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

Percentage Accurate: 73.8% → 82.3%

Time: 17.5s

Alternatives: 19

Speedup: 0.7×

• 58.3% 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: 73.8% 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: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 33.3%

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

   6. Taylor expanded in c around -inf

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

   8. Simplified 49.1%

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

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(b \cdot \left(z + -1 \cdot \frac{i \cdot t}{c}\right)\right)}, \mathsf{\_.f64}\left(0, c\right)\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(z + -1 \cdot \frac{i \cdot t}{c}\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, c\right)\right) \]

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 57.5%

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

   11. Simplified 57.5%

       \[\leadsto \color{blue}{\left(b \cdot \left(z - \frac{t \cdot i}{c}\right)\right)} \cdot \left(0 - c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.0%

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

Alternative 2: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) - z \cdot \left(y \cdot \left(\frac{b \cdot c}{y} - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -8.2e+68)
   (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
   (if (<= z 2.6e+249)
     (+
      (* a (- (* c j) (* x t)))
      (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c)))))
     (- (* j (* a c)) (* z (* y (- (/ (* b c) y) x)))))))

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 <= -8.2e+68) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (z <= 2.6e+249) {
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	} else {
		tmp = (j * (a * c)) - (z * (y * (((b * c) / y) - x)));
	}
	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 <= (-8.2d+68)) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else if (z <= 2.6d+249) then
        tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))))
    else
        tmp = (j * (a * c)) - (z * (y * (((b * c) / y) - x)))
    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 <= -8.2e+68) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (z <= 2.6e+249) {
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	} else {
		tmp = (j * (a * c)) - (z * (y * (((b * c) / y) - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -8.2e+68:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	elif z <= 2.6e+249:
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))))
	else:
		tmp = (j * (a * c)) - (z * (y * (((b * c) / y) - x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -8.2e+68)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (z <= 2.6e+249)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))));
	else
		tmp = Float64(Float64(j * Float64(a * c)) - Float64(z * Float64(y * Float64(Float64(Float64(b * c) / y) - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -8.2e+68)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	elseif (z <= 2.6e+249)
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	else
		tmp = (j * (a * c)) - (z * (y * (((b * c) / y) - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -8.2e+68], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+249], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.1999999999999998e68

   1. Initial program 65.4%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 73.7%

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

   5. Simplified 73.7%

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

   if -8.1999999999999998e68 < z < 2.60000000000000019e249

   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 y around 0

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

   5. Simplified 80.8%

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

   if 2.60000000000000019e249 < z

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 88.3%

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

   8. Simplified 88.3%

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

   9. Taylor expanded in y around inf

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

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

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

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 94.3%

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

   11. Simplified 94.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) - z \cdot \left(y \cdot \left(\frac{b \cdot c}{y} - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+141}:\\ \;\;\;\;t\_2 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= t -6.5e+193)
     (+ t_2 t_1)
     (if (<= t -8e+35)
       (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
       (if (<= t 1.35e+141) (+ t_2 (* z (- (* x y) (* b c)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (t <= -6.5e+193) {
		tmp = t_2 + t_1;
	} else if (t <= -8e+35) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (t <= 1.35e+141) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = j * ((a * c) - (y * i))
    if (t <= (-6.5d+193)) then
        tmp = t_2 + t_1
    else if (t <= (-8d+35)) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else if (t <= 1.35d+141) then
        tmp = t_2 + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (t <= -6.5e+193) {
		tmp = t_2 + t_1;
	} else if (t <= -8e+35) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (t <= 1.35e+141) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if t <= -6.5e+193:
		tmp = t_2 + t_1
	elif t <= -8e+35:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	elif t <= 1.35e+141:
		tmp = t_2 + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (t <= -6.5e+193)
		tmp = Float64(t_2 + t_1);
	elseif (t <= -8e+35)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t <= 1.35e+141)
		tmp = Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (t <= -6.5e+193)
		tmp = t_2 + t_1;
	elseif (t <= -8e+35)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	elseif (t <= 1.35e+141)
		tmp = t_2 + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+193], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[t, -8e+35], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+141], N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.4999999999999997e193

