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

Percentage Accurate: 73.3% → 81.8%

Time: 17.5s

Alternatives: 21

Speedup: 0.5×

• 57.4% 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: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 48.8%

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

4. Final simplification 82.4%

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

Alternative 2: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+83}:\\ \;\;\;\;t\_2 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 280000000:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -4.6e+83)
     (- t_2 (* y (* i j)))
     (if (<= x 280000000.0)
       (+ (+ (* y (* x z)) (* b (* z (- (/ (* t i) z) c)))) t_1)
       (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.6e+83) {
		tmp = t_2 - (y * (i * j));
	} else if (x <= 280000000.0) {
		tmp = ((y * (x * z)) + (b * (z * (((t * i) / z) - c)))) + t_1;
	} else {
		tmp = t_2 + 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 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-4.6d+83)) then
        tmp = t_2 - (y * (i * j))
    else if (x <= 280000000.0d0) then
        tmp = ((y * (x * z)) + (b * (z * (((t * i) / z) - c)))) + t_1
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.6e+83) {
		tmp = t_2 - (y * (i * j));
	} else if (x <= 280000000.0) {
		tmp = ((y * (x * z)) + (b * (z * (((t * i) / z) - c)))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.6e+83:
		tmp = t_2 - (y * (i * j))
	elif x <= 280000000.0:
		tmp = ((y * (x * z)) + (b * (z * (((t * i) / z) - c)))) + t_1
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.6e+83)
		tmp = Float64(t_2 - Float64(y * Float64(i * j)));
	elseif (x <= 280000000.0)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(z * Float64(Float64(Float64(t * i) / z) - c)))) + t_1);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.6e+83)
		tmp = t_2 - (y * (i * j));
	elseif (x <= 280000000.0)
		tmp = ((y * (x * z)) + (b * (z * (((t * i) / z) - c)))) + t_1;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+83], N[(t$95$2 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 280000000.0], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * N[(N[(N[(t * i), $MachinePrecision] / z), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999999e83

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0 71.1%

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

   4. Taylor expanded in c around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. sub-neg 76.4%

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

      3. distribute-rgt-neg-out 76.4%

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

      4. fma-define 76.4%

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

      5. mul-1-neg 76.4%

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

      6. *-commutative 76.4%

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

      7. *-commutative 76.4%

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

      8. unsub-neg 76.4%

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

      9. fma-define 76.4%

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

      10. distribute-rgt-neg-out 76.4%

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

      11. sub-neg 76.4%

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

      12. associate-*l* 79.1%

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

      13. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   if -4.5999999999999999e83 < x < 2.8e8

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-*l* 68.1%

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

   8. Simplified 68.1%

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

   if 2.8e8 < x

   1. Initial program 79.2%

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

   3. Taylor expanded in b around 0 73.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 280000000:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.45e+48)
   (* x (* y z))
   (if (<= z -3.7e-134)
     (* i (* y (- j)))
     (if (<= z 1.85e-285)
       (* t (* b i))
       (if (<= z 1.32e-129)
         (* t (* a (- x)))
         (if (<= z 105000.0)
           (* a (* c j))
           (if (<= z 5e+111) (* y (* x z)) (* b (* z (- c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.45e+48) {
		tmp = x * (y * z);
	} else if (z <= -3.7e-134) {
		tmp = i * (y * -j);
	} else if (z <= 1.85e-285) {
		tmp = t * (b * i);
	} else if (z <= 1.32e-129) {
		tmp = t * (a * -x);
	} else if (z <= 105000.0) {
		tmp = a * (c * j);
	} else if (z <= 5e+111) {
		tmp = y * (x * z);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.45d+48)) then
        tmp = x * (y * z)
    else if (z <= (-3.7d-134)) then
        tmp = i * (y * -j)
    else if (z <= 1.85d-285) then
        tmp = t * (b * i)
    else if (z <= 1.32d-129) then
        tmp = t * (a * -x)
    else if (z <= 105000.0d0) then
        tmp = a * (c * j)
    else if (z <= 5d+111) then
        tmp = y * (x * z)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.45e+48) {
		tmp = x * (y * z);
	} else if (z <= -3.7e-134) {
		tmp = i * (y * -j);
	} else if (z <= 1.85e-285) {
		tmp = t * (b * i);
	} else if (z <= 1.32e-129) {
		tmp = t * (a * -x);
	} else if (z <= 105000.0) {
		tmp = a * (c * j);
	} else if (z <= 5e+111) {
		tmp = y * (x * z);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.45e+48:
		tmp = x * (y * z)
	elif z <= -3.7e-134:
		tmp = i * (y * -j)
	elif z <= 1.85e-285:
		tmp = t * (b * i)
	elif z <= 1.32e-129:
		tmp = t * (a * -x)
	elif z <= 105000.0:
		tmp = a * (c * j)
	elif z <= 5e+111:
		tmp = y * (x * z)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.45e+48)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -3.7e-134)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 1.85e-285)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 1.32e-129)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (z <= 105000.0)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 5e+111)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.45e+48)
		tmp = x * (y * z);
	elseif (z <= -3.7e-134)
		tmp = i * (y * -j);
	elseif (z <= 1.85e-285)
		tmp = t * (b * i);
	elseif (z <= 1.32e-129)
		tmp = t * (a * -x);
	elseif (z <= 105000.0)
		tmp = a * (c * j);
	elseif (z <= 5e+111)
		tmp = y * (x * z);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.45e+48], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-134], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-285], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e-129], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.45000000000000015e48

