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

Percentage Accurate: 73.6% → 84.2%

Time: 29.5s

Alternatives: 24

Speedup: 0.5×

• 58.9% 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: 73.6% 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: 84.2% accurate, 0.2× speedup

Math

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

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)
     (*
      a
      (* j (+ (- c (* t (/ x j))) (/ (- (* x (* y (/ z j))) (* y i)) a)))))))

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 = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	}
	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(a * Float64(j * Float64(Float64(c - Float64(t * Float64(x / j))) + Float64(Float64(Float64(x * Float64(y * Float64(z / j))) - Float64(y * i)) / a))));
	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[(a * N[(j * N[(N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(y * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. fma-define 91.0%

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

      3. *-commutative 91.0%

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

      4. *-commutative 91.0%

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

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   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 b around 0 25.0%

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

   4. Taylor expanded in j around inf 33.3%

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

   5. Taylor expanded in a around inf 50.0%

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

      1. associate-/l* 51.7%

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

      2. distribute-lft-out 58.4%

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

      3. mul-1-neg 58.4%

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

      4. unsub-neg 58.4%

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

      5. associate-/l* 58.4%

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

      6. associate-/l* 61.7%

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

      7. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

4. Final simplification 84.5%

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

Alternative 2: 84.2% accurate, 0.5× speedup

Math

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

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
     (*
      a
      (* j (+ (- c (* t (/ x j))) (/ (- (* x (* y (/ z j))) (* y i)) a)))))))

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 = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	}
	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 = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	}
	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 = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)))
	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(a * Float64(j * Float64(Float64(c - Float64(t * Float64(x / j))) + Float64(Float64(Float64(x * Float64(y * Float64(z / j))) - Float64(y * i)) / a))));
	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 = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	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[(a * N[(j * N[(N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(y * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0 25.0%

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

   4. Taylor expanded in j around inf 33.3%

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

   5. Taylor expanded in a around inf 50.0%

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

      1. associate-/l* 51.7%

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

      2. distribute-lft-out 58.4%

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

      3. mul-1-neg 58.4%

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

      4. unsub-neg 58.4%

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

      5. associate-/l* 58.4%

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

      6. associate-/l* 61.7%

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

      7. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

4. Final simplification 84.5%

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

Alternative 3: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := \left(c - t \cdot \frac{x}{j}\right) \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -1550000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* (- c (* t (/ x j))) (* a j))))
   (if (<= a -1550000000.0)
     t_3
     (if (<= a -1.32e-158)
       t_2
       (if (<= a -2.9e-223)
         t_1
         (if (<= a -6e-261)
           (* i (- (* t b) (* y j)))
           (if (<= a 2.6e-136)
             t_1
             (if (<= a 1.2e+21)
               t_2
               (if (<= a 2.15e+123) (* b (- (* t i) (* z c))) t_3)))))))))

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 t_2 = y * ((x * z) - (i * j));
	double t_3 = (c - (t * (x / j))) * (a * j);
	double tmp;
	if (a <= -1550000000.0) {
		tmp = t_3;
	} else if (a <= -1.32e-158) {
		tmp = t_2;
	} else if (a <= -2.9e-223) {
		tmp = t_1;
	} else if (a <= -6e-261) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 2.6e-136) {
		tmp = t_1;
	} else if (a <= 1.2e+21) {
		tmp = t_2;
	} else if (a <= 2.15e+123) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = (c - (t * (x / j))) * (a * j)
    if (a <= (-1550000000.0d0)) then
        tmp = t_3
    else if (a <= (-1.32d-158)) then
        tmp = t_2
    else if (a <= (-2.9d-223)) then
        tmp = t_1
    else if (a <= (-6d-261)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 2.6d-136) then
        tmp = t_1
    else if (a <= 1.2d+21) then
        tmp = t_2
    else if (a <= 2.15d+123) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_3
    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 t_2 = y * ((x * z) - (i * j));
	double t_3 = (c - (t * (x / j))) * (a * j);
	double tmp;
	if (a <= -1550000000.0) {
		tmp = t_3;
	} else if (a <= -1.32e-158) {
		tmp = t_2;
	} else if (a <= -2.9e-223) {
		tmp = t_1;
	} else if (a <= -6e-261) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 2.6e-136) {
		tmp = t_1;
	} else if (a <= 1.2e+21) {
		tmp = t_2;
	} else if (a <= 2.15e+123) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = (c - (t * (x / j))) * (a * j)
	tmp = 0
	if a <= -1550000000.0:
		tmp = t_3
	elif a <= -1.32e-158:
		tmp = t_2
	elif a <= -2.9e-223:
		tmp = t_1
	elif a <= -6e-261:
		tmp = i * ((t * b) - (y * j))
	elif a <= 2.6e-136:
		tmp = t_1
	elif a <= 1.2e+21:
		tmp = t_2
	elif a <= 2.15e+123:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_3
	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)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(Float64(c - Float64(t * Float64(x / j))) * Float64(a * j))
	tmp = 0.0
	if (a <= -1550000000.0)
		tmp = t_3;
	elseif (a <= -1.32e-158)
		tmp = t_2;
	elseif (a <= -2.9e-223)
		tmp = t_1;
	elseif (a <= -6e-261)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 2.6e-136)
		tmp = t_1;
	elseif (a <= 1.2e+21)
		tmp = t_2;
	elseif (a <= 2.15e+123)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_3;
	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));
	t_2 = y * ((x * z) - (i * j));
	t_3 = (c - (t * (x / j))) * (a * j);
	tmp = 0.0;
	if (a <= -1550000000.0)
		tmp = t_3;
	elseif (a <= -1.32e-158)
		tmp = t_2;
	elseif (a <= -2.9e-223)
		tmp = t_1;
	elseif (a <= -6e-261)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 2.6e-136)
		tmp = t_1;
	elseif (a <= 1.2e+21)
		tmp = t_2;
	elseif (a <= 2.15e+123)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1550000000.0], t$95$3, If[LessEqual[a, -1.32e-158], t$95$2, If[LessEqual[a, -2.9e-223], t$95$1, If[LessEqual[a, -6e-261], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-136], t$95$1, If[LessEqual[a, 1.2e+21], t$95$2, If[LessEqual[a, 2.15e+123], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.55e9 or 2.14999999999999993e123 < a

   1. Initial program 63.6%

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

   3. Taylor expanded in b around 0 64.3%

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

   4. Taylor expanded in j around inf 60.6%

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

   5. Taylor expanded in a around inf 65.5%

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

      1. associate-*r* 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. associate-/l* 70.0%

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

   7. Simplified 70.0%

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

   if -1.55e9 < a < -1.3200000000000001e-158 or 2.59999999999999997e-136 < a < 1.2e21

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   if -1.3200000000000001e-158 < a < -2.9e-223 or -6.0000000000000001e-261 < a < 2.59999999999999997e-136

   1. Initial program 76.8%

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

   3. Taylor expanded in z around inf 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -2.9e-223 < a < -6.0000000000000001e-261

