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

Percentage Accurate: 73.5% → 81.5%

Time: 23.0s

Alternatives: 26

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := j \cdot t\_2\\ \mathbf{if}\;t\_1 + t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (* j t_2)))
   (if (<= (+ t_1 t_3) INFINITY) (fma j t_2 t_1) 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 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double t_3 = j * t_2;
	double tmp;
	if ((t_1 + t_3) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = t_3;
	}
	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))
	t_3 = Float64(j * t_2)
	tmp = 0.0
	if (Float64(t_1 + t_3) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(j * t$95$2), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + t$95$3), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], t$95$3]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. fma-define 88.0%

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

      3. *-commutative 88.0%

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

      4. *-commutative 88.0%

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

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   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 t around inf 17.5%

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

      1. associate--l+ 17.5%

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

      2. mul-1-neg 17.5%

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

      3. distribute-rgt-neg-in 17.5%

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

      4. associate--l+ 17.5%

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

      5. associate-/l* 22.5%

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

      6. mul-1-neg 22.5%

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

      7. +-commutative 22.5%

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

      8. associate--r+ 22.5%

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

   5. Simplified 32.5%

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

   6. Taylor expanded in j around -inf 57.8%

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

4. Final simplification 83.3%

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

Alternative 2: 81.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 t around inf 17.5%

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

      1. associate--l+ 17.5%

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

      2. mul-1-neg 17.5%

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

      3. distribute-rgt-neg-in 17.5%

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

      4. associate--l+ 17.5%

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

      5. associate-/l* 22.5%

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

      6. mul-1-neg 22.5%

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

      7. +-commutative 22.5%

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

      8. associate--r+ 22.5%

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

   5. Simplified 32.5%

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

   6. Taylor expanded in j around -inf 57.8%

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

4. Final simplification 83.3%

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

Alternative 3: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot i - z \cdot c\\ t_2 := b \cdot t\_1\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+217}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{+186}:\\ \;\;\;\;t\_2 - x \cdot \left(z \cdot \left(a \cdot \frac{t}{z} - y\right)\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_4\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-93}:\\ \;\;\;\;t\_4 + t \cdot \left(b \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot \frac{z}{a} - t\right) + b \cdot \frac{t\_1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c)))
        (t_2 (* b t_1))
        (t_3 (* a (- (* c j) (* x t))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= a -7.8e+217)
     t_3
     (if (<= a -3.15e+186)
       (- t_2 (* x (* z (- (* a (/ t z)) y))))
       (if (<= a -2.45e-21)
         (+ (* j (- (* a c) (* y i))) t_4)
         (if (<= a -7.4e-93)
           (+ t_4 (* t (* b (- i (/ (* z c) t)))))
           (if (<= a 3.5e-33)
             (+ (* y (- (* x z) (* i j))) t_2)
             (if (<= a 8.5e+166)
               (* a (+ (* x (- (* y (/ z a)) t)) (* b (/ t_1 a))))
               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 = (t * i) - (z * c);
	double t_2 = b * t_1;
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (a <= -7.8e+217) {
		tmp = t_3;
	} else if (a <= -3.15e+186) {
		tmp = t_2 - (x * (z * ((a * (t / z)) - y)));
	} else if (a <= -2.45e-21) {
		tmp = (j * ((a * c) - (y * i))) + t_4;
	} else if (a <= -7.4e-93) {
		tmp = t_4 + (t * (b * (i - ((z * c) / t))));
	} else if (a <= 3.5e-33) {
		tmp = (y * ((x * z) - (i * j))) + t_2;
	} else if (a <= 8.5e+166) {
		tmp = a * ((x * ((y * (z / a)) - t)) + (b * (t_1 / a)));
	} 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) :: t_4
    real(8) :: tmp
    t_1 = (t * i) - (z * c)
    t_2 = b * t_1
    t_3 = a * ((c * j) - (x * t))
    t_4 = x * ((y * z) - (t * a))
    if (a <= (-7.8d+217)) then
        tmp = t_3
    else if (a <= (-3.15d+186)) then
        tmp = t_2 - (x * (z * ((a * (t / z)) - y)))
    else if (a <= (-2.45d-21)) then
        tmp = (j * ((a * c) - (y * i))) + t_4
    else if (a <= (-7.4d-93)) then
        tmp = t_4 + (t * (b * (i - ((z * c) / t))))
    else if (a <= 3.5d-33) then
        tmp = (y * ((x * z) - (i * j))) + t_2
    else if (a <= 8.5d+166) then
        tmp = a * ((x * ((y * (z / a)) - t)) + (b * (t_1 / a)))
    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 = (t * i) - (z * c);
	double t_2 = b * t_1;
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (a <= -7.8e+217) {
		tmp = t_3;
	} else if (a <= -3.15e+186) {
		tmp = t_2 - (x * (z * ((a * (t / z)) - y)));
	} else if (a <= -2.45e-21) {
		tmp = (j * ((a * c) - (y * i))) + t_4;
	} else if (a <= -7.4e-93) {
		tmp = t_4 + (t * (b * (i - ((z * c) / t))));
	} else if (a <= 3.5e-33) {
		tmp = (y * ((x * z) - (i * j))) + t_2;
	} else if (a <= 8.5e+166) {
		tmp = a * ((x * ((y * (z / a)) - t)) + (b * (t_1 / a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * i) - (z * c)
	t_2 = b * t_1
	t_3 = a * ((c * j) - (x * t))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if a <= -7.8e+217:
		tmp = t_3
	elif a <= -3.15e+186:
		tmp = t_2 - (x * (z * ((a * (t / z)) - y)))
	elif a <= -2.45e-21:
		tmp = (j * ((a * c) - (y * i))) + t_4
	elif a <= -7.4e-93:
		tmp = t_4 + (t * (b * (i - ((z * c) / t))))
	elif a <= 3.5e-33:
		tmp = (y * ((x * z) - (i * j))) + t_2
	elif a <= 8.5e+166:
		tmp = a * ((x * ((y * (z / a)) - t)) + (b * (t_1 / a)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * i) - Float64(z * c))
	t_2 = Float64(b * t_1)
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (a <= -7.8e+217)
		tmp = t_3;
	elseif (a <= -3.15e+186)
		tmp = Float64(t_2 - Float64(x * Float64(z * Float64(Float64(a * Float64(t / z)) - y))));
	elseif (a <= -2.45e-21)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_4);
	elseif (a <= -7.4e-93)
		tmp = Float64(t_4 + Float64(t * Float64(b * Float64(i - Float64(Float64(z * c) / t)))));
	elseif (a <= 3.5e-33)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2);
	elseif (a <= 8.5e+166)
		tmp = Float64(a * Float64(Float64(x * Float64(Float64(y * Float64(z / a)) - t)) + Float64(b * Float64(t_1 / a))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * i) - (z * c);
	t_2 = b * t_1;
	t_3 = a * ((c * j) - (x * t));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (a <= -7.8e+217)
		tmp = t_3;
	elseif (a <= -3.15e+186)
		tmp = t_2 - (x * (z * ((a * (t / z)) - y)));
	elseif (a <= -2.45e-21)
		tmp = (j * ((a * c) - (y * i))) + t_4;
	elseif (a <= -7.4e-93)
		tmp = t_4 + (t * (b * (i - ((z * c) / t))));
	elseif (a <= 3.5e-33)
		tmp = (y * ((x * z) - (i * j))) + t_2;
	elseif (a <= 8.5e+166)
		tmp = a * ((x * ((y * (z / a)) - t)) + (b * (t_1 / a)));
	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[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+217], t$95$3, If[LessEqual[a, -3.15e+186], N[(t$95$2 - N[(x * N[(z * N[(N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.45e-21], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[a, -7.4e-93], N[(t$95$4 + N[(t * N[(b * N[(i - N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-33], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[a, 8.5e+166], N[(a * N[(N[(x * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.79999999999999986e217 or 8.5000000000000001e166 < a

   1. Initial program 56.3%

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

   3. Taylor expanded in a around inf 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

      4. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -7.79999999999999986e217 < a < -3.15e186

   1. Initial program 74.9%

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

   3. Taylor expanded in j around 0 91.5%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -3.15e186 < a < -2.4500000000000001e-21