   1. Initial program 57.3%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around inf 56.4%

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

      1. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   if -2.45000000000000015e48 < z < -3.7e-134

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. distribute-rgt-neg-in 38.4%

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

      3. distribute-rgt-neg-in 38.4%

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

   8. Simplified 38.4%

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

   if -3.7e-134 < z < 1.8499999999999999e-285

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in a around 0 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if 1.8499999999999999e-285 < z < 1.31999999999999992e-129

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. distribute-lft-out-- 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

   8. Simplified 41.7%

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

   if 1.31999999999999992e-129 < z < 105000

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in c around inf 49.1%

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

   if 105000 < z < 4.9999999999999997e111

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in j around -inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. +-commutative 51.4%

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

      5. mul-1-neg 51.4%

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

      6. unsub-neg 51.4%

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

      7. *-commutative 51.4%

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

      8. associate-/l* 51.4%

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

      9. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in i around 0 51.1%

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

       1. *-commutative 51.1%

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

       2. associate-*l* 55.7%

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

       3. *-commutative 55.7%

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

   11. Simplified 55.7%

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

   if 4.9999999999999997e111 < z

   1. Initial program 57.8%

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

   3. Taylor expanded in c around inf 49.5%

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

   4. Taylor expanded in a around 0 44.2%

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

      1. associate-*r* 44.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 44.2%

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

   6. Simplified 44.2%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 650000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.25e+64)
     t_1
     (if (<= z -8.5e-19)
       (* x (* a (- (* c (/ j x)) t)))
       (if (<= z -7e-302)
         (* i (- (* t b) (* y j)))
         (if (<= z 9.5e-143)
           (* t (- (* b i) (* x a)))
           (if (<= z 650000.0) (* a (- (* c j) (* x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.25e+64) {
		tmp = t_1;
	} else if (z <= -8.5e-19) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (z <= -7e-302) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 9.5e-143) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 650000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-2.25d+64)) then
        tmp = t_1
    else if (z <= (-8.5d-19)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (z <= (-7d-302)) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 9.5d-143) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 650000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.25e+64) {
		tmp = t_1;
	} else if (z <= -8.5e-19) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (z <= -7e-302) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 9.5e-143) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 650000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.25e+64:
		tmp = t_1
	elif z <= -8.5e-19:
		tmp = x * (a * ((c * (j / x)) - t))
	elif z <= -7e-302:
		tmp = i * ((t * b) - (y * j))
	elif z <= 9.5e-143:
		tmp = t * ((b * i) - (x * a))
	elif z <= 650000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.25e+64)
		tmp = t_1;
	elseif (z <= -8.5e-19)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (z <= -7e-302)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 9.5e-143)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 650000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.25e+64)
		tmp = t_1;
	elseif (z <= -8.5e-19)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (z <= -7e-302)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 9.5e-143)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 650000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+64], t$95$1, If[LessEqual[z, -8.5e-19], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-302], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-143], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 650000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.24999999999999987e64 or 6.5e5 < z

   1. Initial program 60.4%

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

   3. Taylor expanded in z around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -2.24999999999999987e64 < z < -8.50000000000000003e-19

   1. Initial program 79.6%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in x around inf 50.6%

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

      1. neg-mul-1 50.6%

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

      2. +-commutative 50.6%

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

      3. associate-/l* 55.8%

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

      4. distribute-rgt-neg-in 55.8%

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

      5. distribute-lft-out 65.9%

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

      6. sub-neg 65.9%

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

      7. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   if -8.50000000000000003e-19 < z < -7.0000000000000003e-302

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf 67.0%

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

      1. distribute-lft-out-- 67.0%

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

      2. *-commutative 67.0%

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

      3. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -7.0000000000000003e-302 < z < 9.4999999999999993e-143