   1. Initial program 71.4%

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

   3. Taylor expanded in i around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 1.2e21 < a < 2.14999999999999993e123

   1. Initial program 56.7%

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

   3. Taylor expanded in b around inf 53.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1550000000:\\ \;\;\;\;\left(c - t \cdot \frac{x}{j}\right) \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c - t \cdot \frac{x}{j}\right) \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{-118}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+169}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t b) (- i (* c (/ z t)))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i))))))
   (if (<= x -9e-118)
     t_3
     (if (<= x 7.8e-237)
       t_1
       (if (<= x 1.7e-31)
         t_3
         (if (<= x 8.5e+66) t_1 (if (<= x 1.46e+169) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * b) * (i - (c * (z / t)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (x <= -9e-118) {
		tmp = t_3;
	} else if (x <= 7.8e-237) {
		tmp = t_1;
	} else if (x <= 1.7e-31) {
		tmp = t_3;
	} else if (x <= 8.5e+66) {
		tmp = t_1;
	} else if (x <= 1.46e+169) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (t * b) * (i - (c * (z / t)))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (j * ((a * c) - (y * i)))
    if (x <= (-9d-118)) then
        tmp = t_3
    else if (x <= 7.8d-237) then
        tmp = t_1
    else if (x <= 1.7d-31) then
        tmp = t_3
    else if (x <= 8.5d+66) then
        tmp = t_1
    else if (x <= 1.46d+169) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * b) * (i - (c * (z / t)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (x <= -9e-118) {
		tmp = t_3;
	} else if (x <= 7.8e-237) {
		tmp = t_1;
	} else if (x <= 1.7e-31) {
		tmp = t_3;
	} else if (x <= 8.5e+66) {
		tmp = t_1;
	} else if (x <= 1.46e+169) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * b) * (i - (c * (z / t)))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (j * ((a * c) - (y * i)))
	tmp = 0
	if x <= -9e-118:
		tmp = t_3
	elif x <= 7.8e-237:
		tmp = t_1
	elif x <= 1.7e-31:
		tmp = t_3
	elif x <= 8.5e+66:
		tmp = t_1
	elif x <= 1.46e+169:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * b) * Float64(i - Float64(c * Float64(z / t))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (x <= -9e-118)
		tmp = t_3;
	elseif (x <= 7.8e-237)
		tmp = t_1;
	elseif (x <= 1.7e-31)
		tmp = t_3;
	elseif (x <= 8.5e+66)
		tmp = t_1;
	elseif (x <= 1.46e+169)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * b) * (i - (c * (z / t)));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (x <= -9e-118)
		tmp = t_3;
	elseif (x <= 7.8e-237)
		tmp = t_1;
	elseif (x <= 1.7e-31)
		tmp = t_3;
	elseif (x <= 8.5e+66)
		tmp = t_1;
	elseif (x <= 1.46e+169)
		tmp = t_3;
	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[(N[(t * b), $MachinePrecision] * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e-118], t$95$3, If[LessEqual[x, 7.8e-237], t$95$1, If[LessEqual[x, 1.7e-31], t$95$3, If[LessEqual[x, 8.5e+66], t$95$1, If[LessEqual[x, 1.46e+169], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000001e-118 or 7.7999999999999997e-237 < x < 1.7000000000000001e-31 or 8.5000000000000004e66 < x < 1.45999999999999992e169

   1. Initial program 76.6%

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

   3. Taylor expanded in b around 0 69.7%

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

   if -9.0000000000000001e-118 < x < 7.7999999999999997e-237 or 1.7000000000000001e-31 < x < 8.5000000000000004e66

   1. Initial program 66.1%

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

   3. Taylor expanded in t around inf 71.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in b around inf 61.9%

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

      1. associate-*r* 63.3%

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

      2. associate-/l* 62.9%

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

   8. Simplified 62.9%

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

   if 1.45999999999999992e169 < x

   1. Initial program 46.7%

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

   3. Taylor expanded in b around 0 46.7%

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

   4. Taylor expanded in j around 0 75.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-237}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+66}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{+113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -5e+113)
     t_3
     (if (<= j -3.8e-206)
       t_2
       (if (<= j -2.2e-284)
         t_1
         (if (<= j 4.3e-218)
           (* t (- (* b i) (* x a)))
           (if (<= j 4.5e-117) t_1 (if (<= j 4.5e+26) t_2 t_3))))))))

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 t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5e+113) {
		tmp = t_3;
	} else if (j <= -3.8e-206) {
		tmp = t_2;
	} else if (j <= -2.2e-284) {
		tmp = t_1;
	} else if (j <= 4.3e-218) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.5e-117) {
		tmp = t_1;
	} else if (j <= 4.5e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-5d+113)) then
        tmp = t_3
    else if (j <= (-3.8d-206)) then
        tmp = t_2
    else if (j <= (-2.2d-284)) then
        tmp = t_1
    else if (j <= 4.3d-218) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 4.5d-117) then
        tmp = t_1
    else if (j <= 4.5d+26) then
        tmp = t_2
    else
        tmp = t_3
    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 t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5e+113) {
		tmp = t_3;
	} else if (j <= -3.8e-206) {
		tmp = t_2;
	} else if (j <= -2.2e-284) {
		tmp = t_1;
	} else if (j <= 4.3e-218) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.5e-117) {
		tmp = t_1;
	} else if (j <= 4.5e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -5e+113:
		tmp = t_3
	elif j <= -3.8e-206:
		tmp = t_2
	elif j <= -2.2e-284:
		tmp = t_1
	elif j <= 4.3e-218:
		tmp = t * ((b * i) - (x * a))
	elif j <= 4.5e-117:
		tmp = t_1
	elif j <= 4.5e+26:
		tmp = t_2
	else:
		tmp = t_3
	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)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5e+113)
		tmp = t_3;
	elseif (j <= -3.8e-206)
		tmp = t_2;
	elseif (j <= -2.2e-284)
		tmp = t_1;
	elseif (j <= 4.3e-218)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 4.5e-117)
		tmp = t_1;
	elseif (j <= 4.5e+26)
		tmp = t_2;
	else
		tmp = t_3;
	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));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -5e+113)
		tmp = t_3;
	elseif (j <= -3.8e-206)
		tmp = t_2;
	elseif (j <= -2.2e-284)
		tmp = t_1;
	elseif (j <= 4.3e-218)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 4.5e-117)
		tmp = t_1;
	elseif (j <= 4.5e+26)
		tmp = t_2;
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e+113], t$95$3, If[LessEqual[j, -3.8e-206], t$95$2, If[LessEqual[j, -2.2e-284], t$95$1, If[LessEqual[j, 4.3e-218], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-117], t$95$1, If[LessEqual[j, 4.5e+26], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5e113 or 4.49999999999999978e26 < j

   1. Initial program 59.4%

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

   3. Taylor expanded in j around inf 62.8%

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

      1. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   if -5e113 < j < -3.80000000000000003e-206 or 4.49999999999999969e-117 < j < 4.49999999999999978e26

   1. Initial program 79.3%

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

   3. Taylor expanded in b around 0 64.9%

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

   4. Taylor expanded in j around 0 58.3%

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

   if -3.80000000000000003e-206 < j < -2.2000000000000001e-284 or 4.3e-218 < j < 4.49999999999999969e-117

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 71.2%

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

      1. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if -2.2000000000000001e-284 < j < 4.3e-218