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 74.5%

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

   if -2.4500000000000001e-21 < a < -7.40000000000000005e-93

   1. Initial program 71.7%

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

   3. Taylor expanded in j around 0 86.0%

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

   4. Taylor expanded in t around inf 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-/l* 92.8%

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

      3. mul-1-neg 92.8%

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

      4. distribute-rgt-neg-in 92.8%

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

      5. distribute-lft-out 92.8%

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

      6. *-commutative 92.8%

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

   6. Simplified 92.8%

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

   if -7.40000000000000005e-93 < a < 3.4999999999999999e-33

   1. Initial program 80.3%

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

   3. Taylor expanded in a around 0 75.7%

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

   5. Simplified 76.6%

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

   if 3.4999999999999999e-33 < a < 8.5000000000000001e166

   1. Initial program 78.8%

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

   3. Taylor expanded in j around 0 71.7%

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

   4. Taylor expanded in a around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-lft-neg-out 74.3%

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

      3. +-commutative 74.3%

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

      4. associate-/l* 76.9%

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

      5. *-commutative 76.9%

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

      6. distribute-lft-out 76.9%

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

      7. sub-neg 76.9%

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

      8. associate-/l* 76.9%

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

      9. associate-/l* 79.6%

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

      10. *-commutative 79.6%

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

      11. *-commutative 79.6%

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

   6. Simplified 79.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{+186}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(z \cdot \left(a \cdot \frac{t}{z} - y\right)\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot \frac{z}{a} - t\right) + b \cdot \frac{t \cdot i - z \cdot c}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1800000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(y \cdot \frac{z}{t} - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -3.45e-43)
     t_3
     (if (<= i 3.05e-232)
       t_2
       (if (<= i 2.5e-67)
         t_1
         (if (<= i 1800000000.0)
           (* c (- (* a j) (* z b)))
           (if (<= i 2e+16)
             t_1
             (if (<= i 4.4e+92)
               t_2
               (if (<= i 2.4e+125) (* (* x t) (- (* y (/ z t)) a)) 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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.45e-43) {
		tmp = t_3;
	} else if (i <= 3.05e-232) {
		tmp = t_2;
	} else if (i <= 2.5e-67) {
		tmp = t_1;
	} else if (i <= 1800000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2e+16) {
		tmp = t_1;
	} else if (i <= 4.4e+92) {
		tmp = t_2;
	} else if (i <= 2.4e+125) {
		tmp = (x * t) * ((y * (z / t)) - a);
	} 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 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-3.45d-43)) then
        tmp = t_3
    else if (i <= 3.05d-232) then
        tmp = t_2
    else if (i <= 2.5d-67) then
        tmp = t_1
    else if (i <= 1800000000.0d0) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 2d+16) then
        tmp = t_1
    else if (i <= 4.4d+92) then
        tmp = t_2
    else if (i <= 2.4d+125) then
        tmp = (x * t) * ((y * (z / t)) - a)
    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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.45e-43) {
		tmp = t_3;
	} else if (i <= 3.05e-232) {
		tmp = t_2;
	} else if (i <= 2.5e-67) {
		tmp = t_1;
	} else if (i <= 1800000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2e+16) {
		tmp = t_1;
	} else if (i <= 4.4e+92) {
		tmp = t_2;
	} else if (i <= 2.4e+125) {
		tmp = (x * t) * ((y * (z / t)) - a);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.45e-43:
		tmp = t_3
	elif i <= 3.05e-232:
		tmp = t_2
	elif i <= 2.5e-67:
		tmp = t_1
	elif i <= 1800000000.0:
		tmp = c * ((a * j) - (z * b))
	elif i <= 2e+16:
		tmp = t_1
	elif i <= 4.4e+92:
		tmp = t_2
	elif i <= 2.4e+125:
		tmp = (x * t) * ((y * (z / t)) - a)
	else:
		tmp = t_3
	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(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.45e-43)
		tmp = t_3;
	elseif (i <= 3.05e-232)
		tmp = t_2;
	elseif (i <= 2.5e-67)
		tmp = t_1;
	elseif (i <= 1800000000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 2e+16)
		tmp = t_1;
	elseif (i <= 4.4e+92)
		tmp = t_2;
	elseif (i <= 2.4e+125)
		tmp = Float64(Float64(x * t) * Float64(Float64(y * Float64(z / t)) - a));
	else
		tmp = t_3;
	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 = z * ((x * y) - (b * c));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.45e-43)
		tmp = t_3;
	elseif (i <= 3.05e-232)
		tmp = t_2;
	elseif (i <= 2.5e-67)
		tmp = t_1;
	elseif (i <= 1800000000.0)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 2e+16)
		tmp = t_1;
	elseif (i <= 4.4e+92)
		tmp = t_2;
	elseif (i <= 2.4e+125)
		tmp = (x * t) * ((y * (z / t)) - a);
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.45e-43], t$95$3, If[LessEqual[i, 3.05e-232], t$95$2, If[LessEqual[i, 2.5e-67], t$95$1, If[LessEqual[i, 1800000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e+16], t$95$1, If[LessEqual[i, 4.4e+92], t$95$2, If[LessEqual[i, 2.4e+125], N[(N[(x * t), $MachinePrecision] * N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.44999999999999982e-43 or 2.4e125 < i

   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 0 63.4%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-rgt-neg-in 58.1%

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

      3. mul-1-neg 58.1%

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

      4. associate-*r* 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-*r* 66.1%

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

      7. distribute-lft-in 72.7%

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

      8. +-commutative 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

   8. Simplified 72.7%

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

   if -3.44999999999999982e-43 < i < 3.0500000000000001e-232 or 2e16 < i < 4.39999999999999984e92

   1. Initial program 80.9%

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

   3. Taylor expanded in z around inf 59.8%

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

      1. *-commutative 59.8%

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

      2. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 3.0500000000000001e-232 < i < 2.4999999999999999e-67 or 1.8e9 < i < 2e16

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. associate--l+ 72.1%

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

      5. associate-/l* 67.8%

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

      6. mul-1-neg 67.8%

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

      7. +-commutative 67.8%

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

      8. associate--r+ 67.8%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. associate-*r* 49.6%

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

      2. +-commutative 49.6%

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

      3. mul-1-neg 49.6%

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

      4. unsub-neg 49.6%

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

      5. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in t around 0 49.5%

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

       1. mul-1-neg 49.5%

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

       2. distribute-lft-neg-out 49.5%

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

       3. +-commutative 49.5%

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

       4. *-commutative 49.5%

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

       5. associate-*r* 55.7%

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

       6. distribute-rgt-out 62.3%

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

       7. *-commutative 62.3%

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

       8. *-commutative 62.3%

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

   11. Simplified 62.3%

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

   if 2.4999999999999999e-67 < i < 1.8e9

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   if 4.39999999999999984e92 < i < 2.4e125

   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 t around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-rgt-neg-in 70.6%

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

      4. associate--l+ 70.6%

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

      5. associate-/l* 60.6%

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

      6. mul-1-neg 60.6%

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

      7. +-commutative 60.6%

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

      8. associate--r+ 60.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. +-commutative 70.7%

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

      3. mul-1-neg 70.7%

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

      4. unsub-neg 70.7%

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

      5. associate-/l* 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1800000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(y \cdot \frac{z}{t} - a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.2 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7400000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -8.2e-43)
     t_3
     (if (<= i 4.3e-232)
       t_2
       (if (<= i 2.2e-67)
         t_1
         (if (<= i 7400000.0)
           (* c (- (* a j) (* z b)))
           (if (<= i 3.7e+18)
             t_1
             (if (<= i 2.45e+82)
               t_2
               (if (<= i 1.75e+127) (* t (- (* b i) (* x a))) 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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.2e-43) {
		tmp = t_3;
	} else if (i <= 4.3e-232) {
		tmp = t_2;
	} else if (i <= 2.2e-67) {
		tmp = t_1;
	} else if (i <= 7400000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.7e+18) {
		tmp = t_1;
	} else if (i <= 2.45e+82) {
		tmp = t_2;
	} else if (i <= 1.75e+127) {
		tmp = t * ((b * i) - (x * a));
	} 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 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-8.2d-43)) then
        tmp = t_3
    else if (i <= 4.3d-232) then
        tmp = t_2
    else if (i <= 2.2d-67) then
        tmp = t_1
    else if (i <= 7400000.0d0) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 3.7d+18) then
        tmp = t_1
    else if (i <= 2.45d+82) then
        tmp = t_2
    else if (i <= 1.75d+127) then
        tmp = t * ((b * i) - (x * a))
    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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.2e-43) {
		tmp = t_3;
	} else if (i <= 4.3e-232) {
		tmp = t_2;
	} else if (i <= 2.2e-67) {
		tmp = t_1;
	} else if (i <= 7400000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.7e+18) {
		tmp = t_1;
	} else if (i <= 2.45e+82) {
		tmp = t_2;
	} else if (i <= 1.75e+127) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -8.2e-43:
		tmp = t_3
	elif i <= 4.3e-232:
		tmp = t_2
	elif i <= 2.2e-67:
		tmp = t_1
	elif i <= 7400000.0:
		tmp = c * ((a * j) - (z * b))
	elif i <= 3.7e+18:
		tmp = t_1
	elif i <= 2.45e+82:
		tmp = t_2
	elif i <= 1.75e+127:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	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(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -8.2e-43)
		tmp = t_3;
	elseif (i <= 4.3e-232)
		tmp = t_2;
	elseif (i <= 2.2e-67)
		tmp = t_1;
	elseif (i <= 7400000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 3.7e+18)
		tmp = t_1;
	elseif (i <= 2.45e+82)
		tmp = t_2;
	elseif (i <= 1.75e+127)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	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 = z * ((x * y) - (b * c));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -8.2e-43)
		tmp = t_3;
	elseif (i <= 4.3e-232)
		tmp = t_2;
	elseif (i <= 2.2e-67)
		tmp = t_1;
	elseif (i <= 7400000.0)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 3.7e+18)
		tmp = t_1;
	elseif (i <= 2.45e+82)
		tmp = t_2;
	elseif (i <= 1.75e+127)
		tmp = t * ((b * i) - (x * a));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.2e-43], t$95$3, If[LessEqual[i, 4.3e-232], t$95$2, If[LessEqual[i, 2.2e-67], t$95$1, If[LessEqual[i, 7400000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e+18], t$95$1, If[LessEqual[i, 2.45e+82], t$95$2, If[LessEqual[i, 1.75e+127], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.1999999999999996e-43 or 1.74999999999999989e127 < i

