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

Percentage Accurate: 73.4% → 82.7%

Time: 19.2s

Alternatives: 18

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;t\_1 + j \cdot t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \end{array} \end{array} \]

FPCore

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

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)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = t * (a * ((b * (i / a)) - x));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(t * N[(a * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $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 88.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.7%

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

      2. fma-define 88.7%

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

      3. *-commutative 88.7%

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

      4. *-commutative 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. 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 a around -inf 23.9%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in t around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

      3. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in t around 0 48.5%

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

       1. associate-*r* 48.5%

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

       2. neg-mul-1 48.5%

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

       3. *-commutative 48.5%

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

       4. associate-*r/ 48.7%

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

       5. *-commutative 48.7%

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

       6. associate-*l* 44.3%

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

       7. *-commutative 44.3%

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

       8. associate-*l* 54.9%

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

   11. Simplified 54.9%

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

4. Final simplification 82.6%

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

Alternative 2: 82.7% accurate, 0.5× speedup

Math

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

FPCore

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

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 = t * (a * ((b * (i / a)) - x));
	}
	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 = t * (a * ((b * (i / a)) - x));
	}
	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 = t * (a * ((b * (i / a)) - x))
	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(t * Float64(a * Float64(Float64(b * Float64(i / a)) - x)));
	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 = t * (a * ((b * (i / a)) - x));
	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[(t * N[(a * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $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 88.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around -inf 23.9%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in t around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

      3. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in t around 0 48.5%

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

       1. associate-*r* 48.5%

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

       2. neg-mul-1 48.5%

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

       3. *-commutative 48.5%

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

       4. associate-*r/ 48.7%

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

       5. *-commutative 48.7%

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

       6. associate-*l* 44.3%

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

       7. *-commutative 44.3%

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

       8. associate-*l* 54.9%

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

   11. Simplified 54.9%

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

4. Final simplification 82.6%

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

Alternative 3: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -6e+206)
     t_1
     (if (<= z 1.5e-148)
       (+
        (+ (* x (- (* y z) (* t a))) (* i (* t b)))
        (* j (- (* a c) (* y i))))
       (if (<= z 2.2e+118)
         (+ (* a (- (* c j) (* x t))) (* 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -6e+206) {
		tmp = t_1;
	} else if (z <= 1.5e-148) {
		tmp = ((x * ((y * z) - (t * a))) + (i * (t * b))) + (j * ((a * c) - (y * i)));
	} else if (z <= 2.2e+118) {
		tmp = (a * ((c * j) - (x * t))) + (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 = z * ((x * y) - (b * c))
    if (z <= (-6d+206)) then
        tmp = t_1
    else if (z <= 1.5d-148) then
        tmp = ((x * ((y * z) - (t * a))) + (i * (t * b))) + (j * ((a * c) - (y * i)))
    else if (z <= 2.2d+118) then
        tmp = (a * ((c * j) - (x * t))) + (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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -6e+206) {
		tmp = t_1;
	} else if (z <= 1.5e-148) {
		tmp = ((x * ((y * z) - (t * a))) + (i * (t * b))) + (j * ((a * c) - (y * i)));
	} else if (z <= 2.2e+118) {
		tmp = (a * ((c * j) - (x * t))) + (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 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -6e+206:
		tmp = t_1
	elif z <= 1.5e-148:
		tmp = ((x * ((y * z) - (t * a))) + (i * (t * b))) + (j * ((a * c) - (y * i)))
	elif z <= 2.2e+118:
		tmp = (a * ((c * j) - (x * t))) + (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(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -6e+206)
		tmp = t_1;
	elseif (z <= 1.5e-148)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(t * b))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (z <= 2.2e+118)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + 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 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -6e+206)
		tmp = t_1;
	elseif (z <= 1.5e-148)
		tmp = ((x * ((y * z) - (t * a))) + (i * (t * b))) + (j * ((a * c) - (y * i)));
	elseif (z <= 2.2e+118)
		tmp = (a * ((c * j) - (x * t))) + (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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+206], t$95$1, If[LessEqual[z, 1.5e-148], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+118], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000002e206 or 2.19999999999999986e118 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 81.7%