   1. Initial program 83.0%

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

   3. Taylor expanded in t around inf 74.3%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in t around inf 66.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{+113}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-284}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -1.02 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -16200000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 4100000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+185}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= c -1.02e+58)
     t_1
     (if (<= c -16200000000.0)
       (* x (* y z))
       (if (<= c -1.9e-287)
         (* b (* t i))
         (if (<= c 4100000.0)
           (* y (* x z))
           (if (<= c 2.1e+109)
             (* a (* c j))
             (if (<= c 1.25e+185) (* (* x t) (- a)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (c <= -1.02e+58) {
		tmp = t_1;
	} else if (c <= -16200000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.9e-287) {
		tmp = b * (t * i);
	} else if (c <= 4100000.0) {
		tmp = y * (x * z);
	} else if (c <= 2.1e+109) {
		tmp = a * (c * j);
	} else if (c <= 1.25e+185) {
		tmp = (x * t) * -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * -c)
    if (c <= (-1.02d+58)) then
        tmp = t_1
    else if (c <= (-16200000000.0d0)) then
        tmp = x * (y * z)
    else if (c <= (-1.9d-287)) then
        tmp = b * (t * i)
    else if (c <= 4100000.0d0) then
        tmp = y * (x * z)
    else if (c <= 2.1d+109) then
        tmp = a * (c * j)
    else if (c <= 1.25d+185) then
        tmp = (x * t) * -a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (c <= -1.02e+58) {
		tmp = t_1;
	} else if (c <= -16200000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.9e-287) {
		tmp = b * (t * i);
	} else if (c <= 4100000.0) {
		tmp = y * (x * z);
	} else if (c <= 2.1e+109) {
		tmp = a * (c * j);
	} else if (c <= 1.25e+185) {
		tmp = (x * t) * -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if c <= -1.02e+58:
		tmp = t_1
	elif c <= -16200000000.0:
		tmp = x * (y * z)
	elif c <= -1.9e-287:
		tmp = b * (t * i)
	elif c <= 4100000.0:
		tmp = y * (x * z)
	elif c <= 2.1e+109:
		tmp = a * (c * j)
	elif c <= 1.25e+185:
		tmp = (x * t) * -a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (c <= -1.02e+58)
		tmp = t_1;
	elseif (c <= -16200000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -1.9e-287)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 4100000.0)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 2.1e+109)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= 1.25e+185)
		tmp = Float64(Float64(x * t) * Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (c <= -1.02e+58)
		tmp = t_1;
	elseif (c <= -16200000000.0)
		tmp = x * (y * z);
	elseif (c <= -1.9e-287)
		tmp = b * (t * i);
	elseif (c <= 4100000.0)
		tmp = y * (x * z);
	elseif (c <= 2.1e+109)
		tmp = a * (c * j);
	elseif (c <= 1.25e+185)
		tmp = (x * t) * -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.02e+58], t$95$1, If[LessEqual[c, -16200000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-287], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4100000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+109], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e+185], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.02000000000000005e58 or 1.24999999999999997e185 < c

   1. Initial program 55.5%

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

   3. Taylor expanded in j around 0 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in c around inf 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

   8. Simplified 45.0%

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

   if -1.02000000000000005e58 < c < -1.62e10

   1. Initial program 56.9%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in x around inf 68.0%

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

   if -1.62e10 < c < -1.89999999999999991e-287

   1. Initial program 79.7%

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

   3. Taylor expanded in j around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in i around inf 42.0%

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

   if -1.89999999999999991e-287 < c < 4.1e6

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in x around inf 40.0%

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

   if 4.1e6 < c < 2.1000000000000001e109

   1. Initial program 66.9%

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

   3. Taylor expanded in a around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. mul-1-neg 43.1%

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

      3. unsub-neg 43.1%

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

      4. *-commutative 43.1%

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

      5. *-commutative 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in j around inf 31.1%

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

      1. *-commutative 31.1%

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

   8. Simplified 31.1%

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

   if 2.1000000000000001e109 < c < 1.24999999999999997e185

   1. Initial program 59.9%

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

   3. Taylor expanded in a around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

      5. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in j around 0 42.1%

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

      1. associate-*r* 42.1%

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

      2. neg-mul-1 42.1%

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

      3. *-commutative 42.1%

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

   8. Simplified 42.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -16200000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 4100000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+185}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+93}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.55e+42)
     t_1
     (if (<= x -1.8e-92)
       (* y (- (* x z) (* i j)))
       (if (<= x -1.35e-143)
         (* a (- (* c j) (* x t)))
         (if (<= x 3.6e-94)
           (* i (- (* t b) (* y j)))
           (if (<= x 3.6e+93) (* (* t b) (- i (* c (/ z t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.55e+42) {
		tmp = t_1;
	} else if (x <= -1.8e-92) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.35e-143) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= 3.6e-94) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 3.6e+93) {
		tmp = (t * b) * (i - (c * (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.55d+42)) then
        tmp = t_1
    else if (x <= (-1.8d-92)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= (-1.35d-143)) then
        tmp = a * ((c * j) - (x * t))
    else if (x <= 3.6d-94) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= 3.6d+93) then
        tmp = (t * b) * (i - (c * (z / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.55e+42) {
		tmp = t_1;
	} else if (x <= -1.8e-92) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.35e-143) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= 3.6e-94) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 3.6e+93) {
		tmp = (t * b) * (i - (c * (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.55e+42:
		tmp = t_1
	elif x <= -1.8e-92:
		tmp = y * ((x * z) - (i * j))
	elif x <= -1.35e-143:
		tmp = a * ((c * j) - (x * t))
	elif x <= 3.6e-94:
		tmp = i * ((t * b) - (y * j))
	elif x <= 3.6e+93:
		tmp = (t * b) * (i - (c * (z / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.55e+42)
		tmp = t_1;
	elseif (x <= -1.8e-92)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= -1.35e-143)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (x <= 3.6e-94)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= 3.6e+93)
		tmp = Float64(Float64(t * b) * Float64(i - Float64(c * Float64(z / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.55e+42)
		tmp = t_1;
	elseif (x <= -1.8e-92)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= -1.35e-143)
		tmp = a * ((c * j) - (x * t));
	elseif (x <= 3.6e-94)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= 3.6e+93)
		tmp = (t * b) * (i - (c * (z / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+42], t$95$1, If[LessEqual[x, -1.8e-92], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-143], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-94], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+93], N[(N[(t * b), $MachinePrecision] * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.55e42 or 3.5999999999999999e93 < x

   1. Initial program 67.4%

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

   3. Taylor expanded in b around 0 66.9%

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

   4. Taylor expanded in j around 0 72.2%

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

   if -2.55e42 < x < -1.80000000000000008e-92

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

      4. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   if -1.80000000000000008e-92 < x < -1.35000000000000005e-143

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 89.0%

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

      1. +-commutative 89.0%

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

      2. mul-1-neg 89.0%

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

      3. unsub-neg 89.0%

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

      4. *-commutative 89.0%

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

      5. *-commutative 89.0%

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

   5. Simplified 89.0%

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

   if -1.35000000000000005e-143 < x < 3.6e-94

   1. Initial program 65.3%

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

   3. Taylor expanded in i around inf 54.3%

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

      1. distribute-lft-out-- 54.3%

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

      2. *-commutative 54.3%

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

      3. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   if 3.6e-94 < x < 3.5999999999999999e93

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 71.0%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in b around inf 60.9%