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-out 63.7%

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

      3. neg-sub0 63.7%

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

      4. associate--r- 63.7%

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

      5. neg-sub0 63.7%

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

      6. mul-1-neg 63.7%

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

      7. +-commutative 63.7%

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

      8. mul-1-neg 63.7%

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

      9. unsub-neg 63.7%

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

      10. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   if 9.4999999999999993e-143 < z < 6.5e5

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 650000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 740000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -2.6e+45)
     t_1
     (if (<= z -5.4e-131)
       (* i (* y (- j)))
       (if (<= z 6.5e-285)
         (* t (* b i))
         (if (<= z 1.5e-129)
           (* t (* a (- x)))
           (if (<= z 740000.0) (* 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 = x * (y * z);
	double tmp;
	if (z <= -2.6e+45) {
		tmp = t_1;
	} else if (z <= -5.4e-131) {
		tmp = i * (y * -j);
	} else if (z <= 6.5e-285) {
		tmp = t * (b * i);
	} else if (z <= 1.5e-129) {
		tmp = t * (a * -x);
	} else if (z <= 740000.0) {
		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 = x * (y * z)
    if (z <= (-2.6d+45)) then
        tmp = t_1
    else if (z <= (-5.4d-131)) then
        tmp = i * (y * -j)
    else if (z <= 6.5d-285) then
        tmp = t * (b * i)
    else if (z <= 1.5d-129) then
        tmp = t * (a * -x)
    else if (z <= 740000.0d0) 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 = x * (y * z);
	double tmp;
	if (z <= -2.6e+45) {
		tmp = t_1;
	} else if (z <= -5.4e-131) {
		tmp = i * (y * -j);
	} else if (z <= 6.5e-285) {
		tmp = t * (b * i);
	} else if (z <= 1.5e-129) {
		tmp = t * (a * -x);
	} else if (z <= 740000.0) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.6e+45:
		tmp = t_1
	elif z <= -5.4e-131:
		tmp = i * (y * -j)
	elif z <= 6.5e-285:
		tmp = t * (b * i)
	elif z <= 1.5e-129:
		tmp = t * (a * -x)
	elif z <= 740000.0:
		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(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.6e+45)
		tmp = t_1;
	elseif (z <= -5.4e-131)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 6.5e-285)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 1.5e-129)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (z <= 740000.0)
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.6e+45)
		tmp = t_1;
	elseif (z <= -5.4e-131)
		tmp = i * (y * -j);
	elseif (z <= 6.5e-285)
		tmp = t * (b * i);
	elseif (z <= 1.5e-129)
		tmp = t * (a * -x);
	elseif (z <= 740000.0)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+45], t$95$1, If[LessEqual[z, -5.4e-131], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-285], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-129], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 740000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000007e45 or 7.4e5 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

   8. Simplified 48.6%

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

   if -2.60000000000000007e45 < z < -5.40000000000000042e-131

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. distribute-rgt-neg-in 38.4%

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

      3. distribute-rgt-neg-in 38.4%

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

   8. Simplified 38.4%

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

   if -5.40000000000000042e-131 < z < 6.5e-285

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in a around 0 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if 6.5e-285 < z < 1.4999999999999999e-129

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 63.9%

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

      1. distribute-lft-out-- 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

   8. Simplified 41.7%

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

   if 1.4999999999999999e-129 < z < 7.4e5

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in c around inf 49.1%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 740000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;j \leq -1.9 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* y (* x z)))))
   (if (<= j -1.9e-108)
     t_1
     (if (<= j -1.2e-252)
       (* z (- (* x y) (* b c)))
       (if (<= j 8.5e-39) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (y * (x * z));
	double tmp;
	if (j <= -1.9e-108) {
		tmp = t_1;
	} else if (j <= -1.2e-252) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 8.5e-39) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (y * (x * z))
    if (j <= (-1.9d-108)) then
        tmp = t_1
    else if (j <= (-1.2d-252)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 8.5d-39) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (y * (x * z));
	double tmp;
	if (j <= -1.9e-108) {
		tmp = t_1;
	} else if (j <= -1.2e-252) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 8.5e-39) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (y * (x * z))
	tmp = 0
	if j <= -1.9e-108:
		tmp = t_1
	elif j <= -1.2e-252:
		tmp = z * ((x * y) - (b * c))
	elif j <= 8.5e-39:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)))
	tmp = 0.0
	if (j <= -1.9e-108)
		tmp = t_1;
	elseif (j <= -1.2e-252)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 8.5e-39)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (y * (x * z));
	tmp = 0.0;
	if (j <= -1.9e-108)
		tmp = t_1;
	elseif (j <= -1.2e-252)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 8.5e-39)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.9e-108], t$95$1, If[LessEqual[j, -1.2e-252], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-39], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.89999999999999987e-108 or 8.5000000000000005e-39 < j