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

      1. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -6.0000000000000002e206 < z < 1.49999999999999999e-148

   1. Initial program 76.7%

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

   3. Taylor expanded in i around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. +-commutative 74.7%

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

      3. unsub-neg 74.7%

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

      4. associate-/l* 72.6%

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

      5. associate-/l* 72.1%

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

      6. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in c around 0 74.1%

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

      1. neg-mul-1 74.1%

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

      2. distribute-rgt-neg-in 74.1%

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

   8. Simplified 74.1%

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

   if 1.49999999999999999e-148 < z < 2.19999999999999986e118

   1. Initial program 75.5%

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

   3. Taylor expanded in y around 0 74.8%

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

   5. Simplified 76.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+206}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -880000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -880000000000.0)
     t_1
     (if (<= a -1.28e-219)
       (* t (* b i))
       (if (<= a 1.42e-216)
         (* b (* z (- c)))
         (if (<= a 8.4e-88)
           (* i (* j (- y)))
           (if (<= a 2.65e-24) (* i (* t b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -880000000000.0) {
		tmp = t_1;
	} else if (a <= -1.28e-219) {
		tmp = t * (b * i);
	} else if (a <= 1.42e-216) {
		tmp = b * (z * -c);
	} else if (a <= 8.4e-88) {
		tmp = i * (j * -y);
	} else if (a <= 2.65e-24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-880000000000.0d0)) then
        tmp = t_1
    else if (a <= (-1.28d-219)) then
        tmp = t * (b * i)
    else if (a <= 1.42d-216) then
        tmp = b * (z * -c)
    else if (a <= 8.4d-88) then
        tmp = i * (j * -y)
    else if (a <= 2.65d-24) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -880000000000.0) {
		tmp = t_1;
	} else if (a <= -1.28e-219) {
		tmp = t * (b * i);
	} else if (a <= 1.42e-216) {
		tmp = b * (z * -c);
	} else if (a <= 8.4e-88) {
		tmp = i * (j * -y);
	} else if (a <= 2.65e-24) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -880000000000.0:
		tmp = t_1
	elif a <= -1.28e-219:
		tmp = t * (b * i)
	elif a <= 1.42e-216:
		tmp = b * (z * -c)
	elif a <= 8.4e-88:
		tmp = i * (j * -y)
	elif a <= 2.65e-24:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -880000000000.0)
		tmp = t_1;
	elseif (a <= -1.28e-219)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 1.42e-216)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 8.4e-88)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 2.65e-24)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -880000000000.0)
		tmp = t_1;
	elseif (a <= -1.28e-219)
		tmp = t * (b * i);
	elseif (a <= 1.42e-216)
		tmp = b * (z * -c);
	elseif (a <= 8.4e-88)
		tmp = i * (j * -y);
	elseif (a <= 2.65e-24)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -880000000000.0], t$95$1, If[LessEqual[a, -1.28e-219], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-216], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-88], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-24], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.8e11 or 2.64999999999999984e-24 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in a around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   if -8.8e11 < a < -1.28000000000000002e-219

   1. Initial program 76.3%

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

   3. Taylor expanded in c around 0 78.0%

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

   4. Taylor expanded in i around -inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

      3. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   7. Taylor expanded in j around 0 35.9%

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

      1. *-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-*r* 39.2%

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

   9. Simplified 39.2%

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

   if -1.28000000000000002e-219 < a < 1.42000000000000004e-216

   1. Initial program 87.5%

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

   3. Taylor expanded in a around -inf 50.5%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in c around inf 38.0%

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

      1. associate-*r* 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. associate-/l* 34.8%

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

   8. Simplified 34.8%

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

   9. Taylor expanded in a around 0 43.2%

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

       1. associate-*r* 43.2%

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

       2. neg-mul-1 43.2%

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

   11. Simplified 43.2%

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

   if 1.42000000000000004e-216 < a < 8.3999999999999998e-88

   1. Initial program 81.5%

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

   3. Taylor expanded in c around 0 80.7%

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

   4. Taylor expanded in i around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in j around inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. neg-mul-1 51.0%