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

      1. associate-*r* 63.5%

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

      2. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+93}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\left(b \cdot i - \frac{j \cdot \left(y \cdot i - a \cdot c\right)}{t}\right) - x \cdot a\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.1 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (- (* b i) (/ (* j (- (* y i) (* a c))) t)) (* x a)))))
   (if (<= j -6.5e+148)
     t_1
     (if (<= j -7.1e+99)
       (* i (- (* t b) (* y j)))
       (if (<= j 8e+26)
         (+ (* x (- (* y z) (* t a))) (* 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 = t * (((b * i) - ((j * ((y * i) - (a * c))) / t)) - (x * a));
	double tmp;
	if (j <= -6.5e+148) {
		tmp = t_1;
	} else if (j <= -7.1e+99) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 8e+26) {
		tmp = (x * ((y * z) - (t * a))) + (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 = t * (((b * i) - ((j * ((y * i) - (a * c))) / t)) - (x * a))
    if (j <= (-6.5d+148)) then
        tmp = t_1
    else if (j <= (-7.1d+99)) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= 8d+26) then
        tmp = (x * ((y * z) - (t * a))) + (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 = t * (((b * i) - ((j * ((y * i) - (a * c))) / t)) - (x * a));
	double tmp;
	if (j <= -6.5e+148) {
		tmp = t_1;
	} else if (j <= -7.1e+99) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 8e+26) {
		tmp = (x * ((y * z) - (t * a))) + (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 = t * (((b * i) - ((j * ((y * i) - (a * c))) / t)) - (x * a))
	tmp = 0
	if j <= -6.5e+148:
		tmp = t_1
	elif j <= -7.1e+99:
		tmp = i * ((t * b) - (y * j))
	elif j <= 8e+26:
		tmp = (x * ((y * z) - (t * a))) + (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(t * Float64(Float64(Float64(b * i) - Float64(Float64(j * Float64(Float64(y * i) - Float64(a * c))) / t)) - Float64(x * a)))
	tmp = 0.0
	if (j <= -6.5e+148)
		tmp = t_1;
	elseif (j <= -7.1e+99)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= 8e+26)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + 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 = t * (((b * i) - ((j * ((y * i) - (a * c))) / t)) - (x * a));
	tmp = 0.0;
	if (j <= -6.5e+148)
		tmp = t_1;
	elseif (j <= -7.1e+99)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= 8e+26)
		tmp = (x * ((y * z) - (t * a))) + (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[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+148], t$95$1, If[LessEqual[j, -7.1e+99], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+26], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.49999999999999947e148 or 8.00000000000000038e26 < j

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 65.8%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in z around 0 71.5%

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

   if -6.49999999999999947e148 < j < -7.09999999999999994e99

   1. Initial program 50.9%

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

   3. Taylor expanded in i around inf 87.3%

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

      1. distribute-lft-out-- 87.3%

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

      2. *-commutative 87.3%

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

      3. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   if -7.09999999999999994e99 < j < 8.00000000000000038e26

   1. Initial program 77.9%

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

   3. Taylor expanded in j around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(\left(b \cdot i - \frac{j \cdot \left(y \cdot i - a \cdot c\right)}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;j \leq -7.1 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(b \cdot i - \frac{j \cdot \left(y \cdot i - a \cdot c\right)}{t}\right) - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{-34} \lor \neg \left(j \leq 2.9 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot \left(j \cdot \left(\left(c - t \cdot \frac{x}{j}\right) + \frac{x \cdot \left(y \cdot \frac{z}{j}\right) - y \cdot i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5.6e-34) (not (<= j 2.9e+34)))
   (* a (* j (+ (- c (* t (/ x j))) (/ (- (* x (* y (/ z j))) (* y i)) a))))
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5.6e-34) || !(j <= 2.9e+34)) {
		tmp = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-5.6d-34)) .or. (.not. (j <= 2.9d+34))) then
        tmp = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)))
    else
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5.6e-34) || !(j <= 2.9e+34)) {
		tmp = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -5.6e-34) or not (j <= 2.9e+34):
		tmp = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5.6e-34) || !(j <= 2.9e+34))
		tmp = Float64(a * Float64(j * Float64(Float64(c - Float64(t * Float64(x / j))) + Float64(Float64(Float64(x * Float64(y * Float64(z / j))) - Float64(y * i)) / a))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -5.6e-34) || ~((j <= 2.9e+34)))
		tmp = a * (j * ((c - (t * (x / j))) + (((x * (y * (z / j))) - (y * i)) / a)));
	else
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5.6e-34], N[Not[LessEqual[j, 2.9e+34]], $MachinePrecision]], N[(a * N[(j * N[(N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(y * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.59999999999999994e-34 or 2.9000000000000001e34 < j

   1. Initial program 63.4%

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

   3. Taylor expanded in b around 0 62.9%

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

   4. Taylor expanded in j around inf 65.9%

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

   5. Taylor expanded in a around inf 65.5%

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

      1. associate-/l* 67.7%

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

      2. distribute-lft-out 72.3%

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

      3. mul-1-neg 72.3%

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

      4. unsub-neg 72.3%

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

      5. associate-/l* 73.8%

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

      6. associate-/l* 75.4%

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

      7. associate-/l* 77.5%

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

   7. Simplified 77.5%

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

   if -5.59999999999999994e-34 < j < 2.9000000000000001e34

   1. Initial program 76.2%

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

   3. Taylor expanded in j around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{-34} \lor \neg \left(j \leq 2.9 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot \left(j \cdot \left(\left(c - t \cdot \frac{x}{j}\right) + \frac{x \cdot \left(y \cdot \frac{z}{j}\right) - y \cdot i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9.1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -5.7e+50)
     t_2
     (if (<= x -1.3e-109)
       (* y (- (* x z) (* i j)))
       (if (<= x 6.6e-237)
         t_1
         (if (<= x 1.65e-84)
           (* j (- (* a c) (* y i)))
           (if (<= x 9.1e+80) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.7e+50) {
		tmp = t_2;
	} else if (x <= -1.3e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.6e-237) {
		tmp = t_1;
	} else if (x <= 1.65e-84) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 9.1e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-5.7d+50)) then
        tmp = t_2
    else if (x <= (-1.3d-109)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 6.6d-237) then
        tmp = t_1
    else if (x <= 1.65d-84) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 9.1d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.7e+50) {
		tmp = t_2;
	} else if (x <= -1.3e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.6e-237) {
		tmp = t_1;
	} else if (x <= 1.65e-84) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 9.1e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.7e+50:
		tmp = t_2
	elif x <= -1.3e-109:
		tmp = y * ((x * z) - (i * j))
	elif x <= 6.6e-237:
		tmp = t_1
	elif x <= 1.65e-84:
		tmp = j * ((a * c) - (y * i))
	elif x <= 9.1e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.7e+50)
		tmp = t_2;
	elseif (x <= -1.3e-109)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 6.6e-237)
		tmp = t_1;
	elseif (x <= 1.65e-84)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 9.1e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.7e+50)
		tmp = t_2;
	elseif (x <= -1.3e-109)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 6.6e-237)
		tmp = t_1;
	elseif (x <= 1.65e-84)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 9.1e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.7e+50], t$95$2, If[LessEqual[x, -1.3e-109], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.6e-237], t$95$1, If[LessEqual[x, 1.65e-84], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.1e+80], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.7000000000000002e50 or 9.10000000000000015e80 < x

   1. Initial program 67.4%

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

   3. Taylor expanded in b around 0 66.9%

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

   4. Taylor expanded in j around 0 72.2%

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

   if -5.7000000000000002e50 < x < -1.2999999999999999e-109

   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 inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -1.2999999999999999e-109 < x < 6.6000000000000002e-237 or 1.64999999999999992e-84 < x < 9.10000000000000015e80

