color{blue}{-\left(a \cdot x - b \cdot i\right) \cdot t} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(t \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \left(x \cdot t\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot x\right) \cdot t + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right) \cdot \left(b \cdot \left(i \cdot t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + 1 \cdot \left(\color{blue}{b} \cdot \left(i \cdot t\right)\right) \]

      8. *-lft-identity N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + b \cdot \color{blue}{\left(i \cdot t\right)} \]

      9. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(a \cdot x\right)\right) \cdot t + \left(b \cdot i\right) \cdot \color{blue}{t} \]

      10. distribute-rgt-in N/A

          \[\leadsto t \cdot \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + b \cdot i\right)} \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot x\right)\right) + b \cdot i\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{\left(\mathsf{neg}\left(a \cdot x\right)\right)}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \left(x \cdot \color{blue}{a}\right)\right)\right) \]

      17. *-lowering-*.f64 64.5%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, i\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 64.5%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.7e+146)
     t_1
     (if (<= a 7.2e-14) (* 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 <= -2.7e+146) {
		tmp = t_1;
	} else if (a <= 7.2e-14) {
		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 <= (-2.7d+146)) then
        tmp = t_1
    else if (a <= 7.2d-14) 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 <= -2.7e+146) {
		tmp = t_1;
	} else if (a <= 7.2e-14) {
		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 <= -2.7e+146:
		tmp = t_1
	elif a <= 7.2e-14:
		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 <= -2.7e+146)
		tmp = t_1;
	elseif (a <= 7.2e-14)
		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 <= -2.7e+146)
		tmp = t_1;
	elseif (a <= 7.2e-14)
		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, -2.7e+146], t$95$1, If[LessEqual[a, 7.2e-14], 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 < -2.69999999999999989e146 or 7.1999999999999996e-14 < a

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 62.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -2.69999999999999989e146 < a < 7.1999999999999996e-14

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   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 50.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.00019:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -1.52e+184) t_1 (if (<= t 0.00019) (* 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 <= -1.52e+184) {
		tmp = t_1;
	} else if (t <= 0.00019) {
		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 <= (-1.52d+184)) then
        tmp = t_1
    else if (t <= 0.00019d0) 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 <= -1.52e+184) {
		tmp = t_1;
	} else if (t <= 0.00019) {
		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 <= -1.52e+184:
		tmp = t_1
	elif t <= 0.00019:
		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 <= -1.52e+184)
		tmp = t_1;
	elseif (t <= 0.00019)
		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 <= -1.52e+184)
		tmp = t_1;
	elseif (t <= 0.00019)
		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, -1.52e+184], t$95$1, If[LessEqual[t, 0.00019], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.52e184 or 1.9000000000000001e-4 < t

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 65.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 65.6%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(i, \color{blue}{t}\right)\right) \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.52e184 < t < 1.9000000000000001e-4

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 37.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 37.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 28.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 28.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 0.00019:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.7% 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 71.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
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 38.4%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

5. Simplified 38.4%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 21.9%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

8. Simplified 21.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

9. Final simplification 21.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.4% 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 2024158 
(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)))))