   1. Initial program 74.1%

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

   3. Taylor expanded in b around 0 74.5%

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

   4. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. associate-*l* 68.2%

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

      3. *-commutative 68.2%

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

   6. Simplified 68.2%

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

   if -1.89999999999999987e-108 < j < -1.2000000000000001e-252

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   if -1.2000000000000001e-252 < j < 8.5000000000000005e-39

   1. Initial program 73.4%

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

   3. Taylor expanded in t around inf 56.4%

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

      1. distribute-lft-out-- 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in t around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-out 56.4%

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

      3. neg-sub0 56.4%

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

      4. associate--r- 56.4%

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

      5. neg-sub0 56.4%

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

      6. mul-1-neg 56.4%

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

      7. +-commutative 56.4%

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

      8. mul-1-neg 56.4%

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

      9. unsub-neg 56.4%

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

      10. *-commutative 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 145000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -9.5e+43)
     t_1
     (if (<= z -3.4e-303)
       (* i (- (* t b) (* y j)))
       (if (<= z 3.2e-154)
         (* t (- (* b i) (* x a)))
         (if (<= z 145000.0) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e+43) {
		tmp = t_1;
	} else if (z <= -3.4e-303) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 3.2e-154) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 145000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-9.5d+43)) then
        tmp = t_1
    else if (z <= (-3.4d-303)) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 3.2d-154) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 145000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e+43) {
		tmp = t_1;
	} else if (z <= -3.4e-303) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 3.2e-154) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 145000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9.5e+43:
		tmp = t_1
	elif z <= -3.4e-303:
		tmp = i * ((t * b) - (y * j))
	elif z <= 3.2e-154:
		tmp = t * ((b * i) - (x * a))
	elif z <= 145000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9.5e+43)
		tmp = t_1;
	elseif (z <= -3.4e-303)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 3.2e-154)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 145000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9.5e+43)
		tmp = t_1;
	elseif (z <= -3.4e-303)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 3.2e-154)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 145000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+43], t$95$1, If[LessEqual[z, -3.4e-303], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-154], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 145000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000004e43 or 145000 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   if -9.5000000000000004e43 < z < -3.4e-303

   1. Initial program 79.6%

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

   3. Taylor expanded in i around inf 60.1%

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

      1. distribute-lft-out-- 60.1%

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

      2. *-commutative 60.1%

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

      3. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -3.4e-303 < z < 3.20000000000000005e-154

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-out 63.7%

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

      3. neg-sub0 63.7%

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

      4. associate--r- 63.7%

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

      5. neg-sub0 63.7%

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

      6. mul-1-neg 63.7%

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

      7. +-commutative 63.7%

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

      8. mul-1-neg 63.7%

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

      9. unsub-neg 63.7%

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

      10. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   if 3.20000000000000005e-154 < z < 145000

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 145000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -0.066:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -0.066)
     t_1
     (if (<= y -1.02e-182)
       (* a (- (* c j) (* x t)))
       (if (<= y 2.3e-170)
         (* t (- (* b i) (* x a)))
         (if (<= y 8e-37) (* 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -0.066) {
		tmp = t_1;
	} else if (y <= -1.02e-182) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.3e-170) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 8e-37) {
		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 = y * ((x * z) - (i * j))
    if (y <= (-0.066d0)) then
        tmp = t_1
    else if (y <= (-1.02d-182)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 2.3d-170) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 8d-37) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -0.066) {
		tmp = t_1;
	} else if (y <= -1.02e-182) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.3e-170) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 8e-37) {
		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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -0.066:
		tmp = t_1
	elif y <= -1.02e-182:
		tmp = a * ((c * j) - (x * t))
	elif y <= 2.3e-170:
		tmp = t * ((b * i) - (x * a))
	elif y <= 8e-37:
		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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -0.066)
		tmp = t_1;
	elseif (y <= -1.02e-182)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 2.3e-170)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 8e-37)
		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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -0.066)
		tmp = t_1;
	elseif (y <= -1.02e-182)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 2.3e-170)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 8e-37)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.066], t$95$1, If[LessEqual[y, -1.02e-182], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-170], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-37], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.066000000000000003 or 8.00000000000000053e-37 < y

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -0.066000000000000003 < y < -1.02e-182

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

   5. Simplified 60.4%

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

   if -1.02e-182 < y < 2.29999999999999987e-170

   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 t around inf 61.8%

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

      1. distribute-lft-out-- 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in t around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-rgt-neg-out 61.8%