   1. Initial program 69.0%

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

   3. Taylor expanded in b around inf 56.4%

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

   if 6.6000000000000002e-237 < x < 1.64999999999999992e-84

   1. Initial program 74.0%

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

   3. Taylor expanded in j around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9.1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 15500000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.1e-31)
     t_1
     (if (<= a -1.72e-79)
       (* b (* t i))
       (if (<= a -3.2e-197)
         (* x (* y z))
         (if (<= a 2.05e-246)
           (* b (* z (- c)))
           (if (<= a 15500000000000.0) (* y (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e-31) {
		tmp = t_1;
	} else if (a <= -1.72e-79) {
		tmp = b * (t * i);
	} else if (a <= -3.2e-197) {
		tmp = x * (y * z);
	} else if (a <= 2.05e-246) {
		tmp = b * (z * -c);
	} else if (a <= 15500000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.1d-31)) then
        tmp = t_1
    else if (a <= (-1.72d-79)) then
        tmp = b * (t * i)
    else if (a <= (-3.2d-197)) then
        tmp = x * (y * z)
    else if (a <= 2.05d-246) then
        tmp = b * (z * -c)
    else if (a <= 15500000000000.0d0) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e-31) {
		tmp = t_1;
	} else if (a <= -1.72e-79) {
		tmp = b * (t * i);
	} else if (a <= -3.2e-197) {
		tmp = x * (y * z);
	} else if (a <= 2.05e-246) {
		tmp = b * (z * -c);
	} else if (a <= 15500000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.1e-31:
		tmp = t_1
	elif a <= -1.72e-79:
		tmp = b * (t * i)
	elif a <= -3.2e-197:
		tmp = x * (y * z)
	elif a <= 2.05e-246:
		tmp = b * (z * -c)
	elif a <= 15500000000000.0:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e-31)
		tmp = t_1;
	elseif (a <= -1.72e-79)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= -3.2e-197)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.05e-246)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 15500000000000.0)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e-31)
		tmp = t_1;
	elseif (a <= -1.72e-79)
		tmp = b * (t * i);
	elseif (a <= -3.2e-197)
		tmp = x * (y * z);
	elseif (a <= 2.05e-246)
		tmp = b * (z * -c);
	elseif (a <= 15500000000000.0)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e-31], t$95$1, If[LessEqual[a, -1.72e-79], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-246], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 15500000000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.0999999999999996e-31 or 1.55e13 < a

   1. Initial program 63.3%

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

   3. Taylor expanded in a around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. *-commutative 57.7%

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

      5. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   if -4.0999999999999996e-31 < a < -1.72e-79

   1. Initial program 77.7%

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

   3. Taylor expanded in j around 0 55.0%

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

      1. *-commutative 55.0%

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

      2. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in i around inf 50.2%

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

   if -1.72e-79 < a < -3.1999999999999997e-197

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in x around inf 36.8%

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

   if -3.1999999999999997e-197 < a < 2.04999999999999993e-246

   1. Initial program 74.6%

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

   3. Taylor expanded in j around 0 63.7%

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

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in c around inf 44.6%

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

      1. associate-*r* 44.6%

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

      2. neg-mul-1 44.6%

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

   8. Simplified 44.6%

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

   if 2.04999999999999993e-246 < a < 1.55e13

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in x around inf 36.6%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 15500000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+190}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+303}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.9e+103)
     t_2
     (if (<= j 1.4e+24)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= j 2.5e+190)
         (+ t_1 t_2)
         (if (<= j 1.9e+303)
           (* a (* x (- (/ (* c j) x) t)))
           (* (* y j) (- 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 t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.9e+103) {
		tmp = t_2;
	} else if (j <= 1.4e+24) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 2.5e+190) {
		tmp = t_1 + t_2;
	} else if (j <= 1.9e+303) {
		tmp = a * (x * (((c * j) / x) - t));
	} else {
		tmp = (y * j) * -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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2.9d+103)) then
        tmp = t_2
    else if (j <= 1.4d+24) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (j <= 2.5d+190) then
        tmp = t_1 + t_2
    else if (j <= 1.9d+303) then
        tmp = a * (x * (((c * j) / x) - t))
    else
        tmp = (y * j) * -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 t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.9e+103) {
		tmp = t_2;
	} else if (j <= 1.4e+24) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 2.5e+190) {
		tmp = t_1 + t_2;
	} else if (j <= 1.9e+303) {
		tmp = a * (x * (((c * j) / x) - t));
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.9e+103:
		tmp = t_2
	elif j <= 1.4e+24:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif j <= 2.5e+190:
		tmp = t_1 + t_2
	elif j <= 1.9e+303:
		tmp = a * (x * (((c * j) / x) - t))
	else:
		tmp = (y * j) * -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)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.9e+103)
		tmp = t_2;
	elseif (j <= 1.4e+24)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 2.5e+190)
		tmp = Float64(t_1 + t_2);
	elseif (j <= 1.9e+303)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	else
		tmp = Float64(Float64(y * j) * Float64(-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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.9e+103)
		tmp = t_2;
	elseif (j <= 1.4e+24)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (j <= 2.5e+190)
		tmp = t_1 + t_2;
	elseif (j <= 1.9e+303)
		tmp = a * (x * (((c * j) / x) - t));
	else
		tmp = (y * j) * -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]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+103], t$95$2, If[LessEqual[j, 1.4e+24], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+190], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[j, 1.9e+303], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.8999999999999998e103

   1. Initial program 55.2%

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

   3. Taylor expanded in j around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -2.8999999999999998e103 < j < 1.4000000000000001e24

   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 j around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if 1.4000000000000001e24 < j < 2.50000000000000018e190

   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 b around 0 70.4%

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

   if 2.50000000000000018e190 < j < 1.9e303

   1. Initial program 61.5%

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

   3. Taylor expanded in a around inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. *-commutative 83.4%

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

      5. *-commutative 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   if 1.9e303 < j

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+303}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -75000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+124}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= c -1.5e+58)
     t_1
     (if (<= c -75000000000.0)
       (* x (* y z))
       (if (<= c -1.75e-287)
         (* b (* t i))
         (if (<= c 5.4e+18)
           (* y (* x z))
           (if (<= c 4.2e+124) (* (* y j) (- i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (c <= -1.5e+58) {
		tmp = t_1;
	} else if (c <= -75000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.75e-287) {
		tmp = b * (t * i);
	} else if (c <= 5.4e+18) {
		tmp = y * (x * z);
	} else if (c <= 4.2e+124) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * -c)
    if (c <= (-1.5d+58)) then
        tmp = t_1
    else if (c <= (-75000000000.0d0)) then
        tmp = x * (y * z)
    else if (c <= (-1.75d-287)) then
        tmp = b * (t * i)
    else if (c <= 5.4d+18) then
        tmp = y * (x * z)
    else if (c <= 4.2d+124) then
        tmp = (y * j) * -i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (c <= -1.5e+58) {
		tmp = t_1;
	} else if (c <= -75000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.75e-287) {
		tmp = b * (t * i);
	} else if (c <= 5.4e+18) {
		tmp = y * (x * z);
	} else if (c <= 4.2e+124) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if c <= -1.5e+58:
		tmp = t_1
	elif c <= -75000000000.0:
		tmp = x * (y * z)
	elif c <= -1.75e-287:
		tmp = b * (t * i)
	elif c <= 5.4e+18:
		tmp = y * (x * z)
	elif c <= 4.2e+124:
		tmp = (y * j) * -i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (c <= -1.5e+58)
		tmp = t_1;
	elseif (c <= -75000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -1.75e-287)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 5.4e+18)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 4.2e+124)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (c <= -1.5e+58)
		tmp = t_1;
	elseif (c <= -75000000000.0)
		tmp = x * (y * z);
	elseif (c <= -1.75e-287)
		tmp = b * (t * i);
	elseif (c <= 5.4e+18)
		tmp = y * (x * z);
	elseif (c <= 4.2e+124)
		tmp = (y * j) * -i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+58], t$95$1, If[LessEqual[c, -75000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-287], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e+18], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e+124], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.5000000000000001e58 or 4.20000000000000023e124 < c