   1. Initial program 60.7%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. *-lft-identity N/A

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

      11. metadata-eval N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

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

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

   5. Simplified 77.9%

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

   if -6.4999999999999997e193 < t < -7.9999999999999997e35

   1. Initial program 65.5%

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

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

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

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

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

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

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-commutative N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 76.2%

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

   5. Simplified 76.2%

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

   if -7.9999999999999997e35 < t < 1.35e141

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.3%

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

   5. Simplified 76.3%

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

   if 1.35e141 < t

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 76.2%

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

   5. Simplified 76.2%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+193}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+36}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -9e+193)
     (+ t_2 t_1)
     (if (<= t -7.6e+36)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= t 1.3e+144)
         (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
         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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9e+193) {
		tmp = t_2 + t_1;
	} else if (t <= -7.6e+36) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (t <= 1.3e+144) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} 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 = t * ((b * i) - (x * a))
    if (t <= (-9d+193)) then
        tmp = t_2 + t_1
    else if (t <= (-7.6d+36)) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (t <= 1.3d+144) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9e+193) {
		tmp = t_2 + t_1;
	} else if (t <= -7.6e+36) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (t <= 1.3e+144) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} 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 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -9e+193:
		tmp = t_2 + t_1
	elif t <= -7.6e+36:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif t <= 1.3e+144:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	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(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -9e+193)
		tmp = Float64(t_2 + t_1);
	elseif (t <= -7.6e+36)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t <= 1.3e+144)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	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 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -9e+193)
		tmp = t_2 + t_1;
	elseif (t <= -7.6e+36)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (t <= 1.3e+144)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+193], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[t, -7.6e+36], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+144], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.99999999999999999e193

   1. Initial program 60.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 48.0%

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

   6. Taylor expanded in c around -inf

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

   8. Simplified 70.6%

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

   9. Taylor expanded in c around 0

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

       1. +-commutative N/A

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

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

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

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

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

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

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

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

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

       7. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

       13. *-lowering-*.f64 77.6%

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

   11. Simplified 77.6%

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

   if -8.99999999999999999e193 < t < -7.6000000000000005e36

   1. Initial program 65.5%

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

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

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-in N/A

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

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

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

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

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-commutative N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 76.2%

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

   5. Simplified 76.2%

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

   if -7.6000000000000005e36 < t < 1.2999999999999999e144

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.3%

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

   5. Simplified 76.3%

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

   if 1.2999999999999999e144 < t

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 76.2%

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

   5. Simplified 76.2%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(\frac{b \cdot i}{x} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.06e+183)
   (* t (- (* b i) (* x a)))
   (if (<= t -2.9e-148)
     (- (* j (- (* a c) (* y i))) (* c (* z b)))
     (if (<= t 2.15e+49)
       (+ (* z (- (* x y) (* b c))) (* j (* a c)))
       (* (* x 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 <= -1.06e+183) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -2.9e-148) {
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	} else if (t <= 2.15e+49) {
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	} else {
		tmp = (x * 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 <= (-1.06d+183)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= (-2.9d-148)) then
        tmp = (j * ((a * c) - (y * i))) - (c * (z * b))
    else if (t <= 2.15d+49) then
        tmp = (z * ((x * y) - (b * c))) + (j * (a * c))
    else
        tmp = (x * 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 <= -1.06e+183) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -2.9e-148) {
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	} else if (t <= 2.15e+49) {
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	} else {
		tmp = (x * t) * (((b * i) / x) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.06e+183:
		tmp = t * ((b * i) - (x * a))
	elif t <= -2.9e-148:
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b))
	elif t <= 2.15e+49:
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c))
	else:
		tmp = (x * t) * (((b * i) / x) - a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.06e+183)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= -2.9e-148)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(c * Float64(z * b)));
	elseif (t <= 2.15e+49)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(a * c)));
	else
		tmp = Float64(Float64(x * t) * Float64(Float64(Float64(b * i) / 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 <= -1.06e+183)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= -2.9e-148)
		tmp = (j * ((a * c) - (y * i))) - (c * (z * b));
	elseif (t <= 2.15e+49)
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	else
		tmp = (x * t) * (((b * i) / x) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.06e+183], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-148], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+49], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * N[(N[(N[(b * i), $MachinePrecision] / x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.06e183