   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 0 63.4%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-rgt-neg-in 58.1%

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

      3. mul-1-neg 58.1%

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

      4. associate-*r* 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-*r* 66.1%

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

      7. distribute-lft-in 72.7%

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

      8. +-commutative 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

   8. Simplified 72.7%

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

   if -8.1999999999999996e-43 < i < 4.2999999999999997e-232 or 3.7e18 < i < 2.45e82

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if 4.2999999999999997e-232 < i < 2.2000000000000001e-67 or 7.4e6 < i < 3.7e18

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. associate--l+ 72.1%

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

      5. associate-/l* 67.8%

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

      6. mul-1-neg 67.8%

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

      7. +-commutative 67.8%

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

      8. associate--r+ 67.8%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. associate-*r* 49.6%

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

      2. +-commutative 49.6%

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

      3. mul-1-neg 49.6%

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

      4. unsub-neg 49.6%

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

      5. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in t around 0 49.5%

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

       1. mul-1-neg 49.5%

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

       2. distribute-lft-neg-out 49.5%

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

       3. +-commutative 49.5%

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

       4. *-commutative 49.5%

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

       5. associate-*r* 55.7%

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

       6. distribute-rgt-out 62.3%

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

       7. *-commutative 62.3%

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

       8. *-commutative 62.3%

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

   11. Simplified 62.3%

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

   if 2.2000000000000001e-67 < i < 7.4e6

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   if 2.45e82 < i < 1.74999999999999989e127

   1. Initial program 55.7%

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

   3. Taylor expanded in t around inf 73.1%

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

      1. distribute-lft-out-- 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.2 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 7400000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 14500000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -3.45e-43)
     t_3
     (if (<= i 5e-231)
       t_2
       (if (<= i 4.2e-67)
         t_1
         (if (<= i 14500000000.0)
           (* c (- (* a j) (* z b)))
           (if (<= i 2.5e+16)
             t_1
             (if (<= i 3.9e+89)
               t_2
               (if (<= i 2.3e+126) (* a (- (* c j) (* x t))) 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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.45e-43) {
		tmp = t_3;
	} else if (i <= 5e-231) {
		tmp = t_2;
	} else if (i <= 4.2e-67) {
		tmp = t_1;
	} else if (i <= 14500000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.5e+16) {
		tmp = t_1;
	} else if (i <= 3.9e+89) {
		tmp = t_2;
	} else if (i <= 2.3e+126) {
		tmp = a * ((c * j) - (x * t));
	} 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 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-3.45d-43)) then
        tmp = t_3
    else if (i <= 5d-231) then
        tmp = t_2
    else if (i <= 4.2d-67) then
        tmp = t_1
    else if (i <= 14500000000.0d0) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 2.5d+16) then
        tmp = t_1
    else if (i <= 3.9d+89) then
        tmp = t_2
    else if (i <= 2.3d+126) then
        tmp = a * ((c * j) - (x * t))
    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 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.45e-43) {
		tmp = t_3;
	} else if (i <= 5e-231) {
		tmp = t_2;
	} else if (i <= 4.2e-67) {
		tmp = t_1;
	} else if (i <= 14500000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.5e+16) {
		tmp = t_1;
	} else if (i <= 3.9e+89) {
		tmp = t_2;
	} else if (i <= 2.3e+126) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.45e-43:
		tmp = t_3
	elif i <= 5e-231:
		tmp = t_2
	elif i <= 4.2e-67:
		tmp = t_1
	elif i <= 14500000000.0:
		tmp = c * ((a * j) - (z * b))
	elif i <= 2.5e+16:
		tmp = t_1
	elif i <= 3.9e+89:
		tmp = t_2
	elif i <= 2.3e+126:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_3
	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(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.45e-43)
		tmp = t_3;
	elseif (i <= 5e-231)
		tmp = t_2;
	elseif (i <= 4.2e-67)
		tmp = t_1;
	elseif (i <= 14500000000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 2.5e+16)
		tmp = t_1;
	elseif (i <= 3.9e+89)
		tmp = t_2;
	elseif (i <= 2.3e+126)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_3;
	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 = z * ((x * y) - (b * c));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.45e-43)
		tmp = t_3;
	elseif (i <= 5e-231)
		tmp = t_2;
	elseif (i <= 4.2e-67)
		tmp = t_1;
	elseif (i <= 14500000000.0)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 2.5e+16)
		tmp = t_1;
	elseif (i <= 3.9e+89)
		tmp = t_2;
	elseif (i <= 2.3e+126)
		tmp = a * ((c * j) - (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.45e-43], t$95$3, If[LessEqual[i, 5e-231], t$95$2, If[LessEqual[i, 4.2e-67], t$95$1, If[LessEqual[i, 14500000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+16], t$95$1, If[LessEqual[i, 3.9e+89], t$95$2, If[LessEqual[i, 2.3e+126], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.44999999999999982e-43 or 2.3000000000000001e126 < i

   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 0 63.4%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-rgt-neg-in 58.1%

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

      3. mul-1-neg 58.1%

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

      4. associate-*r* 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-*r* 66.1%

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

      7. distribute-lft-in 72.7%

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

      8. +-commutative 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. *-commutative 72.7%

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

   8. Simplified 72.7%

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

   if -3.44999999999999982e-43 < i < 5.00000000000000023e-231 or 2.5e16 < i < 3.90000000000000011e89

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if 5.00000000000000023e-231 < i < 4.2000000000000003e-67 or 1.45e10 < i < 2.5e16

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. mul-1-neg 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. associate--l+ 72.1%

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

      5. associate-/l* 67.8%

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

      6. mul-1-neg 67.8%

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

      7. +-commutative 67.8%

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

      8. associate--r+ 67.8%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. associate-*r* 49.6%

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

      2. +-commutative 49.6%

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

      3. mul-1-neg 49.6%

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

      4. unsub-neg 49.6%

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

      5. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in t around 0 49.5%

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

       1. mul-1-neg 49.5%

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

       2. distribute-lft-neg-out 49.5%

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

       3. +-commutative 49.5%

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

       4. *-commutative 49.5%

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

       5. associate-*r* 55.7%

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

       6. distribute-rgt-out 62.3%

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

       7. *-commutative 62.3%

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

       8. *-commutative 62.3%

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

   11. Simplified 62.3%

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

   if 4.2000000000000003e-67 < i < 1.45e10

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   if 3.90000000000000011e89 < i < 2.3000000000000001e126