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

   9. Simplified 51.0%

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

   if 8.3999999999999998e-88 < a < 2.64999999999999984e-24

   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 c around 0 61.9%

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

   4. Taylor expanded in i around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

      3. *-commutative 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in j around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. *-commutative 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

   9. Simplified 65.1%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -880000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{t\_1}{a} - x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -9.2e+133)
     t_2
     (if (<= z -2.2e-240)
       (+ (* j (- (* a c) (* y i))) t_1)
       (if (<= z 9e+117) (* a (+ (* c j) (- (/ t_1 a) (* x t)))) 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 = b * (t * i);
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.2e+133) {
		tmp = t_2;
	} else if (z <= -2.2e-240) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (z <= 9e+117) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} 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 = b * (t * i)
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-9.2d+133)) then
        tmp = t_2
    else if (z <= (-2.2d-240)) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if (z <= 9d+117) then
        tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
    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 = b * (t * i);
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.2e+133) {
		tmp = t_2;
	} else if (z <= -2.2e-240) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (z <= 9e+117) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9.2e+133:
		tmp = t_2
	elif z <= -2.2e-240:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif z <= 9e+117:
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9.2e+133)
		tmp = t_2;
	elseif (z <= -2.2e-240)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif (z <= 9e+117)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(t_1 / a) - Float64(x * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9.2e+133)
		tmp = t_2;
	elseif (z <= -2.2e-240)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif (z <= 9e+117)
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+133], t$95$2, If[LessEqual[z, -2.2e-240], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 9e+117], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999996e133 or 9e117 < z

   1. Initial program 63.9%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -9.1999999999999996e133 < z < -2.1999999999999999e-240

   1. Initial program 76.0%

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

   3. Taylor expanded in i around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. +-commutative 69.2%

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

      3. unsub-neg 69.2%

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

      4. associate-/l* 66.5%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in c around 0 70.6%

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

      1. neg-mul-1 70.6%

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

      2. distribute-rgt-neg-in 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in x around 0 65.1%

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

       1. associate-*r* 65.1%

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

       2. neg-mul-1 65.1%

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

       3. *-commutative 65.1%

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

   11. Simplified 65.1%

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

   if -2.1999999999999999e-240 < z < 9e117

   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 a around -inf 76.6%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around inf 64.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{b \cdot \left(t \cdot i\right)}{a} - x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-211}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-87}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -6e+14)
     t_1
     (if (<= a -2.9e-211)
       (* t (* b i))
       (if (<= a 2.7e-216)
         (* b (* z (- c)))
         (if (<= a 4.3e-87)
           (* i (* j (- y)))
           (if (<= a 4.4e-16) (* i (* t b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -6e+14) {
		tmp = t_1;
	} else if (a <= -2.9e-211) {
		tmp = t * (b * i);
	} else if (a <= 2.7e-216) {
		tmp = b * (z * -c);
	} else if (a <= 4.3e-87) {
		tmp = i * (j * -y);
	} else if (a <= 4.4e-16) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-6d+14)) then
        tmp = t_1
    else if (a <= (-2.9d-211)) then
        tmp = t * (b * i)
    else if (a <= 2.7d-216) then
        tmp = b * (z * -c)
    else if (a <= 4.3d-87) then
        tmp = i * (j * -y)
    else if (a <= 4.4d-16) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -6e+14) {
		tmp = t_1;
	} else if (a <= -2.9e-211) {
		tmp = t * (b * i);
	} else if (a <= 2.7e-216) {
		tmp = b * (z * -c);
	} else if (a <= 4.3e-87) {
		tmp = i * (j * -y);
	} else if (a <= 4.4e-16) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -6e+14:
		tmp = t_1
	elif a <= -2.9e-211:
		tmp = t * (b * i)
	elif a <= 2.7e-216:
		tmp = b * (z * -c)
	elif a <= 4.3e-87:
		tmp = i * (j * -y)
	elif a <= 4.4e-16:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -6e+14)
		tmp = t_1;
	elseif (a <= -2.9e-211)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.7e-216)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 4.3e-87)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 4.4e-16)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -6e+14)
		tmp = t_1;
	elseif (a <= -2.9e-211)
		tmp = t * (b * i);
	elseif (a <= 2.7e-216)
		tmp = b * (z * -c);
	elseif (a <= 4.3e-87)
		tmp = i * (j * -y);
	elseif (a <= 4.4e-16)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+14], t$95$1, If[LessEqual[a, -2.9e-211], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-216], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-87], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-16], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6e14 or 4.40000000000000001e-16 < a