   1. Initial program 62.6%

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

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

   if -1.06e183 < t < -2.8999999999999998e-148

   1. Initial program 74.4%

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

   3. Taylor expanded in 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. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

      8. *-lowering-*.f64 64.3%

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

   5. Simplified 64.3%

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

   if -2.8999999999999998e-148 < t < 2.15e49

   1. Initial program 81.2%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 72.0%

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

   8. Simplified 72.0%

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

   if 2.15e49 < t

   1. Initial program 60.8%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 73.0%

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

   6. Taylor expanded in c around -inf

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

   8. Simplified 60.9%

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

   9. Taylor expanded in x around inf

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

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. unsub-neg N/A

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

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

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

   11. Simplified 48.6%

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

   12. Taylor expanded in t around -inf

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

       1. associate-*r* N/A

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

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

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

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

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

       4. +-commutative N/A

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

       5. mul-1-neg N/A

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

       6. unsub-neg N/A

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

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

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

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

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

       9. *-commutative N/A

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

       10. *-lowering-*.f64 66.8%

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

   14. Simplified 66.8%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(\frac{b \cdot i}{x} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -4.8e+35)
     (+ t_1 (* y (- (* x z) (* i j))))
     (if (<= t 1.2e+139)
       (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.8e+35) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else if (t <= 1.2e+139) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-4.8d+35)) then
        tmp = t_1 + (y * ((x * z) - (i * j)))
    else if (t <= 1.2d+139) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.8e+35) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else if (t <= 1.2e+139) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -4.8e+35:
		tmp = t_1 + (y * ((x * z) - (i * j)))
	elif t <= 1.2e+139:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.8e+35)
		tmp = Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (t <= 1.2e+139)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -4.8e+35)
		tmp = t_1 + (y * ((x * z) - (i * j)));
	elseif (t <= 1.2e+139)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+35], N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+139], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000029e35

   1. Initial program 62.8%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 59.7%

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

   6. Taylor expanded in c around -inf

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

   8. Simplified 65.9%

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

   9. Taylor expanded in c around 0

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

       1. +-commutative N/A

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

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

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

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

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

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

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

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

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

       7. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

       13. *-lowering-*.f64 70.2%

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

   11. Simplified 70.2%

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

   if -4.80000000000000029e35 < t < 1.20000000000000004e139

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.3%

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

   5. Simplified 76.3%

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

   if 1.20000000000000004e139 < t

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 76.2%

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

   5. Simplified 76.2%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -4e+65)
     t_1
     (if (<= t 2e+144)
       (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4e+65) {
		tmp = t_1;
	} else if (t <= 2e+144) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-4d+65)) then
        tmp = t_1
    else if (t <= 2d+144) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4e+65) {
		tmp = t_1;
	} else if (t <= 2e+144) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -4e+65:
		tmp = t_1
	elif t <= 2e+144:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4e+65)
		tmp = t_1;
	elseif (t <= 2e+144)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -4e+65)
		tmp = t_1;
	elseif (t <= 2e+144)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+65], t$95$1, If[LessEqual[t, 2e+144], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4e65 or 2.00000000000000005e144 < t

   1. Initial program 63.2%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

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

      12. --lowering--.f64 69.7%

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

   5. Simplified 69.7%

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

   if -4e65 < t < 2.00000000000000005e144

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1.9e+72)
     t_1
     (if (<= b 1.1e+114)
       (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.9e+72) {
		tmp = t_1;
	} else if (b <= 1.1e+114) {
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-1.9d+72)) then
        tmp = t_1
    else if (b <= 1.1d+114) then
        tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.9e+72) {
		tmp = t_1;
	} else if (b <= 1.1e+114) {
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.9e+72:
		tmp = t_1
	elif b <= 1.1e+114:
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.9e+72)
		tmp = t_1;
	elseif (b <= 1.1e+114)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.9e+72)
		tmp = t_1;
	elseif (b <= 1.1e+114)
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+72], t$95$1, If[LessEqual[b, 1.1e+114], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.90000000000000003e72 or 1.1e114 < b