   1. Initial program 55.7%

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

   3. Taylor expanded in a around inf 64.3%

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

      1. +-commutative 64.3%

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

      2. mul-1-neg 64.3%

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

      3. unsub-neg 64.3%

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

      4. *-commutative 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 14500000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -0.0146:\\ \;\;\;\;t\_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* a c) (* y i))) t_1))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -1.65e+153)
     t_3
     (if (<= b -6.5e+137)
       t_2
       (if (<= b -4.8e+109)
         (* b (* t i))
         (if (<= b -0.0146)
           (- t_1 (* z (* b c)))
           (if (<= b 2.15e+155) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.65e+153) {
		tmp = t_3;
	} else if (b <= -6.5e+137) {
		tmp = t_2;
	} else if (b <= -4.8e+109) {
		tmp = b * (t * i);
	} else if (b <= -0.0146) {
		tmp = t_1 - (z * (b * c));
	} else if (b <= 2.15e+155) {
		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 = x * ((y * z) - (t * a))
    t_2 = (j * ((a * c) - (y * i))) + t_1
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-1.65d+153)) then
        tmp = t_3
    else if (b <= (-6.5d+137)) then
        tmp = t_2
    else if (b <= (-4.8d+109)) then
        tmp = b * (t * i)
    else if (b <= (-0.0146d0)) then
        tmp = t_1 - (z * (b * c))
    else if (b <= 2.15d+155) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.65e+153) {
		tmp = t_3;
	} else if (b <= -6.5e+137) {
		tmp = t_2;
	} else if (b <= -4.8e+109) {
		tmp = b * (t * i);
	} else if (b <= -0.0146) {
		tmp = t_1 - (z * (b * c));
	} else if (b <= 2.15e+155) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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))) + t_1
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.65e+153:
		tmp = t_3
	elif b <= -6.5e+137:
		tmp = t_2
	elif b <= -4.8e+109:
		tmp = b * (t * i)
	elif b <= -0.0146:
		tmp = t_1 - (z * (b * c))
	elif b <= 2.15e+155:
		tmp = t_2
	else:
		tmp = t_3
	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(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.65e+153)
		tmp = t_3;
	elseif (b <= -6.5e+137)
		tmp = t_2;
	elseif (b <= -4.8e+109)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -0.0146)
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	elseif (b <= 2.15e+155)
		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 = x * ((y * z) - (t * a));
	t_2 = (j * ((a * c) - (y * i))) + t_1;
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.65e+153)
		tmp = t_3;
	elseif (b <= -6.5e+137)
		tmp = t_2;
	elseif (b <= -4.8e+109)
		tmp = b * (t * i);
	elseif (b <= -0.0146)
		tmp = t_1 - (z * (b * c));
	elseif (b <= 2.15e+155)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+153], t$95$3, If[LessEqual[b, -6.5e+137], t$95$2, If[LessEqual[b, -4.8e+109], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -0.0146], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+155], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.64999999999999997e153 or 2.1500000000000001e155 < b

   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 b around inf 78.3%

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

   if -1.64999999999999997e153 < b < -6.5000000000000002e137 or -0.0146000000000000001 < b < 2.1500000000000001e155

   1. Initial program 72.4%

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

   3. Taylor expanded in b around 0 71.9%

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

   if -6.5000000000000002e137 < b < -4.79999999999999975e109

   1. Initial program 75.0%

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

   3. Taylor expanded in t around inf 75.0%

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

      1. distribute-lft-out-- 75.0%

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

      2. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in a around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -4.79999999999999975e109 < b < -0.0146000000000000001

   1. Initial program 90.2%

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

   3. Taylor expanded in j around 0 90.4%

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

   4. Taylor expanded in c around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -0.0146:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -220000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-121}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* z (* x y))))
   (if (<= y -2.9e+180)
     t_2
     (if (<= y -220000.0)
       t_1
       (if (<= y -3.35e-286)
         (* (* z c) (- b))
         (if (<= y 6.8e-140)
           (* j (* a c))
           (if (<= y 3e-121)
             (* i (* t b))
             (if (<= y 1.9e-34)
               (* a (* c j))
               (if (<= y 8.8e+153) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -2.9e+180) {
		tmp = t_2;
	} else if (y <= -220000.0) {
		tmp = t_1;
	} else if (y <= -3.35e-286) {
		tmp = (z * c) * -b;
	} else if (y <= 6.8e-140) {
		tmp = j * (a * c);
	} else if (y <= 3e-121) {
		tmp = i * (t * b);
	} else if (y <= 1.9e-34) {
		tmp = a * (c * j);
	} else if (y <= 8.8e+153) {
		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 = i * (y * -j)
    t_2 = z * (x * y)
    if (y <= (-2.9d+180)) then
        tmp = t_2
    else if (y <= (-220000.0d0)) then
        tmp = t_1
    else if (y <= (-3.35d-286)) then
        tmp = (z * c) * -b
    else if (y <= 6.8d-140) then
        tmp = j * (a * c)
    else if (y <= 3d-121) then
        tmp = i * (t * b)
    else if (y <= 1.9d-34) then
        tmp = a * (c * j)
    else if (y <= 8.8d+153) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -2.9e+180) {
		tmp = t_2;
	} else if (y <= -220000.0) {
		tmp = t_1;
	} else if (y <= -3.35e-286) {
		tmp = (z * c) * -b;
	} else if (y <= 6.8e-140) {
		tmp = j * (a * c);
	} else if (y <= 3e-121) {
		tmp = i * (t * b);
	} else if (y <= 1.9e-34) {
		tmp = a * (c * j);
	} else if (y <= 8.8e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = z * (x * y)
	tmp = 0
	if y <= -2.9e+180:
		tmp = t_2
	elif y <= -220000.0:
		tmp = t_1
	elif y <= -3.35e-286:
		tmp = (z * c) * -b
	elif y <= 6.8e-140:
		tmp = j * (a * c)
	elif y <= 3e-121:
		tmp = i * (t * b)
	elif y <= 1.9e-34:
		tmp = a * (c * j)
	elif y <= 8.8e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -2.9e+180)
		tmp = t_2;
	elseif (y <= -220000.0)
		tmp = t_1;
	elseif (y <= -3.35e-286)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 6.8e-140)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 3e-121)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 1.9e-34)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 8.8e+153)
		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 = i * (y * -j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (y <= -2.9e+180)
		tmp = t_2;
	elseif (y <= -220000.0)
		tmp = t_1;
	elseif (y <= -3.35e-286)
		tmp = (z * c) * -b;
	elseif (y <= 6.8e-140)
		tmp = j * (a * c);
	elseif (y <= 3e-121)
		tmp = i * (t * b);
	elseif (y <= 1.9e-34)
		tmp = a * (c * j);
	elseif (y <= 8.8e+153)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+180], t$95$2, If[LessEqual[y, -220000.0], t$95$1, If[LessEqual[y, -3.35e-286], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 6.8e-140], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-121], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-34], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+153], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.90000000000000007e180 or 8.7999999999999998e153 < y

   1. Initial program 68.9%

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

   3. Taylor expanded in a around 0 65.4%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in x around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*r* 54.5%

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

   8. Simplified 54.5%

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

   if -2.90000000000000007e180 < y < -2.2e5 or 1.9000000000000001e-34 < y < 8.7999999999999998e153

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

      5. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in z around 0 42.3%

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

      1. associate-*r* 42.3%

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

      2. neg-mul-1 42.3%

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

      3. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   if -2.2e5 < y < -3.34999999999999998e-286

   1. Initial program 84.7%

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

   3. Taylor expanded in j around 0 74.0%

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

   4. Taylor expanded in c around inf 39.1%

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

      1. associate-*r* 39.1%

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

      2. neg-mul-1 39.1%

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

      3. *-commutative 39.1%

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

   6. Simplified 39.1%

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

   if -3.34999999999999998e-286 < y < 6.80000000000000017e-140

   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 a around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in j around inf 40.6%

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

      1. associate-*r* 44.5%

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

   8. Simplified 44.5%

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

   if 6.80000000000000017e-140 < y < 2.9999999999999999e-121

   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 t around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in a around 0 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*r* 63.3%

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

   8. Simplified 63.3%

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

   if 2.9999999999999999e-121 < y < 1.9000000000000001e-34

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in j around inf 42.8%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+180}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -220000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-286}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-121}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.65 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 7.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.65e-46)
     t_2
     (if (<= i -8.5e-246)
       (* c (- (* a j) (* z b)))
       (if (<= i 5.4e-199)
         t_1
         (if (<= i 5.2e-142)
           (* x (* y z))
           (if (<= i 7.1e-16)
             t_1
             (if (<= i 8.5e+108) (* b (- (* t i) (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.65e-46) {
		tmp = t_2;
	} else if (i <= -8.5e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.4e-199) {
		tmp = t_1;
	} else if (i <= 5.2e-142) {
		tmp = x * (y * z);
	} else if (i <= 7.1e-16) {
		tmp = t_1;
	} else if (i <= 8.5e+108) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.65d-46)) then
        tmp = t_2
    else if (i <= (-8.5d-246)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 5.4d-199) then
        tmp = t_1
    else if (i <= 5.2d-142) then
        tmp = x * (y * z)
    else if (i <= 7.1d-16) then
        tmp = t_1
    else if (i <= 8.5d+108) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.65e-46) {
		tmp = t_2;
	} else if (i <= -8.5e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.4e-199) {
		tmp = t_1;
	} else if (i <= 5.2e-142) {
		tmp = x * (y * z);
	} else if (i <= 7.1e-16) {
		tmp = t_1;
	} else if (i <= 8.5e+108) {
		tmp = b * ((t * i) - (z * c));
	} 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 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.65e-46:
		tmp = t_2
	elif i <= -8.5e-246:
		tmp = c * ((a * j) - (z * b))
	elif i <= 5.4e-199:
		tmp = t_1
	elif i <= 5.2e-142:
		tmp = x * (y * z)
	elif i <= 7.1e-16:
		tmp = t_1
	elif i <= 8.5e+108:
		tmp = b * ((t * i) - (z * c))
	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(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.65e-46)
		tmp = t_2;
	elseif (i <= -8.5e-246)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 5.4e-199)
		tmp = t_1;
	elseif (i <= 5.2e-142)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 7.1e-16)
		tmp = t_1;
	elseif (i <= 8.5e+108)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.65e-46)
		tmp = t_2;
	elseif (i <= -8.5e-246)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 5.4e-199)
		tmp = t_1;
	elseif (i <= 5.2e-142)
		tmp = x * (y * z);
	elseif (i <= 7.1e-16)
		tmp = t_1;
	elseif (i <= 8.5e+108)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.65e-46], t$95$2, If[LessEqual[i, -8.5e-246], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.4e-199], t$95$1, If[LessEqual[i, 5.2e-142], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.1e-16], t$95$1, If[LessEqual[i, 8.5e+108], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.65000000000000009e-46 or 8.50000000000000016e108 < i