   1. Initial program 65.2%

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

   3. Taylor expanded in a around -inf 75.3%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in c around inf 56.1%

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

      1. associate-*r* 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in j around inf 46.2%

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

   if -6e14 < a < -2.90000000000000014e-211

   1. Initial program 76.3%

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

   3. Taylor expanded in c around 0 78.0%

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

   4. Taylor expanded in i around -inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

      3. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   7. Taylor expanded in j around 0 35.9%

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

      1. *-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-*r* 39.2%

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

   9. Simplified 39.2%

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

   if -2.90000000000000014e-211 < a < 2.6999999999999999e-216

   1. Initial program 87.5%

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

   3. Taylor expanded in a around -inf 50.5%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in c around inf 38.0%

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

      1. associate-*r* 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. associate-/l* 34.8%

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

   8. Simplified 34.8%

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

   9. Taylor expanded in a around 0 43.2%

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

       1. associate-*r* 43.2%

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

       2. neg-mul-1 43.2%

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

   11. Simplified 43.2%

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

   if 2.6999999999999999e-216 < a < 4.29999999999999995e-87

   1. Initial program 81.5%

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

   3. Taylor expanded in c around 0 80.7%

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

   4. Taylor expanded in i around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in j around inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. neg-mul-1 51.0%

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

   9. Simplified 51.0%

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

   if 4.29999999999999995e-87 < a < 4.40000000000000001e-16

   1. Initial program 71.1%

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

   3. Taylor expanded in c around 0 64.7%

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

   4. Taylor expanded in i around -inf 67.5%

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

      1. associate-*r* 67.5%

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

      2. neg-mul-1 67.5%

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

      3. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in j around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. *-commutative 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

   9. Simplified 60.7%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-211}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-87}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -920000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -920000000000.0)
     t_1
     (if (<= a -6.2e-217)
       (* t (* b i))
       (if (<= a 2.5e-218)
         (* b (* z (- c)))
         (if (<= a 1.55e-87)
           (* i (* j (- y)))
           (if (<= a 1e-14) (* b (* t i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -920000000000.0) {
		tmp = t_1;
	} else if (a <= -6.2e-217) {
		tmp = t * (b * i);
	} else if (a <= 2.5e-218) {
		tmp = b * (z * -c);
	} else if (a <= 1.55e-87) {
		tmp = i * (j * -y);
	} else if (a <= 1e-14) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-920000000000.0d0)) then
        tmp = t_1
    else if (a <= (-6.2d-217)) then
        tmp = t * (b * i)
    else if (a <= 2.5d-218) then
        tmp = b * (z * -c)
    else if (a <= 1.55d-87) then
        tmp = i * (j * -y)
    else if (a <= 1d-14) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -920000000000.0) {
		tmp = t_1;
	} else if (a <= -6.2e-217) {
		tmp = t * (b * i);
	} else if (a <= 2.5e-218) {
		tmp = b * (z * -c);
	} else if (a <= 1.55e-87) {
		tmp = i * (j * -y);
	} else if (a <= 1e-14) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -920000000000.0:
		tmp = t_1
	elif a <= -6.2e-217:
		tmp = t * (b * i)
	elif a <= 2.5e-218:
		tmp = b * (z * -c)
	elif a <= 1.55e-87:
		tmp = i * (j * -y)
	elif a <= 1e-14:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -920000000000.0)
		tmp = t_1;
	elseif (a <= -6.2e-217)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.5e-218)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 1.55e-87)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 1e-14)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -920000000000.0)
		tmp = t_1;
	elseif (a <= -6.2e-217)
		tmp = t * (b * i);
	elseif (a <= 2.5e-218)
		tmp = b * (z * -c);
	elseif (a <= 1.55e-87)
		tmp = i * (j * -y);
	elseif (a <= 1e-14)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -920000000000.0], t$95$1, If[LessEqual[a, -6.2e-217], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-218], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-87], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-14], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.2e11 or 9.99999999999999999e-15 < a