   1. Initial program 55.8%

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

   3. Taylor expanded in j around 0 54.2%

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

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in c around inf 42.5%

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

      1. associate-*r* 42.5%

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

      2. neg-mul-1 42.5%

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

   8. Simplified 42.5%

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

   if -1.5000000000000001e58 < c < -7.5e10

   1. Initial program 56.9%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in x around inf 68.0%

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

   if -7.5e10 < c < -1.75e-287

   1. Initial program 79.7%

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

   3. Taylor expanded in j around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in i around inf 42.0%

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

   if -1.75e-287 < c < 5.4e18

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around inf 37.8%

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

   if 5.4e18 < c < 4.20000000000000023e124

   1. Initial program 61.2%

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

   3. Taylor expanded in y around inf 40.4%

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

      1. +-commutative 40.4%

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

      2. mul-1-neg 40.4%

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

      3. unsub-neg 40.4%

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

      4. *-commutative 40.4%

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

   5. Simplified 40.4%

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

   6. Taylor expanded in x around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. neg-mul-1 40.0%

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

   8. Simplified 40.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -75000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+124}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := \left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* (* x t) (- a))))
   (if (<= x -5.5e+216)
     t_2
     (if (<= x -6e-109)
       t_1
       (if (<= x -2.4e-302)
         (* b (* t i))
         (if (<= x 1.3e+19) (* c (* a j)) (if (<= x 5e+144) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = (x * t) * -a;
	double tmp;
	if (x <= -5.5e+216) {
		tmp = t_2;
	} else if (x <= -6e-109) {
		tmp = t_1;
	} else if (x <= -2.4e-302) {
		tmp = b * (t * i);
	} else if (x <= 1.3e+19) {
		tmp = c * (a * j);
	} else if (x <= 5e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = (x * t) * -a
    if (x <= (-5.5d+216)) then
        tmp = t_2
    else if (x <= (-6d-109)) then
        tmp = t_1
    else if (x <= (-2.4d-302)) then
        tmp = b * (t * i)
    else if (x <= 1.3d+19) then
        tmp = c * (a * j)
    else if (x <= 5d+144) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = (x * t) * -a;
	double tmp;
	if (x <= -5.5e+216) {
		tmp = t_2;
	} else if (x <= -6e-109) {
		tmp = t_1;
	} else if (x <= -2.4e-302) {
		tmp = b * (t * i);
	} else if (x <= 1.3e+19) {
		tmp = c * (a * j);
	} else if (x <= 5e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = (x * t) * -a
	tmp = 0
	if x <= -5.5e+216:
		tmp = t_2
	elif x <= -6e-109:
		tmp = t_1
	elif x <= -2.4e-302:
		tmp = b * (t * i)
	elif x <= 1.3e+19:
		tmp = c * (a * j)
	elif x <= 5e+144:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(Float64(x * t) * Float64(-a))
	tmp = 0.0
	if (x <= -5.5e+216)
		tmp = t_2;
	elseif (x <= -6e-109)
		tmp = t_1;
	elseif (x <= -2.4e-302)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 1.3e+19)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 5e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = (x * t) * -a;
	tmp = 0.0;
	if (x <= -5.5e+216)
		tmp = t_2;
	elseif (x <= -6e-109)
		tmp = t_1;
	elseif (x <= -2.4e-302)
		tmp = b * (t * i);
	elseif (x <= 1.3e+19)
		tmp = c * (a * j);
	elseif (x <= 5e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, If[LessEqual[x, -5.5e+216], t$95$2, If[LessEqual[x, -6e-109], t$95$1, If[LessEqual[x, -2.4e-302], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+19], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+144], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5e216 or 4.9999999999999999e144 < x

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in j around 0 60.2%

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

      1. associate-*r* 60.2%

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

      2. neg-mul-1 60.2%

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

      3. *-commutative 60.2%

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

   8. Simplified 60.2%

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

   if -5.5e216 < x < -6.00000000000000043e-109 or 1.3e19 < x < 4.9999999999999999e144

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in x around inf 37.2%

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

   if -6.00000000000000043e-109 < x < -2.40000000000000022e-302

   1. Initial program 61.6%

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

   3. Taylor expanded in j around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in i around inf 41.1%

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

   if -2.40000000000000022e-302 < x < 1.3e19

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 53.6%

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

   4. Taylor expanded in j around inf 53.5%

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

   5. Taylor expanded in a around inf 35.0%

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

      1. associate-*r* 34.9%

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

      2. mul-1-neg 34.9%

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

      3. unsub-neg 34.9%

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

      4. associate-/l* 34.8%

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

   7. Simplified 34.8%

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

   8. Taylor expanded in c around inf 27.3%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+216}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{-6} \lor \neg \left(j \leq 7600000000\right):\\ \;\;\;\;j \cdot \left(\left(a \cdot c - \frac{x \cdot \left(t \cdot a - y \cdot z\right)}{j}\right) - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.2e-6) (not (<= j 7600000000.0)))
   (* j (- (- (* a c) (/ (* x (- (* t a) (* y z))) j)) (* y i)))
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.2e-6) || !(j <= 7600000000.0)) {
		tmp = j * (((a * c) - ((x * ((t * a) - (y * z))) / j)) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6.2d-6)) .or. (.not. (j <= 7600000000.0d0))) then
        tmp = j * (((a * c) - ((x * ((t * a) - (y * z))) / j)) - (y * i))
    else
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.2e-6) || !(j <= 7600000000.0)) {
		tmp = j * (((a * c) - ((x * ((t * a) - (y * z))) / j)) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.2e-6) or not (j <= 7600000000.0):
		tmp = j * (((a * c) - ((x * ((t * a) - (y * z))) / j)) - (y * i))
	else:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.2e-6) || !(j <= 7600000000.0))
		tmp = Float64(j * Float64(Float64(Float64(a * c) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) / j)) - Float64(y * i)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.2e-6) || ~((j <= 7600000000.0)))
		tmp = j * (((a * c) - ((x * ((t * a) - (y * z))) / j)) - (y * i));
	else
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.2e-6], N[Not[LessEqual[j, 7600000000.0]], $MachinePrecision]], N[(j * N[(N[(N[(a * c), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.1999999999999999e-6 or 7.6e9 < j

   1. Initial program 62.4%

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

   3. Taylor expanded in b around 0 64.0%

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

   4. Taylor expanded in j around inf 67.9%

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

   if -6.1999999999999999e-6 < j < 7.6e9

   1. Initial program 77.2%

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

   3. Taylor expanded in j around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{-6} \lor \neg \left(j \leq 7600000000\right):\\ \;\;\;\;j \cdot \left(\left(a \cdot c - \frac{x \cdot \left(t \cdot a - y \cdot z\right)}{j}\right) - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -27000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 62000 \lor \neg \left(c \leq 2.1 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.9e+58)
   (* j (* a c))
   (if (<= c -27000000000.0)
     (* x (* y z))
     (if (<= c -2.5e-287)
       (* b (* t i))
       (if (or (<= c 62000.0) (not (<= c 2.1e+110)))
         (* y (* x z))
         (* a (* c j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.9e+58) {
		tmp = j * (a * c);
	} else if (c <= -27000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -2.5e-287) {
		tmp = b * (t * i);
	} else if ((c <= 62000.0) || !(c <= 2.1e+110)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-3.9d+58)) then
        tmp = j * (a * c)
    else if (c <= (-27000000000.0d0)) then
        tmp = x * (y * z)
    else if (c <= (-2.5d-287)) then
        tmp = b * (t * i)
    else if ((c <= 62000.0d0) .or. (.not. (c <= 2.1d+110))) then
        tmp = y * (x * z)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.9e+58) {
		tmp = j * (a * c);
	} else if (c <= -27000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -2.5e-287) {
		tmp = b * (t * i);
	} else if ((c <= 62000.0) || !(c <= 2.1e+110)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.9e+58:
		tmp = j * (a * c)
	elif c <= -27000000000.0:
		tmp = x * (y * z)
	elif c <= -2.5e-287:
		tmp = b * (t * i)
	elif (c <= 62000.0) or not (c <= 2.1e+110):
		tmp = y * (x * z)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3.9e+58)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -27000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -2.5e-287)
		tmp = Float64(b * Float64(t * i));
	elseif ((c <= 62000.0) || !(c <= 2.1e+110))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -3.9e+58)
		tmp = j * (a * c);
	elseif (c <= -27000000000.0)
		tmp = x * (y * z);
	elseif (c <= -2.5e-287)
		tmp = b * (t * i);
	elseif ((c <= 62000.0) || ~((c <= 2.1e+110)))
		tmp = y * (x * z);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.9e+58], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -27000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.5e-287], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 62000.0], N[Not[LessEqual[c, 2.1e+110]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.9000000000000001e58