   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 a around 0 62.8%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in z around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-rgt-neg-in 56.9%

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

      3. mul-1-neg 56.9%

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

      4. associate-*r* 63.5%

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

      5. *-commutative 63.5%

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

      6. associate-*r* 64.5%

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

      7. distribute-lft-in 70.7%

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

      8. +-commutative 70.7%

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

      9. mul-1-neg 70.7%

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

      10. unsub-neg 70.7%

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

      11. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -2.65000000000000009e-46 < i < -8.4999999999999998e-246

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -8.4999999999999998e-246 < i < 5.39999999999999979e-199 or 5.1999999999999999e-142 < i < 7.1e-16

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   if 5.39999999999999979e-199 < i < 5.1999999999999999e-142

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0 56.0%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around inf 52.1%

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

      1. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if 7.1e-16 < i < 8.50000000000000016e108

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 62.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.65 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 7.1 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{+46} \lor \neg \left(b \leq -5 \cdot 10^{-18}\right) \land b \leq 1.95 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -7e+169)
     t_1
     (if (or (<= b -2.15e+46) (and (not (<= b -5e-18)) (<= b 1.95e+155)))
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (+ (* y (- (* x z) (* i j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e+169) {
		tmp = t_1;
	} else if ((b <= -2.15e+46) || (!(b <= -5e-18) && (b <= 1.95e+155))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + 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 <= (-7d+169)) then
        tmp = t_1
    else if ((b <= (-2.15d+46)) .or. (.not. (b <= (-5d-18))) .and. (b <= 1.95d+155)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (y * ((x * z) - (i * j))) + 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 <= -7e+169) {
		tmp = t_1;
	} else if ((b <= -2.15e+46) || (!(b <= -5e-18) && (b <= 1.95e+155))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + 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 <= -7e+169:
		tmp = t_1
	elif (b <= -2.15e+46) or (not (b <= -5e-18) and (b <= 1.95e+155)):
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (y * ((x * z) - (i * j))) + 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 <= -7e+169)
		tmp = t_1;
	elseif ((b <= -2.15e+46) || (!(b <= -5e-18) && (b <= 1.95e+155)))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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 <= -7e+169)
		tmp = t_1;
	elseif ((b <= -2.15e+46) || (~((b <= -5e-18)) && (b <= 1.95e+155)))
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (y * ((x * z) - (i * j))) + 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, -7e+169], t$95$1, If[Or[LessEqual[b, -2.15e+46], And[N[Not[LessEqual[b, -5e-18]], $MachinePrecision], LessEqual[b, 1.95e+155]]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000038e169

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 85.7%

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

   if -7.00000000000000038e169 < b < -2.15000000000000002e46 or -5.00000000000000036e-18 < b < 1.9499999999999999e155

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 72.8%

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

   if -2.15000000000000002e46 < b < -5.00000000000000036e-18 or 1.9499999999999999e155 < b

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 76.7%

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

   5. Simplified 76.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{+46} \lor \neg \left(b \leq -5 \cdot 10^{-18}\right) \land b \leq 1.95 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -0.0055:\\ \;\;\;\;t\_1 + t\_3\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_3\\ \end{array} \end{array} \]

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))) t_1))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -6.5e+153)
     t_3
     (if (<= b -1.15e+138)
       t_2
       (if (<= b -0.0055)
         (+ t_1 t_3)
         (if (<= b 1.95e+155) t_2 (+ (* y (- (* x z) (* i j))) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+153) {
		tmp = t_3;
	} else if (b <= -1.15e+138) {
		tmp = t_2;
	} else if (b <= -0.0055) {
		tmp = t_1 + t_3;
	} else if (b <= 1.95e+155) {
		tmp = t_2;
	} else {
		tmp = (y * ((x * z) - (i * j))) + 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 = x * ((y * z) - (t * a))
    t_2 = (j * ((a * c) - (y * i))) + t_1
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-6.5d+153)) then
        tmp = t_3
    else if (b <= (-1.15d+138)) then
        tmp = t_2
    else if (b <= (-0.0055d0)) then
        tmp = t_1 + t_3
    else if (b <= 1.95d+155) then
        tmp = t_2
    else
        tmp = (y * ((x * z) - (i * j))) + 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+153) {
		tmp = t_3;
	} else if (b <= -1.15e+138) {
		tmp = t_2;
	} else if (b <= -0.0055) {
		tmp = t_1 + t_3;
	} else if (b <= 1.95e+155) {
		tmp = t_2;
	} else {
		tmp = (y * ((x * z) - (i * j))) + t_3;
	}
	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))) + t_1
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -6.5e+153:
		tmp = t_3
	elif b <= -1.15e+138:
		tmp = t_2
	elif b <= -0.0055:
		tmp = t_1 + t_3
	elif b <= 1.95e+155:
		tmp = t_2
	else:
		tmp = (y * ((x * z) - (i * j))) + t_3
	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(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.5e+153)
		tmp = t_3;
	elseif (b <= -1.15e+138)
		tmp = t_2;
	elseif (b <= -0.0055)
		tmp = Float64(t_1 + t_3);
	elseif (b <= 1.95e+155)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_3);
	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))) + t_1;
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.5e+153)
		tmp = t_3;
	elseif (b <= -1.15e+138)
		tmp = t_2;
	elseif (b <= -0.0055)
		tmp = t_1 + t_3;
	elseif (b <= 1.95e+155)
		tmp = t_2;
	else
		tmp = (y * ((x * z) - (i * j))) + t_3;
	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[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+153], t$95$3, If[LessEqual[b, -1.15e+138], t$95$2, If[LessEqual[b, -0.0055], N[(t$95$1 + t$95$3), $MachinePrecision], If[LessEqual[b, 1.95e+155], t$95$2, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.49999999999999972e153

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 85.7%

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

   if -6.49999999999999972e153 < b < -1.15000000000000004e138 or -0.0054999999999999997 < b < 1.9499999999999999e155

   1. Initial program 72.4%

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

   3. Taylor expanded in b around 0 71.9%

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

   if -1.15000000000000004e138 < b < -0.0054999999999999997

   1. Initial program 88.5%

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

   3. Taylor expanded in j around 0 88.6%

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

   if 1.9499999999999999e155 < b

   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 a around 0 73.7%

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

   5. Simplified 73.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -0.0055:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{+101}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq 1.48 \cdot 10^{+264}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= i -3.5e-46)
     t_1
     (if (<= i -3.2e-291)
       (* z (* c (- b)))
       (if (<= i 2.25e-141)
         (* y (* x z))
         (if (<= i 1.02e-15)
           (* a (* c j))
           (if (<= i 1.08e+101)
             (* (* z c) (- b))
             (if (<= i 1.48e+264) t_1 (- (* y (* i j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (i <= -3.5e-46) {
		tmp = t_1;
	} else if (i <= -3.2e-291) {
		tmp = z * (c * -b);
	} else if (i <= 2.25e-141) {
		tmp = y * (x * z);
	} else if (i <= 1.02e-15) {
		tmp = a * (c * j);
	} else if (i <= 1.08e+101) {
		tmp = (z * c) * -b;
	} else if (i <= 1.48e+264) {
		tmp = t_1;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (i <= (-3.5d-46)) then
        tmp = t_1
    else if (i <= (-3.2d-291)) then
        tmp = z * (c * -b)
    else if (i <= 2.25d-141) then
        tmp = y * (x * z)
    else if (i <= 1.02d-15) then
        tmp = a * (c * j)
    else if (i <= 1.08d+101) then
        tmp = (z * c) * -b
    else if (i <= 1.48d+264) then
        tmp = t_1
    else
        tmp = -(y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (i <= -3.5e-46) {
		tmp = t_1;
	} else if (i <= -3.2e-291) {
		tmp = z * (c * -b);
	} else if (i <= 2.25e-141) {
		tmp = y * (x * z);
	} else if (i <= 1.02e-15) {
		tmp = a * (c * j);
	} else if (i <= 1.08e+101) {
		tmp = (z * c) * -b;
	} else if (i <= 1.48e+264) {
		tmp = t_1;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if i <= -3.5e-46:
		tmp = t_1
	elif i <= -3.2e-291:
		tmp = z * (c * -b)
	elif i <= 2.25e-141:
		tmp = y * (x * z)
	elif i <= 1.02e-15:
		tmp = a * (c * j)
	elif i <= 1.08e+101:
		tmp = (z * c) * -b
	elif i <= 1.48e+264:
		tmp = t_1
	else:
		tmp = -(y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -3.5e-46)
		tmp = t_1;
	elseif (i <= -3.2e-291)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 2.25e-141)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.02e-15)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 1.08e+101)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (i <= 1.48e+264)
		tmp = t_1;
	else
		tmp = Float64(-Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (i <= -3.5e-46)
		tmp = t_1;
	elseif (i <= -3.2e-291)
		tmp = z * (c * -b);
	elseif (i <= 2.25e-141)
		tmp = y * (x * z);
	elseif (i <= 1.02e-15)
		tmp = a * (c * j);
	elseif (i <= 1.08e+101)
		tmp = (z * c) * -b;
	elseif (i <= 1.48e+264)
		tmp = t_1;
	else
		tmp = -(y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e-46], t$95$1, If[LessEqual[i, -3.2e-291], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.25e-141], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e-15], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.08e+101], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[i, 1.48e+264], t$95$1, (-N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision])]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.5000000000000002e-46 or 1.07999999999999999e101 < i < 1.4800000000000001e264