   1. Initial program 68.2%

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

   3. Taylor expanded in 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 76.4%

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

   5. Simplified 76.4%

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

   if -1.90000000000000003e72 < b < 1.1e114

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 73.0%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(\frac{b \cdot i}{x} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5e+64)
   (* t (- (* b i) (* x a)))
   (if (<= t 1.4e+49)
     (+ (* z (- (* x y) (* b c))) (* j (* a c)))
     (* (* x 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 <= -5e+64) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 1.4e+49) {
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	} else {
		tmp = (x * 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 <= (-5d+64)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= 1.4d+49) then
        tmp = (z * ((x * y) - (b * c))) + (j * (a * c))
    else
        tmp = (x * 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 <= -5e+64) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 1.4e+49) {
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	} else {
		tmp = (x * t) * (((b * i) / x) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5e+64:
		tmp = t * ((b * i) - (x * a))
	elif t <= 1.4e+49:
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c))
	else:
		tmp = (x * t) * (((b * i) / x) - a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5e+64)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= 1.4e+49)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(a * c)));
	else
		tmp = Float64(Float64(x * t) * Float64(Float64(Float64(b * i) / 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 <= -5e+64)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= 1.4e+49)
		tmp = (z * ((x * y) - (b * c))) + (j * (a * c));
	else
		tmp = (x * t) * (((b * i) / x) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5e+64], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+49], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * N[(N[(N[(b * i), $MachinePrecision] / x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e64

   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 66.7%

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

   5. Simplified 66.7%

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

   if -5e64 < t < 1.3999999999999999e49

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 69.0%

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

   8. Simplified 69.0%

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

   if 1.3999999999999999e49 < t

   1. Initial program 60.8%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 73.0%

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

   6. Taylor expanded in c around -inf

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

   8. Simplified 60.9%

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

   9. Taylor expanded in x around inf

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

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. unsub-neg N/A

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

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

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

   11. Simplified 48.6%

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

   12. Taylor expanded in t around -inf

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

       1. associate-*r* N/A

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

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

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

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

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

       4. +-commutative N/A

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

       5. mul-1-neg N/A

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

       6. unsub-neg N/A

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

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

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

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

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

       9. *-commutative N/A

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

       10. *-lowering-*.f64 66.8%

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

   14. Simplified 66.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(\frac{b \cdot i}{x} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -2.45e+69)
     t_1
     (if (<= b 1.35e+102) (+ (* j (- (* a c) (* y i))) (* y (* x z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.45e+69) {
		tmp = t_1;
	} else if (b <= 1.35e+102) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-2.45d+69)) then
        tmp = t_1
    else if (b <= 1.35d+102) then
        tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.45e+69) {
		tmp = t_1;
	} else if (b <= 1.35e+102) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.45e+69:
		tmp = t_1
	elif b <= 1.35e+102:
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.45e+69)
		tmp = t_1;
	elseif (b <= 1.35e+102)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.45e+69)
		tmp = t_1;
	elseif (b <= 1.35e+102)
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+69], t$95$1, If[LessEqual[b, 1.35e+102], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.45e69 or 1.3500000000000001e102 < b

   1. Initial program 68.3%

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

   3. Taylor expanded in 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 75.0%

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

   5. Simplified 75.0%

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

   if -2.45e69 < b < 1.3500000000000001e102

   1. Initial program 74.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   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 60.4%