   1. Initial program 53.5%

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

   3. Taylor expanded in b around 0 48.4%

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

   4. Taylor expanded in j around inf 50.6%

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

   5. Taylor expanded in c around inf 38.1%

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

      1. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if -3.9000000000000001e58 < c < -2.7e10

   1. Initial program 56.9%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in x around inf 68.0%

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

   if -2.7e10 < c < -2.50000000000000013e-287

   1. Initial program 79.7%

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

   3. Taylor expanded in j around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in i around inf 42.0%

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

   if -2.50000000000000013e-287 < c < 62000 or 2.10000000000000015e110 < c

   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 inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in x around inf 36.7%

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

   if 62000 < c < 2.10000000000000015e110

   1. Initial program 68.2%

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

   3. Taylor expanded in a around inf 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

      4. *-commutative 45.4%

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

      5. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in j around inf 30.1%

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

      1. *-commutative 30.1%

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

   8. Simplified 30.1%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -27000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 62000 \lor \neg \left(c \leq 2.1 \cdot 10^{+110}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -6.7e-109)
     t_2
     (if (<= x 4.7e-237)
       t_1
       (if (<= x 1.7e-84)
         (* j (- (* a c) (* y i)))
         (if (<= x 3.6e+81) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.7e-109) {
		tmp = t_2;
	} else if (x <= 4.7e-237) {
		tmp = t_1;
	} else if (x <= 1.7e-84) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 3.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-6.7d-109)) then
        tmp = t_2
    else if (x <= 4.7d-237) then
        tmp = t_1
    else if (x <= 1.7d-84) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 3.6d+81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.7e-109) {
		tmp = t_2;
	} else if (x <= 4.7e-237) {
		tmp = t_1;
	} else if (x <= 1.7e-84) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 3.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6.7e-109:
		tmp = t_2
	elif x <= 4.7e-237:
		tmp = t_1
	elif x <= 1.7e-84:
		tmp = j * ((a * c) - (y * i))
	elif x <= 3.6e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6.7e-109)
		tmp = t_2;
	elseif (x <= 4.7e-237)
		tmp = t_1;
	elseif (x <= 1.7e-84)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 3.6e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6.7e-109)
		tmp = t_2;
	elseif (x <= 4.7e-237)
		tmp = t_1;
	elseif (x <= 1.7e-84)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 3.6e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.7e-109], t$95$2, If[LessEqual[x, 4.7e-237], t$95$1, If[LessEqual[x, 1.7e-84], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.70000000000000002e-109 or 3.60000000000000005e81 < x

   1. Initial program 69.1%

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

   3. Taylor expanded in b around 0 66.4%

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

   4. Taylor expanded in j around 0 64.6%

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

   if -6.70000000000000002e-109 < x < 4.6999999999999998e-237 or 1.7000000000000001e-84 < x < 3.60000000000000005e81

   1. Initial program 69.0%

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

   3. Taylor expanded in b around inf 56.4%

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

   if 4.6999999999999998e-237 < x < 1.7000000000000001e-84

   1. Initial program 74.0%

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

   3. Taylor expanded in j around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -44000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1080000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -44000000000000.0)
     t_2
     (if (<= b -5e-209)
       t_1
       (if (<= b -1.25e-271)
         (* y (* x z))
         (if (<= b 1080000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -44000000000000.0) {
		tmp = t_2;
	} else if (b <= -5e-209) {
		tmp = t_1;
	} else if (b <= -1.25e-271) {
		tmp = y * (x * z);
	} else if (b <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-44000000000000.0d0)) then
        tmp = t_2
    else if (b <= (-5d-209)) then
        tmp = t_1
    else if (b <= (-1.25d-271)) then
        tmp = y * (x * z)
    else if (b <= 1080000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -44000000000000.0) {
		tmp = t_2;
	} else if (b <= -5e-209) {
		tmp = t_1;
	} else if (b <= -1.25e-271) {
		tmp = y * (x * z);
	} else if (b <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -44000000000000.0:
		tmp = t_2
	elif b <= -5e-209:
		tmp = t_1
	elif b <= -1.25e-271:
		tmp = y * (x * z)
	elif b <= 1080000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -44000000000000.0)
		tmp = t_2;
	elseif (b <= -5e-209)
		tmp = t_1;
	elseif (b <= -1.25e-271)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -44000000000000.0)
		tmp = t_2;
	elseif (b <= -5e-209)
		tmp = t_1;
	elseif (b <= -1.25e-271)
		tmp = y * (x * z);
	elseif (b <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -44000000000000.0], t$95$2, If[LessEqual[b, -5e-209], t$95$1, If[LessEqual[b, -1.25e-271], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1080000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4e13 or 1.08e12 < b

   1. Initial program 75.7%

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

   3. Taylor expanded in b around inf 60.5%

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

   if -4.4e13 < b < -5.0000000000000005e-209 or -1.2500000000000001e-271 < b < 1.08e12

   1. Initial program 66.1%

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

   3. Taylor expanded in a around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. *-commutative 51.0%

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

      5. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if -5.0000000000000005e-209 < b < -1.2500000000000001e-271

   1. Initial program 48.8%

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

   3. Taylor expanded in y around inf 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in x around inf 63.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -44000000000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1080000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3.6e-99)
     (- t_1 (* i (* y j)))
     (if (<= x 1.7e-94)
       (* i (- (* t b) (* y j)))
       (if (<= x 1.4e+85) (* (* t b) (- i (* c (/ z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.6e-99) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 1.7e-94) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 1.4e+85) {
		tmp = (t * b) * (i - (c * (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3.6d-99)) then
        tmp = t_1 - (i * (y * j))
    else if (x <= 1.7d-94) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= 1.4d+85) then
        tmp = (t * b) * (i - (c * (z / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.6e-99) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 1.7e-94) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 1.4e+85) {
		tmp = (t * b) * (i - (c * (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.6e-99:
		tmp = t_1 - (i * (y * j))
	elif x <= 1.7e-94:
		tmp = i * ((t * b) - (y * j))
	elif x <= 1.4e+85:
		tmp = (t * b) * (i - (c * (z / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.6e-99)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (x <= 1.7e-94)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= 1.4e+85)
		tmp = Float64(Float64(t * b) * Float64(i - Float64(c * Float64(z / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.6e-99)
		tmp = t_1 - (i * (y * j));
	elseif (x <= 1.7e-94)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= 1.4e+85)
		tmp = (t * b) * (i - (c * (z / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e-99], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-94], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+85], N[(N[(t * b), $MachinePrecision] * N[(i - N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.6000000000000001e-99