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in a around 0 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r* 42.3%

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

   8. Simplified 42.3%

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

   if -3.5000000000000002e-46 < i < -3.2000000000000002e-291

   1. Initial program 81.9%

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

   3. Taylor expanded in j around 0 64.0%

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

   4. Taylor expanded in c around inf 34.9%

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

      1. mul-1-neg 34.9%

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

      2. *-commutative 34.9%

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

      3. *-commutative 34.9%

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

      4. associate-*r* 37.0%

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

      5. *-commutative 37.0%

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

      6. distribute-rgt-neg-out 37.0%

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

      7. *-commutative 37.0%

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

      8. distribute-lft-neg-in 37.0%

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

   6. Simplified 37.0%

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

   if -3.2000000000000002e-291 < i < 2.25e-141

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in z around inf 39.9%

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

   if 2.25e-141 < i < 1.02e-15

   1. Initial program 70.6%

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

   3. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in j around inf 49.1%

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

   if 1.02e-15 < i < 1.07999999999999999e101

   1. Initial program 76.4%

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

   3. Taylor expanded in j around 0 81.5%

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

   4. Taylor expanded in c around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. neg-mul-1 45.2%

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

      3. *-commutative 45.2%

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

   6. Simplified 45.2%

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

   if 1.4800000000000001e264 < i

   1. Initial program 30.7%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. *-commutative 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

   8. Simplified 90.2%

      \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{+101}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq 1.48 \cdot 10^{+264}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.24 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.76 \cdot 10^{+264}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))) (t_2 (* i (* t b))))
   (if (<= i -3.4e-46)
     t_2
     (if (<= i -4.4e-291)
       t_1
       (if (<= i 2.4e-141)
         (* y (* x z))
         (if (<= i 5.2e-16)
           (* a (* c j))
           (if (<= i 1.24e+98)
             t_1
             (if (<= i 1.76e+264) t_2 (- (* y (* i j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -3.4e-46) {
		tmp = t_2;
	} else if (i <= -4.4e-291) {
		tmp = t_1;
	} else if (i <= 2.4e-141) {
		tmp = y * (x * z);
	} else if (i <= 5.2e-16) {
		tmp = a * (c * j);
	} else if (i <= 1.24e+98) {
		tmp = t_1;
	} else if (i <= 1.76e+264) {
		tmp = t_2;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = i * (t * b)
    if (i <= (-3.4d-46)) then
        tmp = t_2
    else if (i <= (-4.4d-291)) then
        tmp = t_1
    else if (i <= 2.4d-141) then
        tmp = y * (x * z)
    else if (i <= 5.2d-16) then
        tmp = a * (c * j)
    else if (i <= 1.24d+98) then
        tmp = t_1
    else if (i <= 1.76d+264) then
        tmp = t_2
    else
        tmp = -(y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -3.4e-46) {
		tmp = t_2;
	} else if (i <= -4.4e-291) {
		tmp = t_1;
	} else if (i <= 2.4e-141) {
		tmp = y * (x * z);
	} else if (i <= 5.2e-16) {
		tmp = a * (c * j);
	} else if (i <= 1.24e+98) {
		tmp = t_1;
	} else if (i <= 1.76e+264) {
		tmp = t_2;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = i * (t * b)
	tmp = 0
	if i <= -3.4e-46:
		tmp = t_2
	elif i <= -4.4e-291:
		tmp = t_1
	elif i <= 2.4e-141:
		tmp = y * (x * z)
	elif i <= 5.2e-16:
		tmp = a * (c * j)
	elif i <= 1.24e+98:
		tmp = t_1
	elif i <= 1.76e+264:
		tmp = t_2
	else:
		tmp = -(y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -3.4e-46)
		tmp = t_2;
	elseif (i <= -4.4e-291)
		tmp = t_1;
	elseif (i <= 2.4e-141)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 5.2e-16)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 1.24e+98)
		tmp = t_1;
	elseif (i <= 1.76e+264)
		tmp = t_2;
	else
		tmp = Float64(-Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (i <= -3.4e-46)
		tmp = t_2;
	elseif (i <= -4.4e-291)
		tmp = t_1;
	elseif (i <= 2.4e-141)
		tmp = y * (x * z);
	elseif (i <= 5.2e-16)
		tmp = a * (c * j);
	elseif (i <= 1.24e+98)
		tmp = t_1;
	elseif (i <= 1.76e+264)
		tmp = t_2;
	else
		tmp = -(y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.4e-46], t$95$2, If[LessEqual[i, -4.4e-291], t$95$1, If[LessEqual[i, 2.4e-141], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e-16], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.24e+98], t$95$1, If[LessEqual[i, 1.76e+264], t$95$2, (-N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision])]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.39999999999999996e-46 or 1.23999999999999992e98 < i < 1.76e264

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in a around 0 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r* 42.3%

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

   8. Simplified 42.3%

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

   if -3.39999999999999996e-46 < i < -4.40000000000000005e-291 or 5.1999999999999997e-16 < i < 1.23999999999999992e98

   1. Initial program 80.1%

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

   3. Taylor expanded in j around 0 69.7%

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

   4. Taylor expanded in c around inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. *-commutative 38.3%

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

      3. *-commutative 38.3%

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

      4. associate-*r* 39.7%

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

      5. *-commutative 39.7%

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

      6. distribute-rgt-neg-out 39.7%

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

      7. *-commutative 39.7%

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

      8. distribute-lft-neg-in 39.7%

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

   6. Simplified 39.7%

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

   if -4.40000000000000005e-291 < i < 2.4000000000000001e-141

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in z around inf 39.9%

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

   if 2.4000000000000001e-141 < i < 5.1999999999999997e-16

   1. Initial program 70.6%

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

   3. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in j around inf 49.1%

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

   if 1.76e264 < i

   1. Initial program 30.7%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. *-commutative 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.24 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.76 \cdot 10^{+264}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(z \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (- (* x z) (* i j))) (* t (* b i))))
        (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -5.2e+107)
     t_2
     (if (<= a -9.2e-70)
       t_1
       (if (<= a -2.7e-88)
         (* c (- (* a j) (* z b)))
         (if (<= a 5.5e-20)
           t_1
           (if (<= a 2.5e+62) (* b (* z (- (* i (/ t z)) c))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (t * (b * i));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.2e+107) {
		tmp = t_2;
	} else if (a <= -9.2e-70) {
		tmp = t_1;
	} else if (a <= -2.7e-88) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 5.5e-20) {
		tmp = t_1;
	} else if (a <= 2.5e+62) {
		tmp = b * (z * ((i * (t / z)) - c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) + (t * (b * i))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-5.2d+107)) then
        tmp = t_2
    else if (a <= (-9.2d-70)) then
        tmp = t_1
    else if (a <= (-2.7d-88)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 5.5d-20) then
        tmp = t_1
    else if (a <= 2.5d+62) then
        tmp = b * (z * ((i * (t / z)) - c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (t * (b * i));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.2e+107) {
		tmp = t_2;
	} else if (a <= -9.2e-70) {
		tmp = t_1;
	} else if (a <= -2.7e-88) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 5.5e-20) {
		tmp = t_1;
	} else if (a <= 2.5e+62) {
		tmp = b * (z * ((i * (t / z)) - c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) + (t * (b * i))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.2e+107:
		tmp = t_2
	elif a <= -9.2e-70:
		tmp = t_1
	elif a <= -2.7e-88:
		tmp = c * ((a * j) - (z * b))
	elif a <= 5.5e-20:
		tmp = t_1
	elif a <= 2.5e+62:
		tmp = b * (z * ((i * (t / z)) - c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(b * i)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.2e+107)
		tmp = t_2;
	elseif (a <= -9.2e-70)
		tmp = t_1;
	elseif (a <= -2.7e-88)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 5.5e-20)
		tmp = t_1;
	elseif (a <= 2.5e+62)
		tmp = Float64(b * Float64(z * Float64(Float64(i * Float64(t / z)) - c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) + (t * (b * i));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.2e+107)
		tmp = t_2;
	elseif (a <= -9.2e-70)
		tmp = t_1;
	elseif (a <= -2.7e-88)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 5.5e-20)
		tmp = t_1;
	elseif (a <= 2.5e+62)
		tmp = b * (z * ((i * (t / z)) - c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+107], t$95$2, If[LessEqual[a, -9.2e-70], t$95$1, If[LessEqual[a, -2.7e-88], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-20], t$95$1, If[LessEqual[a, 2.5e+62], N[(b * N[(z * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.2000000000000002e107 or 2.50000000000000014e62 < a