   1. Initial program 65.2%

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

   3. Taylor expanded in a around -inf 75.3%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in c around inf 56.1%

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

      1. associate-*r* 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in j around inf 46.2%

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

   if -9.2e11 < a < -6.1999999999999997e-217

   1. Initial program 76.3%

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

   3. Taylor expanded in c around 0 78.0%

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

   4. Taylor expanded in i around -inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

      3. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   7. Taylor expanded in j around 0 35.9%

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

      1. *-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-*r* 39.2%

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

   9. Simplified 39.2%

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

   if -6.1999999999999997e-217 < a < 2.50000000000000021e-218

   1. Initial program 87.5%

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

   3. Taylor expanded in a around -inf 50.5%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in c around inf 38.0%

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

      1. associate-*r* 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. associate-/l* 34.8%

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

   8. Simplified 34.8%

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

   9. Taylor expanded in a around 0 43.2%

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

       1. associate-*r* 43.2%

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

       2. neg-mul-1 43.2%

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

   11. Simplified 43.2%

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

   if 2.50000000000000021e-218 < a < 1.54999999999999999e-87

   1. Initial program 81.5%

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

   3. Taylor expanded in c around 0 80.7%

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

   4. Taylor expanded in i around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in j around inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. neg-mul-1 51.0%

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

   9. Simplified 51.0%

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

   if 1.54999999999999999e-87 < a < 9.99999999999999999e-15

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in t around inf 53.9%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -920000000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -4.5e-62)
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
   (if (<= y 1.55e+126)
     (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
     (* y (- (* x z) (* 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 (y <= -4.5e-62) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (y <= 1.55e+126) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = y * ((x * z) - (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 (y <= (-4.5d-62)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (y <= 1.55d+126) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else
        tmp = y * ((x * z) - (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 (y <= -4.5e-62) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (y <= 1.55e+126) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -4.5e-62:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif y <= 1.55e+126:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -4.5e-62)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (y <= 1.55e+126)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(y * Float64(Float64(x * z) - 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 (y <= -4.5e-62)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (y <= 1.55e+126)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -4.5e-62], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+126], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000018e-62

   1. Initial program 72.4%

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

   3. Taylor expanded in b around 0 67.9%

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

   if -4.50000000000000018e-62 < y < 1.55e126

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 72.6%

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

   5. Simplified 74.7%

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

   if 1.55e126 < y

   1. Initial program 57.6%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

      4. *-commutative 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+73}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -5e+73)
     (- t_1 (* i (* y j)))
     (if (<= x 2.8e+74)
       (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
       (+ t_1 (* b (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5e+73) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 2.8e+74) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 + (b * (t * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-5d+73)) then
        tmp = t_1 - (i * (y * j))
    else if (x <= 2.8d+74) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1 + (b * (t * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5e+73) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 2.8e+74) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 + (b * (t * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5e+73:
		tmp = t_1 - (i * (y * j))
	elif x <= 2.8e+74:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1 + (b * (t * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5e+73)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (x <= 2.8e+74)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5e+73)
		tmp = t_1 - (i * (y * j));
	elseif (x <= 2.8e+74)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1 + (b * (t * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+73], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+74], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999976e73

   1. Initial program 72.4%

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

   3. Taylor expanded in b around 0 69.5%

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

   4. Taylor expanded in c around 0 69.7%

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

      1. neg-mul-1 69.7%

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

      2. +-commutative 69.7%

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

      3. *-commutative 69.7%

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

      4. unsub-neg 69.7%

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

   6. Simplified 69.7%

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

   if -4.99999999999999976e73 < x < 2.80000000000000002e74

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 69.8%

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

   5. Simplified 71.5%

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

   if 2.80000000000000002e74 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in i around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. +-commutative 67.6%

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

      3. unsub-neg 67.6%

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

      4. associate-/l* 67.6%

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

      5. associate-/l* 69.8%

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

      6. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in c around 0 70.0%

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

      1. neg-mul-1 70.0%

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

      2. distribute-rgt-neg-in 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in j around 0 74.8%