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

      3. neg-sub0 61.8%

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

      4. associate--r- 61.8%

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

      5. neg-sub0 61.8%

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

      6. mul-1-neg 61.8%

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

      7. +-commutative 61.8%

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

      8. mul-1-neg 61.8%

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

      9. unsub-neg 61.8%

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

      10. *-commutative 61.8%

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

   8. Simplified 61.8%

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

   if 2.29999999999999987e-170 < y < 8.00000000000000053e-37

   1. Initial program 84.6%

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

   3. Taylor expanded in b around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.066:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-64} \lor \neg \left(x \leq 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= x -9.2e-64) (not (<= x 1e-16)))
     (+ (* x (- (* y z) (* t a))) t_1)
     (+ t_1 (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -9.2e-64) || !(x <= 1e-16)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((x <= (-9.2d-64)) .or. (.not. (x <= 1d-16))) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -9.2e-64) || !(x <= 1e-16)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (x <= -9.2e-64) or not (x <= 1e-16):
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if ((x <= -9.2e-64) || !(x <= 1e-16))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((x <= -9.2e-64) || ~((x <= 1e-16)))
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9.2e-64], N[Not[LessEqual[x, 1e-16]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2000000000000006e-64 or 9.9999999999999998e-17 < x

   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 b around 0 71.2%

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

   if -9.2000000000000006e-64 < x < 9.9999999999999998e-17

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-64} \lor \neg \left(x \leq 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+73} \lor \neg \left(z \leq 7 \cdot 10^{+98}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -4.9e+73) (not (<= z 7e+98)))
   (* z (- (* x y) (* b c)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.9e+73) || !(z <= 7e+98)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-4.9d+73)) .or. (.not. (z <= 7d+98))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.9e+73) || !(z <= 7e+98)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -4.9e+73) or not (z <= 7e+98):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -4.9e+73) || !(z <= 7e+98))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -4.9e+73) || ~((z <= 7e+98)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -4.9e+73], N[Not[LessEqual[z, 7e+98]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8999999999999999e73 or 7e98 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -4.8999999999999999e73 < z < 7e98

   1. Initial program 82.3%

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

   3. Taylor expanded in b around 0 69.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+73} \lor \neg \left(z \leq 7 \cdot 10^{+98}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 520000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -3.4e+45)
     t_1
     (if (<= z -4.8e-136)
       (* i (* y (- j)))
       (if (<= z 4.6e-136)
         (* t (* b i))
         (if (<= z 520000.0) (* 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 = x * (y * z);
	double tmp;
	if (z <= -3.4e+45) {
		tmp = t_1;
	} else if (z <= -4.8e-136) {
		tmp = i * (y * -j);
	} else if (z <= 4.6e-136) {
		tmp = t * (b * i);
	} else if (z <= 520000.0) {
		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 = x * (y * z)
    if (z <= (-3.4d+45)) then
        tmp = t_1
    else if (z <= (-4.8d-136)) then
        tmp = i * (y * -j)
    else if (z <= 4.6d-136) then
        tmp = t * (b * i)
    else if (z <= 520000.0d0) 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 = x * (y * z);
	double tmp;
	if (z <= -3.4e+45) {
		tmp = t_1;
	} else if (z <= -4.8e-136) {
		tmp = i * (y * -j);
	} else if (z <= 4.6e-136) {
		tmp = t * (b * i);
	} else if (z <= 520000.0) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -3.4e+45:
		tmp = t_1
	elif z <= -4.8e-136:
		tmp = i * (y * -j)
	elif z <= 4.6e-136:
		tmp = t * (b * i)
	elif z <= 520000.0:
		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(x * Float64(y * z))
	tmp = 0.0
	if (z <= -3.4e+45)
		tmp = t_1;
	elseif (z <= -4.8e-136)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 4.6e-136)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 520000.0)
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -3.4e+45)
		tmp = t_1;
	elseif (z <= -4.8e-136)
		tmp = i * (y * -j);
	elseif (z <= 4.6e-136)
		tmp = t * (b * i);
	elseif (z <= 520000.0)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+45], t$95$1, If[LessEqual[z, -4.8e-136], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-136], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 520000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4e45 or 5.2e5 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

   8. Simplified 48.6%

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

   if -3.4e45 < z < -4.7999999999999997e-136

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. distribute-rgt-neg-in 38.4%

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

      3. distribute-rgt-neg-in 38.4%

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

   8. Simplified 38.4%

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

   if -4.7999999999999997e-136 < z < 4.59999999999999997e-136

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. distribute-lft-out-- 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in a around 0 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 4.59999999999999997e-136 < z < 5.2e5