   1. Initial program 74.3%

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

   3. Taylor expanded in b around 0 69.7%

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

   4. Taylor expanded in c around 0 67.3%

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

      1. +-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. mul-1-neg 67.3%

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

      4. unsub-neg 67.3%

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

      5. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   if -3.6000000000000001e-99 < x < 1.6999999999999999e-94

   1. Initial program 66.2%

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

   3. Taylor expanded in i around inf 55.1%

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

      1. distribute-lft-out-- 55.1%

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

      2. *-commutative 55.1%

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

      3. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   if 1.6999999999999999e-94 < x < 1.4e85

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 71.0%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in b around inf 60.9%

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

      1. associate-*r* 63.5%

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

      2. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   if 1.4e85 < x

   1. Initial program 59.5%

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

   3. Taylor expanded in b around 0 59.9%

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

   4. Taylor expanded in j around 0 73.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - c \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -80000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= c -9.5e+57)
     (* j (* a c))
     (if (<= c -80000000000.0)
       t_1
       (if (<= c -6.2e-288)
         (* b (* t i))
         (if (<= c 1.7e+61) t_1 (* a (* c j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (c <= -9.5e+57) {
		tmp = j * (a * c);
	} else if (c <= -80000000000.0) {
		tmp = t_1;
	} else if (c <= -6.2e-288) {
		tmp = b * (t * i);
	} else if (c <= 1.7e+61) {
		tmp = t_1;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (c <= (-9.5d+57)) then
        tmp = j * (a * c)
    else if (c <= (-80000000000.0d0)) then
        tmp = t_1
    else if (c <= (-6.2d-288)) then
        tmp = b * (t * i)
    else if (c <= 1.7d+61) then
        tmp = t_1
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (c <= -9.5e+57) {
		tmp = j * (a * c);
	} else if (c <= -80000000000.0) {
		tmp = t_1;
	} else if (c <= -6.2e-288) {
		tmp = b * (t * i);
	} else if (c <= 1.7e+61) {
		tmp = t_1;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if c <= -9.5e+57:
		tmp = j * (a * c)
	elif c <= -80000000000.0:
		tmp = t_1
	elif c <= -6.2e-288:
		tmp = b * (t * i)
	elif c <= 1.7e+61:
		tmp = t_1
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (c <= -9.5e+57)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -80000000000.0)
		tmp = t_1;
	elseif (c <= -6.2e-288)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 1.7e+61)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (c <= -9.5e+57)
		tmp = j * (a * c);
	elseif (c <= -80000000000.0)
		tmp = t_1;
	elseif (c <= -6.2e-288)
		tmp = b * (t * i);
	elseif (c <= 1.7e+61)
		tmp = t_1;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e+57], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -80000000000.0], t$95$1, If[LessEqual[c, -6.2e-288], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+61], t$95$1, N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.4999999999999997e57

   1. Initial program 53.5%

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

   3. Taylor expanded in b around 0 48.4%

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

   4. Taylor expanded in j around inf 50.6%

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

   5. Taylor expanded in c around inf 38.1%

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

      1. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if -9.4999999999999997e57 < c < -8e10 or -6.19999999999999967e-288 < c < 1.70000000000000013e61

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in x around inf 38.4%

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

   if -8e10 < c < -6.19999999999999967e-288

   1. Initial program 79.7%

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

   3. Taylor expanded in j around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in i around inf 42.0%

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

   if 1.70000000000000013e61 < c

   1. Initial program 58.3%

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

   3. Taylor expanded in a around inf 36.2%

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

      1. +-commutative 36.2%

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

      2. mul-1-neg 36.2%

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

      3. unsub-neg 36.2%

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

      4. *-commutative 36.2%

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

      5. *-commutative 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in j around inf 27.3%

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

      1. *-commutative 27.3%

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

   8. Simplified 27.3%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -80000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1650000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -8.2e+192)
     t_1
     (if (<= b -7.2e-95)
       (* c (- (* a j) (* z b)))
       (if (<= b 1650000000000.0) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.2e+192) {
		tmp = t_1;
	} else if (b <= -7.2e-95) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1650000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-8.2d+192)) then
        tmp = t_1
    else if (b <= (-7.2d-95)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 1650000000000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.2e+192) {
		tmp = t_1;
	} else if (b <= -7.2e-95) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1650000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -8.2e+192:
		tmp = t_1
	elif b <= -7.2e-95:
		tmp = c * ((a * j) - (z * b))
	elif b <= 1650000000000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8.2e+192)
		tmp = t_1;
	elseif (b <= -7.2e-95)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 1650000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.2e+192)
		tmp = t_1;
	elseif (b <= -7.2e-95)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 1650000000000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+192], t$95$1, If[LessEqual[b, -7.2e-95], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1650000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.20000000000000006e192 or 1.65e12 < b

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 66.8%

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

   if -8.20000000000000006e192 < b < -7.2e-95

   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 c around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -7.2e-95 < b < 1.65e12

   1. Initial program 62.3%

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

   3. Taylor expanded in a around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

      5. *-commutative 52.1%

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

   5. Simplified 52.1%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1650000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+59} \lor \neg \left(b \leq 6.4 \cdot 10^{-104}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -6e+59) (not (<= b 6.4e-104))) (* b (* t i)) (* j (* a 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 ((b <= -6e+59) || !(b <= 6.4e-104)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * 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 ((b <= (-6d+59)) .or. (.not. (b <= 6.4d-104))) then
        tmp = b * (t * i)
    else
        tmp = j * (a * 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 ((b <= -6e+59) || !(b <= 6.4e-104)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -6e+59) or not (b <= 6.4e-104):
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -6e+59) || !(b <= 6.4e-104))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -6e+59) || ~((b <= 6.4e-104)))
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -6e+59], N[Not[LessEqual[b, 6.4e-104]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.0000000000000001e59 or 6.39999999999999978e-104 < b

   1. Initial program 73.5%

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

   3. Taylor expanded in j around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in i around inf 37.1%

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

   if -6.0000000000000001e59 < b < 6.39999999999999978e-104

   1. Initial program 65.6%

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

   3. Taylor expanded in b around 0 66.3%

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

   4. Taylor expanded in j around inf 62.6%

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

   5. Taylor expanded in c around inf 25.4%

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

      1. *-commutative 25.4%

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

   7. Simplified 25.4%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+59} \lor \neg \left(b \leq 6.4 \cdot 10^{-104}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+149} \lor \neg \left(j \leq 180000000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3.1e+149) (not (<= j 180000000.0)))
   (* a (* c j))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.1e+149) || !(j <= 180000000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-3.1d+149)) .or. (.not. (j <= 180000000.0d0))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.1e+149) || !(j <= 180000000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3.1e+149) or not (j <= 180000000.0):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3.1e+149) || !(j <= 180000000.0))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -3.1e+149) || ~((j <= 180000000.0)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3.1e+149], N[Not[LessEqual[j, 180000000.0]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.09999999999999987e149 or 1.8e8 < j

   1. Initial program 60.7%

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

   3. Taylor expanded in a around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in j around inf 39.8%

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

      1. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if -3.09999999999999987e149 < j < 1.8e8

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in i around inf 26.0%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+149} \lor \neg \left(j \leq 180000000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.5% 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 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 a around inf 38.9%

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

   1. +-commutative 38.9%

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

   2. mul-1-neg 38.9%

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

   3. unsub-neg 38.9%

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

   4. *-commutative 38.9%

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

   5. *-commutative 38.9%

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

5. Simplified 38.9%

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

6. Taylor expanded in j around inf 19.2%

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

   1. *-commutative 19.2%

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

8. Simplified 19.2%

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

9. Final simplification 19.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))