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

       1. associate-*r* 74.8%

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

       2. neg-mul-1 74.8%

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

       3. *-commutative 74.8%

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

   11. Simplified 74.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+134} \lor \neg \left(z \leq 5.5 \cdot 10^{+116}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.52e+134) (not (<= z 5.5e+116)))
   (* z (- (* x y) (* b c)))
   (+ (* j (- (* a c) (* y i))) (* 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 ((z <= -1.52e+134) || !(z <= 5.5e+116)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (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 ((z <= (-1.52d+134)) .or. (.not. (z <= 5.5d+116))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (j * ((a * c) - (y * i))) + (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 ((z <= -1.52e+134) || !(z <= 5.5e+116)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.52e+134) or not (z <= 5.5e+116):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.52e+134) || !(z <= 5.5e+116))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + 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 ((z <= -1.52e+134) || ~((z <= 5.5e+116)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.52e+134], N[Not[LessEqual[z, 5.5e+116]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5200000000000001e134 or 5.50000000000000035e116 < z

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf 76.2%

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

      1. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   if -1.5200000000000001e134 < z < 5.50000000000000035e116

   1. Initial program 76.7%

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

   3. Taylor expanded in i around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. +-commutative 73.6%

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

      3. unsub-neg 73.6%

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

      4. associate-/l* 72.0%

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

      5. associate-/l* 71.0%

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

      6. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in c around 0 71.6%

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

      1. neg-mul-1 71.6%

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

      2. distribute-rgt-neg-in 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in x around 0 61.0%

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

       1. associate-*r* 61.0%

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

       2. neg-mul-1 61.0%

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

       3. *-commutative 61.0%

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

   11. Simplified 61.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+134} \lor \neg \left(z \leq 5.5 \cdot 10^{+116}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -260:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(z \cdot \left(\frac{j}{z} - \frac{b}{a}\right)\right)\\ \mathbf{elif}\;c \leq 5500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -260.0)
   (* (* a c) (* z (- (/ j z) (/ b a))))
   (if (<= c 5500000000000.0)
     (- (* x (- (* y z) (* t a))) (* i (* y j)))
     (* 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 tmp;
	if (c <= -260.0) {
		tmp = (a * c) * (z * ((j / z) - (b / a)));
	} else if (c <= 5500000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-260.0d0)) then
        tmp = (a * c) * (z * ((j / z) - (b / a)))
    else if (c <= 5500000000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -260.0) {
		tmp = (a * c) * (z * ((j / z) - (b / a)));
	} else if (c <= 5500000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -260.0:
		tmp = (a * c) * (z * ((j / z) - (b / a)))
	elif c <= 5500000000000.0:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -260.0)
		tmp = Float64(Float64(a * c) * Float64(z * Float64(Float64(j / z) - Float64(b / a))));
	elseif (c <= 5500000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	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)
	tmp = 0.0;
	if (c <= -260.0)
		tmp = (a * c) * (z * ((j / z) - (b / a)));
	elseif (c <= 5500000000000.0)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -260.0], N[(N[(a * c), $MachinePrecision] * N[(z * N[(N[(j / z), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5500000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -260

   1. Initial program 65.5%

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

   3. Taylor expanded in a around -inf 62.1%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in c around inf 59.9%

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

      1. associate-*r* 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in z around inf 65.9%