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in c around inf 47.5%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 520000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{+102} \lor \neg \left(c \leq 3.7 \cdot 10^{+84}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.4e+102) (not (<= c 3.7e+84)))
   (* c (- (* a j) (* z b)))
   (- (* x (- (* y z) (* t a))) (* y (* i j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.4e+102) || !(c <= 3.7e+84)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-6.4d+102)) .or. (.not. (c <= 3.7d+84))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = (x * ((y * z) - (t * a))) - (y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.4e+102) || !(c <= 3.7e+84)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -6.4e+102) or not (c <= 3.7e+84):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -6.4e+102) || !(c <= 3.7e+84))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -6.4e+102) || ~((c <= 3.7e+84)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -6.4e+102], N[Not[LessEqual[c, 3.7e+84]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.3999999999999999e102 or 3.7e84 < c

   1. Initial program 58.0%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -6.3999999999999999e102 < c < 3.7e84

   1. Initial program 79.8%

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

   3. Taylor expanded in b around 0 68.4%

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

   4. Taylor expanded in c around 0 61.8%

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

      1. +-commutative 61.8%

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

      2. sub-neg 61.8%

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

      3. distribute-rgt-neg-out 61.8%

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

      4. fma-define 61.8%

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

      5. mul-1-neg 61.8%

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

      6. *-commutative 61.8%

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

      7. *-commutative 61.8%

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

      8. unsub-neg 61.8%

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

      9. fma-define 61.8%

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

      10. distribute-rgt-neg-out 61.8%

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

      11. sub-neg 61.8%

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

      12. associate-*l* 62.4%

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

      13. *-commutative 62.4%

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

   6. Simplified 62.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{+102} \lor \neg \left(c \leq 3.7 \cdot 10^{+84}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 130000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -9.2e+57)
     t_1
     (if (<= z 7.4e-140)
       (* t (- (* b i) (* x a)))
       (if (<= z 130000.0) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.2e+57) {
		tmp = t_1;
	} else if (z <= 7.4e-140) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 130000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-9.2d+57)) then
        tmp = t_1
    else if (z <= 7.4d-140) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 130000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.2e+57) {
		tmp = t_1;
	} else if (z <= 7.4e-140) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 130000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9.2e+57:
		tmp = t_1
	elif z <= 7.4e-140:
		tmp = t * ((b * i) - (x * a))
	elif z <= 130000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9.2e+57)
		tmp = t_1;
	elseif (z <= 7.4e-140)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 130000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9.2e+57)
		tmp = t_1;
	elseif (z <= 7.4e-140)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 130000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+57], t$95$1, If[LessEqual[z, 7.4e-140], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 130000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999995e57 or 1.3e5 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -9.1999999999999995e57 < z < 7.39999999999999955e-140

   1. Initial program 81.9%

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

   3. Taylor expanded in t around inf 54.4%

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

      1. distribute-lft-out-- 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-rgt-neg-out 54.4%

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

      3. neg-sub0 54.4%

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

      4. associate--r- 54.4%

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

      5. neg-sub0 54.4%

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

      6. mul-1-neg 54.4%

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

      7. +-commutative 54.4%

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

      8. mul-1-neg 54.4%

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

      9. unsub-neg 54.4%

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

      10. *-commutative 54.4%

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

   8. Simplified 54.4%

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

   if 7.39999999999999955e-140 < z < 1.3e5

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 130000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -6.5e-50)
     t_1
     (if (<= j -7.5e-157)
       (* y (* x z))
       (if (<= j 3.3e+137) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6.5e-50) {
		tmp = t_1;
	} else if (j <= -7.5e-157) {
		tmp = y * (x * z);
	} else if (j <= 3.3e+137) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-6.5d-50)) then
        tmp = t_1
    else if (j <= (-7.5d-157)) then
        tmp = y * (x * z)
    else if (j <= 3.3d+137) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6.5e-50) {
		tmp = t_1;
	} else if (j <= -7.5e-157) {
		tmp = y * (x * z);
	} else if (j <= 3.3e+137) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -6.5e-50:
		tmp = t_1
	elif j <= -7.5e-157:
		tmp = y * (x * z)
	elif j <= 3.3e+137:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.5e-50)
		tmp = t_1;
	elseif (j <= -7.5e-157)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.3e+137)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.5e-50)
		tmp = t_1;
	elseif (j <= -7.5e-157)
		tmp = y * (x * z);
	elseif (j <= 3.3e+137)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e-50], t$95$1, If[LessEqual[j, -7.5e-157], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e+137], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.49999999999999987e-50 or 3.30000000000000003e137 < j