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

   5. Simplified 60.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -360:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.64 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -360.0)
     t_1
     (if (<= a -1.64e-105)
       (+ (* j (* a c)) (* z (* x y)))
       (if (<= a 4.8e+56) (* 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 <= -360.0) {
		tmp = t_1;
	} else if (a <= -1.64e-105) {
		tmp = (j * (a * c)) + (z * (x * y));
	} else if (a <= 4.8e+56) {
		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 <= (-360.0d0)) then
        tmp = t_1
    else if (a <= (-1.64d-105)) then
        tmp = (j * (a * c)) + (z * (x * y))
    else if (a <= 4.8d+56) 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 <= -360.0) {
		tmp = t_1;
	} else if (a <= -1.64e-105) {
		tmp = (j * (a * c)) + (z * (x * y));
	} else if (a <= 4.8e+56) {
		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 <= -360.0:
		tmp = t_1
	elif a <= -1.64e-105:
		tmp = (j * (a * c)) + (z * (x * y))
	elif a <= 4.8e+56:
		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 <= -360.0)
		tmp = t_1;
	elseif (a <= -1.64e-105)
		tmp = Float64(Float64(j * Float64(a * c)) + Float64(z * Float64(x * y)));
	elseif (a <= 4.8e+56)
		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 <= -360.0)
		tmp = t_1;
	elseif (a <= -1.64e-105)
		tmp = (j * (a * c)) + (z * (x * y));
	elseif (a <= 4.8e+56)
		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, -360.0], t$95$1, If[LessEqual[a, -1.64e-105], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+56], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -360 or 4.80000000000000027e56 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in 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 67.4%

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

   5. Simplified 67.4%

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

   if -360 < a < -1.64e-105

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 65.0%

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

   11. Simplified 65.0%

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

   if -1.64e-105 < a < 4.80000000000000027e56

   1. Initial program 77.9%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 57.3%

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

   5. Simplified 57.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -360:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.64 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.55e-20)
     t_1
     (if (<= a 1.3e-303)
       (* z (- (* x y) (* b c)))
       (if (<= a 1.55e+57) (* 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 <= -2.55e-20) {
		tmp = t_1;
	} else if (a <= 1.3e-303) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 1.55e+57) {
		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 <= (-2.55d-20)) then
        tmp = t_1
    else if (a <= 1.3d-303) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 1.55d+57) 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 <= -2.55e-20) {
		tmp = t_1;
	} else if (a <= 1.3e-303) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 1.55e+57) {
		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 <= -2.55e-20:
		tmp = t_1
	elif a <= 1.3e-303:
		tmp = z * ((x * y) - (b * c))
	elif a <= 1.55e+57:
		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 <= -2.55e-20)
		tmp = t_1;
	elseif (a <= 1.3e-303)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 1.55e+57)
		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 <= -2.55e-20)
		tmp = t_1;
	elseif (a <= 1.3e-303)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 1.55e+57)
		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, -2.55e-20], t$95$1, If[LessEqual[a, 1.3e-303], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+57], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.55000000000000009e-20 or 1.55000000000000007e57 < a

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 66.6%

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

   5. Simplified 66.6%

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

   if -2.55000000000000009e-20 < a < 1.30000000000000002e-303

   1. Initial program 75.7%

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

   3. Taylor expanded in 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 53.5%

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

   5. Simplified 53.5%

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

   if 1.30000000000000002e-303 < a < 1.55000000000000007e57

   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 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 64.2%

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

   5. Simplified 64.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9.2e-43) t_1 (if (<= a 8e+61) (* 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 <= -9.2e-43) {
		tmp = t_1;
	} else if (a <= 8e+61) {
		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 <= (-9.2d-43)) then
        tmp = t_1
    else if (a <= 8d+61) 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 <= -9.2e-43) {
		tmp = t_1;
	} else if (a <= 8e+61) {
		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 <= -9.2e-43:
		tmp = t_1
	elif a <= 8e+61:
		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 <= -9.2e-43)
		tmp = t_1;
	elseif (a <= 8e+61)
		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 <= -9.2e-43)
		tmp = t_1;
	elseif (a <= 8e+61)
		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, -9.2e-43], t$95$1, If[LessEqual[a, 8e+61], 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 < -9.1999999999999995e-43 or 7.9999999999999996e61 < a

   1. Initial program 68.2%

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

   3. Taylor expanded in a around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 65.1%

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

   5. Simplified 65.1%

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

   if -9.1999999999999995e-43 < a < 7.9999999999999996e61

   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 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 55.0%