   1. Initial program 64.8%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -5.2000000000000002e107 < a < -9.20000000000000002e-70 or -2.69999999999999995e-88 < a < 5.4999999999999996e-20

   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 a around 0 69.8%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around inf 63.7%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

   8. Simplified 66.3%

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

   if -9.20000000000000002e-70 < a < -2.69999999999999995e-88

   1. Initial program 60.0%

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

   3. Taylor expanded in c around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 5.4999999999999996e-20 < a < 2.50000000000000014e62

   1. Initial program 78.1%

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

   3. Taylor expanded in j around 0 74.4%

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

   4. Taylor expanded in b around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in z around inf 70.2%

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

      1. associate-/l* 74.4%

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

   9. Simplified 74.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(z \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* z (* b c))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.5e-43)
     t_2
     (if (<= i 2.8e-46)
       t_1
       (if (<= i 4.2e-16) (* j (* a c)) (if (<= i 2.05e+98) 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 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e-43) {
		tmp = t_2;
	} else if (i <= 2.8e-46) {
		tmp = t_1;
	} else if (i <= 4.2e-16) {
		tmp = j * (a * c);
	} else if (i <= 2.05e+98) {
		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 = (x * ((y * z) - (t * a))) - (z * (b * c))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.5d-43)) then
        tmp = t_2
    else if (i <= 2.8d-46) then
        tmp = t_1
    else if (i <= 4.2d-16) then
        tmp = j * (a * c)
    else if (i <= 2.05d+98) 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 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e-43) {
		tmp = t_2;
	} else if (i <= 2.8e-46) {
		tmp = t_1;
	} else if (i <= 4.2e-16) {
		tmp = j * (a * c);
	} else if (i <= 2.05e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) - (z * (b * c))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.5e-43:
		tmp = t_2
	elif i <= 2.8e-46:
		tmp = t_1
	elif i <= 4.2e-16:
		tmp = j * (a * c)
	elif i <= 2.05e+98:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.5e-43)
		tmp = t_2;
	elseif (i <= 2.8e-46)
		tmp = t_1;
	elseif (i <= 4.2e-16)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 2.05e+98)
		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 = (x * ((y * z) - (t * a))) - (z * (b * c));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.5e-43)
		tmp = t_2;
	elseif (i <= 2.8e-46)
		tmp = t_1;
	elseif (i <= 4.2e-16)
		tmp = j * (a * c);
	elseif (i <= 2.05e+98)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.5e-43], t$95$2, If[LessEqual[i, 2.8e-46], t$95$1, If[LessEqual[i, 4.2e-16], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.05e+98], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.50000000000000002e-43 or 2.05e98 < i

   1. Initial program 66.5%

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

   3. Taylor expanded in a around 0 63.1%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in z around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-rgt-neg-in 58.1%

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

      3. mul-1-neg 58.1%

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

      4. associate-*r* 63.9%

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

      5. *-commutative 63.9%

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

      6. associate-*r* 64.8%

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

      7. distribute-lft-in 71.0%

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

      8. +-commutative 71.0%

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

      9. mul-1-neg 71.0%

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

      10. unsub-neg 71.0%

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

      11. *-commutative 71.0%

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

   8. Simplified 71.0%

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

   if -1.50000000000000002e-43 < i < 2.7999999999999998e-46 or 4.2000000000000002e-16 < i < 2.05e98

   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 j around 0 69.9%

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

   4. Taylor expanded in c around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 65.7%

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

   6. Simplified 65.7%

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

   if 2.7999999999999998e-46 < i < 4.2000000000000002e-16

   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 a around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

      4. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in j around inf 83.3%

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

      1. associate-*r* 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+263}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* i (* t b))))
   (if (<= i -3.5e-46)
     t_2
     (if (<= i -3e-291)
       t_1
       (if (<= i 2.4e-139)
         (* y (* x z))
         (if (<= i 7.2e-16)
           t_1
           (if (<= i 3.3e+263) t_2 (- (* y (* i j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -3.5e-46) {
		tmp = t_2;
	} else if (i <= -3e-291) {
		tmp = t_1;
	} else if (i <= 2.4e-139) {
		tmp = y * (x * z);
	} else if (i <= 7.2e-16) {
		tmp = t_1;
	} else if (i <= 3.3e+263) {
		tmp = t_2;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = i * (t * b)
    if (i <= (-3.5d-46)) then
        tmp = t_2
    else if (i <= (-3d-291)) then
        tmp = t_1
    else if (i <= 2.4d-139) then
        tmp = y * (x * z)
    else if (i <= 7.2d-16) then
        tmp = t_1
    else if (i <= 3.3d+263) then
        tmp = t_2
    else
        tmp = -(y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -3.5e-46) {
		tmp = t_2;
	} else if (i <= -3e-291) {
		tmp = t_1;
	} else if (i <= 2.4e-139) {
		tmp = y * (x * z);
	} else if (i <= 7.2e-16) {
		tmp = t_1;
	} else if (i <= 3.3e+263) {
		tmp = t_2;
	} else {
		tmp = -(y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = i * (t * b)
	tmp = 0
	if i <= -3.5e-46:
		tmp = t_2
	elif i <= -3e-291:
		tmp = t_1
	elif i <= 2.4e-139:
		tmp = y * (x * z)
	elif i <= 7.2e-16:
		tmp = t_1
	elif i <= 3.3e+263:
		tmp = t_2
	else:
		tmp = -(y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -3.5e-46)
		tmp = t_2;
	elseif (i <= -3e-291)
		tmp = t_1;
	elseif (i <= 2.4e-139)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 7.2e-16)
		tmp = t_1;
	elseif (i <= 3.3e+263)
		tmp = t_2;
	else
		tmp = Float64(-Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (i <= -3.5e-46)
		tmp = t_2;
	elseif (i <= -3e-291)
		tmp = t_1;
	elseif (i <= 2.4e-139)
		tmp = y * (x * z);
	elseif (i <= 7.2e-16)
		tmp = t_1;
	elseif (i <= 3.3e+263)
		tmp = t_2;
	else
		tmp = -(y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e-46], t$95$2, If[LessEqual[i, -3e-291], t$95$1, If[LessEqual[i, 2.4e-139], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e-16], t$95$1, If[LessEqual[i, 3.3e+263], t$95$2, (-N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision])]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.5000000000000002e-46 or 7.19999999999999965e-16 < i < 3.3e263

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 48.6%

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

      1. distribute-lft-out-- 48.6%

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

      2. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in a around 0 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-*r* 39.5%

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

   8. Simplified 39.5%

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

   if -3.5000000000000002e-46 < i < -3.0000000000000001e-291 or 2.40000000000000015e-139 < i < 7.19999999999999965e-16