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

   if -260 < c < 5.5e12

   1. Initial program 79.4%

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

   3. Taylor expanded in b around 0 63.4%

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

   4. Taylor expanded in c around 0 60.0%

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

      1. neg-mul-1 60.0%

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

      2. +-commutative 60.0%

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

      3. *-commutative 60.0%

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

      4. unsub-neg 60.0%

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

   6. Simplified 60.0%

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

   if 5.5e12 < c

   1. Initial program 69.7%

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

   3. Taylor expanded in c around inf 70.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -260:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(z \cdot \left(\frac{j}{z} - \frac{b}{a}\right)\right)\\ \mathbf{elif}\;c \leq 5500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.55e+134)
   (* x (* y z))
   (if (<= z 3.2e-162)
     (* a (* c j))
     (if (<= z 8.6e+118) (* a (- (* x t))) (* z (* b (- c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.55e+134) {
		tmp = x * (y * z);
	} else if (z <= 3.2e-162) {
		tmp = a * (c * j);
	} else if (z <= 8.6e+118) {
		tmp = a * -(x * t);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.55d+134)) then
        tmp = x * (y * z)
    else if (z <= 3.2d-162) then
        tmp = a * (c * j)
    else if (z <= 8.6d+118) then
        tmp = a * -(x * t)
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.55e+134) {
		tmp = x * (y * z);
	} else if (z <= 3.2e-162) {
		tmp = a * (c * j);
	} else if (z <= 8.6e+118) {
		tmp = a * -(x * t);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.55e+134:
		tmp = x * (y * z)
	elif z <= 3.2e-162:
		tmp = a * (c * j)
	elif z <= 8.6e+118:
		tmp = a * -(x * t)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.55e+134)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 3.2e-162)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 8.6e+118)
		tmp = Float64(a * Float64(-Float64(x * t)));
	else
		tmp = Float64(z * Float64(b * 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 <= -1.55e+134)
		tmp = x * (y * z);
	elseif (z <= 3.2e-162)
		tmp = a * (c * j);
	elseif (z <= 8.6e+118)
		tmp = a * -(x * t);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.55e+134], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-162], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+118], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.54999999999999991e134

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf 55.1%

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

   if -1.54999999999999991e134 < z < 3.19999999999999975e-162

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in c around inf 34.4%

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

   if 3.19999999999999975e-162 < z < 8.6000000000000006e118

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in c around 0 35.6%

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

      1. associate-*r* 35.6%

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

      2. neg-mul-1 35.6%

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

   8. Simplified 35.6%

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

   if 8.6000000000000006e118 < z

   1. Initial program 59.6%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. *-commutative 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-lft-neg-out 61.9%

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

      3. *-commutative 61.9%

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

   8. Simplified 61.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+15} \lor \neg \left(a \leq 4 \cdot 10^{-11}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -7.2e+15) (not (<= a 4e-11)))
   (* 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 <= -7.2e+15) || !(a <= 4e-11)) {
		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 <= (-7.2d+15)) .or. (.not. (a <= 4d-11))) 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 <= -7.2e+15) || !(a <= 4e-11)) {
		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 <= -7.2e+15) or not (a <= 4e-11):
		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 <= -7.2e+15) || !(a <= 4e-11))
		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 <= -7.2e+15) || ~((a <= 4e-11)))
		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, -7.2e+15], N[Not[LessEqual[a, 4e-11]], $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 < -7.2e15 or 3.99999999999999976e-11 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if -7.2e15 < a < 3.99999999999999976e-11

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+15} \lor \neg \left(a \leq 4 \cdot 10^{-11}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(a \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.1e-9)
   (* t (* a (- (/ (* c j) t) x)))
   (if (<= a 3.6e-11) (* b (- (* t i) (* z c))) (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.1e-9) {
		tmp = t * (a * (((c * j) / t) - x));
	} else if (a <= 3.6e-11) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.1d-9)) then
        tmp = t * (a * (((c * j) / t) - x))
    else if (a <= 3.6d-11) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.1e-9) {
		tmp = t * (a * (((c * j) / t) - x));
	} else if (a <= 3.6e-11) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.1e-9:
		tmp = t * (a * (((c * j) / t) - x))
	elif a <= 3.6e-11:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.1e-9)
		tmp = Float64(t * Float64(a * Float64(Float64(Float64(c * j) / t) - x)));
	elseif (a <= 3.6e-11)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.1e-9)
		tmp = t * (a * (((c * j) / t) - x));
	elseif (a <= 3.6e-11)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.1e-9], N[(t * N[(a * N[(N[(N[(c * j), $MachinePrecision] / t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-11], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.10000000000000019e-9

   1. Initial program 64.8%

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

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. mul-1-neg 66.2%

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

      3. unsub-neg 66.2%

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

      4. associate-/l* 66.2%

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

      5. associate-/l* 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in a around 0 67.8%

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

   if -2.10000000000000019e-9 < a < 3.59999999999999985e-11

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   if 3.59999999999999985e-11 < a