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

   5. Simplified 55.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -880000000:\\ \;\;\;\;y \cdot \left(0 - i \cdot j\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -880000000.0)
   (* y (- 0.0 (* i j)))
   (if (<= i 5.2e+106) (* a (- (* c j) (* x t))) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -880000000.0) {
		tmp = y * (0.0 - (i * j));
	} else if (i <= 5.2e+106) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-880000000.0d0)) then
        tmp = y * (0.0d0 - (i * j))
    else if (i <= 5.2d+106) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -880000000.0) {
		tmp = y * (0.0 - (i * j));
	} else if (i <= 5.2e+106) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -880000000.0:
		tmp = y * (0.0 - (i * j))
	elif i <= 5.2e+106:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -880000000.0)
		tmp = Float64(y * Float64(0.0 - Float64(i * j)));
	elseif (i <= 5.2e+106)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -880000000.0)
		tmp = y * (0.0 - (i * j));
	elseif (i <= 5.2e+106)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -880000000.0], N[(y * N[(0.0 - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+106], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.8e8

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(j \cdot y\right) \cdot i\right) \cdot -1 \]

      3. *-commutative N/A

         \[\leadsto \left(\left(y \cdot j\right) \cdot i\right) \cdot -1 \]

      4. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(j \cdot i\right)\right) \cdot -1 \]

      5. *-commutative N/A

         \[\leadsto \left(y \cdot \left(i \cdot j\right)\right) \cdot -1 \]

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

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

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

      12. *-lowering-*.f64 44.0%

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

   8. Simplified 44.0%

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

      1. sub0-neg N/A

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

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

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

      3. *-lowering-*.f64 44.0%

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

   10. Applied egg-rr 44.0%

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

   if -8.8e8 < i < 5.20000000000000039e106

   1. Initial program 77.3%

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

   3. Taylor expanded in 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 50.2%

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

   5. Simplified 50.2%

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

   if 5.20000000000000039e106 < i

   1. Initial program 59.8%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

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

      12. --lowering--.f64 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 54.7%

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

   8. Simplified 54.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 58.6%

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

   10. Applied egg-rr 58.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -880000000:\\ \;\;\;\;y \cdot \left(0 - i \cdot j\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7500000:\\ \;\;\;\;y \cdot \left(0 - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -7500000.0)
   (* y (- 0.0 (* i j)))
   (if (<= i 1.12e+14) (* a (* c j)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -7500000.0) {
		tmp = y * (0.0 - (i * j));
	} else if (i <= 1.12e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-7500000.0d0)) then
        tmp = y * (0.0d0 - (i * j))
    else if (i <= 1.12d+14) then
        tmp = a * (c * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -7500000.0) {
		tmp = y * (0.0 - (i * j));
	} else if (i <= 1.12e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -7500000.0:
		tmp = y * (0.0 - (i * j))
	elif i <= 1.12e+14:
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -7500000.0)
		tmp = Float64(y * Float64(0.0 - Float64(i * j)));
	elseif (i <= 1.12e+14)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -7500000.0)
		tmp = y * (0.0 - (i * j));
	elseif (i <= 1.12e+14)
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -7500000.0], N[(y * N[(0.0 - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.12e+14], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -7.5e6

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(j \cdot y\right) \cdot i\right) \cdot -1 \]

      3. *-commutative N/A

         \[\leadsto \left(\left(y \cdot j\right) \cdot i\right) \cdot -1 \]

      4. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(j \cdot i\right)\right) \cdot -1 \]

      5. *-commutative N/A

         \[\leadsto \left(y \cdot \left(i \cdot j\right)\right) \cdot -1 \]