   1. Initial program 73.3%

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

   3. Taylor expanded in b around 0 78.6%

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

   4. Taylor expanded in j around inf 70.5%

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

   if -6.49999999999999987e-50 < j < -7.500000000000001e-157

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in j around -inf 32.8%

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

      1. mul-1-neg 32.8%

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

      2. *-commutative 32.8%

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

      3. distribute-rgt-neg-in 32.8%

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

      4. +-commutative 32.8%

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

      5. mul-1-neg 32.8%

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

      6. unsub-neg 32.8%

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

      7. *-commutative 32.8%

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

      8. associate-/l* 32.7%

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

      9. *-commutative 32.7%

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

   8. Simplified 32.7%

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

   9. Taylor expanded in i around 0 48.6%

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

       1. *-commutative 48.6%

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

       2. associate-*l* 52.7%

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

       3. *-commutative 52.7%

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

   11. Simplified 52.7%

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

   if -7.500000000000001e-157 < j < 3.30000000000000003e137

   1. Initial program 75.3%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. distribute-lft-out-- 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-rgt-neg-out 49.2%

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

      3. neg-sub0 49.2%

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

      4. associate--r- 49.2%

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

      5. neg-sub0 49.2%

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

      6. mul-1-neg 49.2%

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

      7. +-commutative 49.2%

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

      8. mul-1-neg 49.2%

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

      9. unsub-neg 49.2%

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

      10. *-commutative 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 550000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -5.1e+27)
     t_1
     (if (<= z 5.2e-138)
       (* b (* t i))
       (if (<= z 550000.0) (* 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 = x * (y * z);
	double tmp;
	if (z <= -5.1e+27) {
		tmp = t_1;
	} else if (z <= 5.2e-138) {
		tmp = b * (t * i);
	} else if (z <= 550000.0) {
		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 = x * (y * z)
    if (z <= (-5.1d+27)) then
        tmp = t_1
    else if (z <= 5.2d-138) then
        tmp = b * (t * i)
    else if (z <= 550000.0d0) 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 = x * (y * z);
	double tmp;
	if (z <= -5.1e+27) {
		tmp = t_1;
	} else if (z <= 5.2e-138) {
		tmp = b * (t * i);
	} else if (z <= 550000.0) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -5.1e+27:
		tmp = t_1
	elif z <= 5.2e-138:
		tmp = b * (t * i)
	elif z <= 550000.0:
		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(x * Float64(y * z))
	tmp = 0.0
	if (z <= -5.1e+27)
		tmp = t_1;
	elseif (z <= 5.2e-138)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 550000.0)
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -5.1e+27)
		tmp = t_1;
	elseif (z <= 5.2e-138)
		tmp = b * (t * i);
	elseif (z <= 550000.0)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+27], t$95$1, If[LessEqual[z, 5.2e-138], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1e27 or 5.5e5 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf 55.2%

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

      1. +-commutative 55.2%

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

      2. mul-1-neg 55.2%

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

      3. unsub-neg 55.2%

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

      4. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in z around inf 47.4%

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

      1. *-commutative 47.4%

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

   8. Simplified 47.4%

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

   if -5.1e27 < z < 5.2e-138

   1. Initial program 82.1%

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

   3. Taylor expanded in t around inf 55.5%

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

      1. distribute-lft-out-- 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in a around 0 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

   if 5.2e-138 < z < 5.5e5

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in c around inf 47.5%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 550000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+55} \lor \neg \left(j \leq 1.05 \cdot 10^{+128}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.1e+55) (not (<= j 1.05e+128)))
   (* j (- (* a c) (* y i)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+55) || !(j <= 1.05e+128)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.1d+55)) .or. (.not. (j <= 1.05d+128))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+55) || !(j <= 1.05e+128)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.1e+55) or not (j <= 1.05e+128):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.1e+55) || !(j <= 1.05e+128))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.1e+55) || ~((j <= 1.05e+128)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.1e+55], N[Not[LessEqual[j, 1.05e+128]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.10000000000000005e55 or 1.05e128 < j

   1. Initial program 73.0%

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

   3. Taylor expanded in b around 0 84.1%

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

   4. Taylor expanded in j around inf 75.5%

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

   if -1.10000000000000005e55 < j < 1.05e128

   1. Initial program 72.3%

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

   3. Taylor expanded in b around inf 44.7%

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

      1. *-commutative 44.7%

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

   5. Simplified 44.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+55} \lor \neg \left(j \leq 1.05 \cdot 10^{+128}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+28} \lor \neg \left(a \leq 2.7 \cdot 10^{-93}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.65e+28) (not (<= a 2.7e-93)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.65e+28) || !(a <= 2.7e-93)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.65d+28)) .or. (.not. (a <= 2.7d-93))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.65e+28) || !(a <= 2.7e-93)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.65e+28) or not (a <= 2.7e-93):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.65e+28) || !(a <= 2.7e-93))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.65e+28) || ~((a <= 2.7e-93)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.65e+28], N[Not[LessEqual[a, 2.7e-93]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65e28 or 2.7000000000000001e-93 < a