   1. Initial program 64.8%

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

   3. Taylor expanded in a around inf 69.6%

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

      1. +-commutative 69.6%

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

      2. mul-1-neg 69.6%

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

      3. unsub-neg 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(a \cdot \left(\frac{c \cdot j}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -4.3e+133)
   (* x (* y z))
   (if (<= z 1.7e-20) (* a (* c j)) (* z (* b (- c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -4.3e+133) {
		tmp = x * (y * z);
	} else if (z <= 1.7e-20) {
		tmp = a * (c * j);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-4.3d+133)) then
        tmp = x * (y * z)
    else if (z <= 1.7d-20) then
        tmp = a * (c * j)
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -4.3e+133) {
		tmp = x * (y * z);
	} else if (z <= 1.7e-20) {
		tmp = a * (c * j);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -4.3e+133:
		tmp = x * (y * z)
	elif z <= 1.7e-20:
		tmp = a * (c * j)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -4.3e+133)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.7e-20)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(z * Float64(b * 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 <= -4.3e+133)
		tmp = x * (y * z);
	elseif (z <= 1.7e-20)
		tmp = a * (c * j);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -4.3e+133], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-20], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999994e133

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf 55.1%

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

   if -4.29999999999999994e133 < z < 1.6999999999999999e-20

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in c around inf 33.8%

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

   if 1.6999999999999999e-20 < z

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. distribute-lft-neg-out 45.0%

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

      3. *-commutative 45.0%

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

   8. Simplified 45.0%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3800000000000 \lor \neg \left(a \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3800000000000.0) (not (<= a 9.5e-16)))
   (* j (* a c))
   (* 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 ((a <= -3800000000000.0) || !(a <= 9.5e-16)) {
		tmp = j * (a * c);
	} 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 ((a <= (-3800000000000.0d0)) .or. (.not. (a <= 9.5d-16))) then
        tmp = j * (a * c)
    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 ((a <= -3800000000000.0) || !(a <= 9.5e-16)) {
		tmp = j * (a * c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -3800000000000.0) or not (a <= 9.5e-16):
		tmp = j * (a * c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3800000000000.0) || !(a <= 9.5e-16))
		tmp = Float64(j * Float64(a * c));
	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 ((a <= -3800000000000.0) || ~((a <= 9.5e-16)))
		tmp = j * (a * c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3800000000000.0], N[Not[LessEqual[a, 9.5e-16]], $MachinePrecision]], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8e12 or 9.5000000000000005e-16 < a

   1. Initial program 65.2%

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

   3. Taylor expanded in a around -inf 75.3%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in c around inf 56.1%

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

      1. associate-*r* 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in j around inf 46.2%

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

   if -3.8e12 < a < 9.5000000000000005e-16

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in t around inf 32.0%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3800000000000 \lor \neg \left(a \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1760000000000 \lor \neg \left(a \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1760000000000.0) (not (<= a 4.5e-20)))
   (* 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 ((a <= -1760000000000.0) || !(a <= 4.5e-20)) {
		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 ((a <= (-1760000000000.0d0)) .or. (.not. (a <= 4.5d-20))) 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 ((a <= -1760000000000.0) || !(a <= 4.5e-20)) {
		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 (a <= -1760000000000.0) or not (a <= 4.5e-20):
		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 ((a <= -1760000000000.0) || !(a <= 4.5e-20))
		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 ((a <= -1760000000000.0) || ~((a <= 4.5e-20)))
		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[a, -1760000000000.0], N[Not[LessEqual[a, 4.5e-20]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.76e12 or 4.5000000000000001e-20 < a

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in c around inf 44.7%

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

   if -1.76e12 < a < 4.5000000000000001e-20

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in t around inf 32.0%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1760000000000 \lor \neg \left(a \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.7%

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

3. Taylor expanded in a around inf 41.3%

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

   1. +-commutative 41.3%

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

   2. mul-1-neg 41.3%

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

   3. unsub-neg 41.3%

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

5. Simplified 41.3%

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

6. Taylor expanded in c around inf 25.9%

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

Developer Target 1: 59.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024136 
(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)))))