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

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

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

      12. *-lowering-*.f64 44.0%

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

   8. Simplified 44.0%

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

      1. sub0-neg N/A

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

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

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

      3. *-lowering-*.f64 44.0%

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

   10. Applied egg-rr 44.0%

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

   if -7.5e6 < i < 1.12e14

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 36.0%

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

   8. Simplified 36.0%

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

   if 1.12e14 < i

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 47.4%

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

   8. Simplified 47.4%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 48.8%

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

   10. Applied egg-rr 48.8%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7500000:\\ \;\;\;\;y \cdot \left(0 - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.85 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.85e+176)
   (* b (* t i))
   (if (<= i 7e+15) (* a (* c j)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.85e+176) {
		tmp = b * (t * i);
	} else if (i <= 7e+15) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.85d+176)) then
        tmp = b * (t * i)
    else if (i <= 7d+15) then
        tmp = a * (c * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.85e+176) {
		tmp = b * (t * i);
	} else if (i <= 7e+15) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.85e+176:
		tmp = b * (t * i)
	elif i <= 7e+15:
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.85e+176)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 7e+15)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.85e+176)
		tmp = b * (t * i);
	elseif (i <= 7e+15)
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.85e+176], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e+15], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.8500000000000002e176

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 43.4%

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

   8. Simplified 43.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 48.4%

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

   10. Applied egg-rr 48.4%

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

   if -3.8500000000000002e176 < i < 7e15

   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 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 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 33.4%

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

   8. Simplified 33.4%

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

   if 7e15 < i

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 47.4%

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

   8. Simplified 47.4%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 48.8%

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

   10. Applied egg-rr 48.8%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.85 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.66 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -1.85e+176) t_1 (if (<= i 2.66e+14) (* 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 = t * (b * i);
	double tmp;
	if (i <= -1.85e+176) {
		tmp = t_1;
	} else if (i <= 2.66e+14) {
		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 = t * (b * i)
    if (i <= (-1.85d+176)) then
        tmp = t_1
    else if (i <= 2.66d+14) 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 = t * (b * i);
	double tmp;
	if (i <= -1.85e+176) {
		tmp = t_1;
	} else if (i <= 2.66e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -1.85e+176:
		tmp = t_1
	elif i <= 2.66e+14:
		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(t * Float64(b * i))
	tmp = 0.0
	if (i <= -1.85e+176)
		tmp = t_1;
	elseif (i <= 2.66e+14)
		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 = t * (b * i);
	tmp = 0.0;
	if (i <= -1.85e+176)
		tmp = t_1;
	elseif (i <= 2.66e+14)
		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[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e+176], t$95$1, If[LessEqual[i, 2.66e+14], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.8499999999999999e176 or 2.66e14 < i

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 46.4%

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

   8. Simplified 46.4%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 48.7%

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

   10. Applied egg-rr 48.7%

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

   if -1.8499999999999999e176 < i < 2.66e14

   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 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 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 33.4%

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

   8. Simplified 33.4%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{+176}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 2.66 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -1.75 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= i -1.75e+175) t_1 (if (<= i 3.9e+14) (* 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 = i * (t * b);
	double tmp;
	if (i <= -1.75e+175) {
		tmp = t_1;
	} else if (i <= 3.9e+14) {
		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 = i * (t * b)
    if (i <= (-1.75d+175)) then
        tmp = t_1
    else if (i <= 3.9d+14) 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 = i * (t * b);
	double tmp;
	if (i <= -1.75e+175) {
		tmp = t_1;
	} else if (i <= 3.9e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if i <= -1.75e+175:
		tmp = t_1
	elif i <= 3.9e+14:
		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(i * Float64(t * b))
	tmp = 0.0
	if (i <= -1.75e+175)
		tmp = t_1;
	elseif (i <= 3.9e+14)
		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 = i * (t * b);
	tmp = 0.0;
	if (i <= -1.75e+175)
		tmp = t_1;
	elseif (i <= 3.9e+14)
		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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.75e+175], t$95$1, If[LessEqual[i, 3.9e+14], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.7500000000000002e175 or 3.9e14 < i

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(i \cdot b\right) \cdot t \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 46.4%

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

   8. Simplified 46.4%

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

   if -1.7500000000000002e175 < i < 3.9e14

   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 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 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 33.4%

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

   8. Simplified 33.4%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{+175}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
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 42.5%

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

5. Simplified 42.5%

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

6. Taylor expanded in j around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 27.8%

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

8. Simplified 27.8%

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

9. Final simplification 27.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.6% 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 2024161 
(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)))))