   1. Initial program 66.1%

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

   3. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   if -1.65e28 < a < 2.7000000000000001e-93

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 46.2%

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

      1. *-commutative 46.2%

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

   5. Simplified 46.2%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+28} \lor \neg \left(a \leq 2.7 \cdot 10^{-93}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3e+92)
   (* x (* y z))
   (if (<= z 1.22e+121) (* a (- (* c j) (* x t))) (* b (* z (- c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3e+92) {
		tmp = x * (y * z);
	} else if (z <= 1.22e+121) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3d+92)) then
        tmp = x * (y * z)
    else if (z <= 1.22d+121) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3e+92) {
		tmp = x * (y * z);
	} else if (z <= 1.22e+121) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3e+92:
		tmp = x * (y * z)
	elif z <= 1.22e+121:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3e+92)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.22e+121)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3e+92)
		tmp = x * (y * z);
	elseif (z <= 1.22e+121)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3e+92], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+121], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000013e92

   1. Initial program 56.1%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -3.00000000000000013e92 < z < 1.22000000000000011e121

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. mul-1-neg 46.4%

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

      3. unsub-neg 46.4%

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

   5. Simplified 46.4%

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

   if 1.22000000000000011e121 < z

   1. Initial program 56.8%

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

   3. Taylor expanded in c around inf 50.8%

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

   4. Taylor expanded in a around 0 45.2%

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

      1. associate-*r* 45.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 45.2%

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

   6. Simplified 45.2%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.4 \cdot 10^{+43} \lor \neg \left(j \leq 2.2 \cdot 10^{+138}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.4e+43) (not (<= j 2.2e+138))) (* c (* a j)) (* 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 ((j <= -6.4e+43) || !(j <= 2.2e+138)) {
		tmp = c * (a * j);
	} 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 ((j <= (-6.4d+43)) .or. (.not. (j <= 2.2d+138))) then
        tmp = c * (a * j)
    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 ((j <= -6.4e+43) || !(j <= 2.2e+138)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.4e+43) or not (j <= 2.2e+138):
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.4e+43) || !(j <= 2.2e+138))
		tmp = Float64(c * Float64(a * j));
	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 ((j <= -6.4e+43) || ~((j <= 2.2e+138)))
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.4e+43], N[Not[LessEqual[j, 2.2e+138]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.40000000000000029e43 or 2.2000000000000001e138 < j

   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 c around inf 45.9%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -6.40000000000000029e43 < j < 2.2000000000000001e138

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 43.8%

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

      1. distribute-lft-out-- 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in a around 0 27.2%

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

      1. *-commutative 27.2%

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

   8. Simplified 27.2%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.4 \cdot 10^{+43} \lor \neg \left(j \leq 2.2 \cdot 10^{+138}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+43} \lor \neg \left(j \leq 5.3 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1e+43) (not (<= j 5.3e+138))) (* a (* c j)) (* 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 ((j <= -1e+43) || !(j <= 5.3e+138)) {
		tmp = a * (c * j);
	} 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 ((j <= (-1d+43)) .or. (.not. (j <= 5.3d+138))) then
        tmp = a * (c * j)
    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 ((j <= -1e+43) || !(j <= 5.3e+138)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1e+43) or not (j <= 5.3e+138):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1e+43) || !(j <= 5.3e+138))
		tmp = Float64(a * Float64(c * j));
	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 ((j <= -1e+43) || ~((j <= 5.3e+138)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1e+43], N[Not[LessEqual[j, 5.3e+138]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.00000000000000001e43 or 5.29999999999999984e138 < j

   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 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in c around inf 43.4%

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

   if -1.00000000000000001e43 < j < 5.29999999999999984e138

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 43.8%

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

      1. distribute-lft-out-- 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in a around 0 27.2%

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

      1. *-commutative 27.2%

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

   8. Simplified 27.2%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+43} \lor \neg \left(j \leq 5.3 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.3% 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 72.5%

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

3. Taylor expanded in a around inf 37.1%

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

   1. +-commutative 37.1%

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

   2. mul-1-neg 37.1%

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

   3. unsub-neg 37.1%

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

5. Simplified 37.1%

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

6. Taylor expanded in c around inf 20.6%

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

Developer Target 1: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024163 
(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)))))