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around inf 39.7%

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

   if -3.0000000000000001e-291 < i < 2.40000000000000015e-139

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in z around inf 39.9%

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

   if 3.3e263 < i

   1. Initial program 30.7%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. *-commutative 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+263}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+263}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* i (* t b))))
   (if (<= i -6.5e-46)
     t_2
     (if (<= i -5.2e-291)
       t_1
       (if (<= i 3.3e-139)
         (* y (* x z))
         (if (<= i 8.2e-16)
           t_1
           (if (<= i 6.2e+263) t_2 (* j (- (* y 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 = a * (c * j);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -6.5e-46) {
		tmp = t_2;
	} else if (i <= -5.2e-291) {
		tmp = t_1;
	} else if (i <= 3.3e-139) {
		tmp = y * (x * z);
	} else if (i <= 8.2e-16) {
		tmp = t_1;
	} else if (i <= 6.2e+263) {
		tmp = t_2;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = i * (t * b)
    if (i <= (-6.5d-46)) then
        tmp = t_2
    else if (i <= (-5.2d-291)) then
        tmp = t_1
    else if (i <= 3.3d-139) then
        tmp = y * (x * z)
    else if (i <= 8.2d-16) then
        tmp = t_1
    else if (i <= 6.2d+263) then
        tmp = t_2
    else
        tmp = j * -(y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -6.5e-46) {
		tmp = t_2;
	} else if (i <= -5.2e-291) {
		tmp = t_1;
	} else if (i <= 3.3e-139) {
		tmp = y * (x * z);
	} else if (i <= 8.2e-16) {
		tmp = t_1;
	} else if (i <= 6.2e+263) {
		tmp = t_2;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = i * (t * b)
	tmp = 0
	if i <= -6.5e-46:
		tmp = t_2
	elif i <= -5.2e-291:
		tmp = t_1
	elif i <= 3.3e-139:
		tmp = y * (x * z)
	elif i <= 8.2e-16:
		tmp = t_1
	elif i <= 6.2e+263:
		tmp = t_2
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -6.5e-46)
		tmp = t_2;
	elseif (i <= -5.2e-291)
		tmp = t_1;
	elseif (i <= 3.3e-139)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 8.2e-16)
		tmp = t_1;
	elseif (i <= 6.2e+263)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (i <= -6.5e-46)
		tmp = t_2;
	elseif (i <= -5.2e-291)
		tmp = t_1;
	elseif (i <= 3.3e-139)
		tmp = y * (x * z);
	elseif (i <= 8.2e-16)
		tmp = t_1;
	elseif (i <= 6.2e+263)
		tmp = t_2;
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.5e-46], t$95$2, If[LessEqual[i, -5.2e-291], t$95$1, If[LessEqual[i, 3.3e-139], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e-16], t$95$1, If[LessEqual[i, 6.2e+263], t$95$2, N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -6.49999999999999966e-46 or 8.20000000000000012e-16 < i < 6.2000000000000005e263

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 48.6%

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

      1. distribute-lft-out-- 48.6%

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

      2. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in a around 0 36.5%

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

      1. *-commutative 36.5%

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

      2. associate-*r* 39.5%

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

   8. Simplified 39.5%

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

   if -6.49999999999999966e-46 < i < -5.1999999999999997e-291 or 3.3e-139 < i < 8.20000000000000012e-16

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around inf 39.7%

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

   if -5.1999999999999997e-291 < i < 3.3e-139

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in z around inf 39.9%

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

   if 6.2000000000000005e263 < i

   1. Initial program 30.7%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-*r* 80.8%

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

      4. *-commutative 80.8%

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

      5. distribute-rgt-neg-out 80.8%

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

      6. *-commutative 80.8%

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

      7. distribute-rgt-neg-in 80.8%

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

   8. Simplified 80.8%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+263}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -8.5e-43)
     t_1
     (if (<= i 4.2e-142)
       (* z (- (* x y) (* b c)))
       (if (<= i 7.6e-16)
         (* a (- (* c j) (* x t)))
         (if (<= i 7.8e+108) (* 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.5e-43) {
		tmp = t_1;
	} else if (i <= 4.2e-142) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 7.6e-16) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.8e+108) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-8.5d-43)) then
        tmp = t_1
    else if (i <= 4.2d-142) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 7.6d-16) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 7.8d+108) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.5e-43) {
		tmp = t_1;
	} else if (i <= 4.2e-142) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 7.6e-16) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.8e+108) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -8.5e-43:
		tmp = t_1
	elif i <= 4.2e-142:
		tmp = z * ((x * y) - (b * c))
	elif i <= 7.6e-16:
		tmp = a * ((c * j) - (x * t))
	elif i <= 7.8e+108:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -8.5e-43)
		tmp = t_1;
	elseif (i <= 4.2e-142)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 7.6e-16)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 7.8e+108)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -8.5e-43)
		tmp = t_1;
	elseif (i <= 4.2e-142)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 7.6e-16)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 7.8e+108)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e-43], t$95$1, If[LessEqual[i, 4.2e-142], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.6e-16], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e+108], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.50000000000000056e-43 or 7.79999999999999969e108 < i

   1. Initial program 65.9%

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

   3. Taylor expanded in a around 0 62.5%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-rgt-neg-in 57.4%

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

      3. mul-1-neg 57.4%

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

      4. associate-*r* 64.1%

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

      5. *-commutative 64.1%

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

      6. associate-*r* 65.1%

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

      7. distribute-lft-in 71.3%

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

      8. +-commutative 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

      11. *-commutative 71.3%

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

   8. Simplified 71.3%

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

   if -8.50000000000000056e-43 < i < 4.1999999999999999e-142

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   if 4.1999999999999999e-142 < i < 7.60000000000000024e-16

   1. Initial program 71.6%

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

   3. Taylor expanded in a around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. mul-1-neg 61.3%

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

      3. unsub-neg 61.3%

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

      4. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if 7.60000000000000024e-16 < i < 7.79999999999999969e108

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 62.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.55e+28)
     t_1
     (if (<= y 3.5e-233)
       (* b (- (* t i) (* z c)))
       (if (<= y 2.1e-28)
         (* c (- (* a j) (* z b)))
         (if (<= y 7e+156) (* i (- (* t b) (* y j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.55e+28) {
		tmp = t_1;
	} else if (y <= 3.5e-233) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 2.1e-28) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 7e+156) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.55d+28)) then
        tmp = t_1
    else if (y <= 3.5d-233) then
        tmp = b * ((t * i) - (z * c))
    else if (y <= 2.1d-28) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 7d+156) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.55e+28) {
		tmp = t_1;
	} else if (y <= 3.5e-233) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 2.1e-28) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 7e+156) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.55e+28:
		tmp = t_1
	elif y <= 3.5e-233:
		tmp = b * ((t * i) - (z * c))
	elif y <= 2.1e-28:
		tmp = c * ((a * j) - (z * b))
	elif y <= 7e+156:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.55e+28)
		tmp = t_1;
	elseif (y <= 3.5e-233)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (y <= 2.1e-28)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 7e+156)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.55e+28)
		tmp = t_1;
	elseif (y <= 3.5e-233)
		tmp = b * ((t * i) - (z * c));
	elseif (y <= 2.1e-28)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 7e+156)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+28], t$95$1, If[LessEqual[y, 3.5e-233], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-28], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+156], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55e28 or 7.0000000000000006e156 < y

   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 y around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -1.55e28 < y < 3.49999999999999991e-233

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 54.2%

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

   if 3.49999999999999991e-233 < y < 2.10000000000000006e-28

   1. Initial program 77.4%

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

   3. Taylor expanded in c around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if 2.10000000000000006e-28 < y < 7.0000000000000006e156

   1. Initial program 66.3%

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

   3. Taylor expanded in a around 0 66.0%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in z around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-in 56.4%

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

      3. mul-1-neg 56.4%

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

      4. associate-*r* 56.4%

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

      5. *-commutative 56.4%

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

      6. associate-*r* 54.6%

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

      7. distribute-lft-in 61.9%

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

      8. +-commutative 61.9%

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

      9. mul-1-neg 61.9%

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

      10. unsub-neg 61.9%

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

      11. *-commutative 61.9%

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

   8. Simplified 61.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -7.6e+108)
     t_2
     (if (<= a -8e-234)
       t_1
       (if (<= a 1.2e-231) (* z (* x y)) (if (<= a 8.5e+63) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.6e+108) {
		tmp = t_2;
	} else if (a <= -8e-234) {
		tmp = t_1;
	} else if (a <= 1.2e-231) {
		tmp = z * (x * y);
	} else if (a <= 8.5e+63) {
		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 = a * ((c * j) - (x * t))
    if (a <= (-7.6d+108)) then
        tmp = t_2
    else if (a <= (-8d-234)) then
        tmp = t_1
    else if (a <= 1.2d-231) then
        tmp = z * (x * y)
    else if (a <= 8.5d+63) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.6e+108) {
		tmp = t_2;
	} else if (a <= -8e-234) {
		tmp = t_1;
	} else if (a <= 1.2e-231) {
		tmp = z * (x * y);
	} else if (a <= 8.5e+63) {
		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 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7.6e+108:
		tmp = t_2
	elif a <= -8e-234:
		tmp = t_1
	elif a <= 1.2e-231:
		tmp = z * (x * y)
	elif a <= 8.5e+63:
		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(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.6e+108)
		tmp = t_2;
	elseif (a <= -8e-234)
		tmp = t_1;
	elseif (a <= 1.2e-231)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 8.5e+63)
		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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7.6e+108)
		tmp = t_2;
	elseif (a <= -8e-234)
		tmp = t_1;
	elseif (a <= 1.2e-231)
		tmp = z * (x * y);
	elseif (a <= 8.5e+63)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e+108], t$95$2, If[LessEqual[a, -8e-234], t$95$1, If[LessEqual[a, 1.2e-231], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.60000000000000015e108 or 8.5000000000000004e63 < a

   1. Initial program 64.8%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -7.60000000000000015e108 < a < -7.9999999999999997e-234 or 1.19999999999999996e-231 < a < 8.5000000000000004e63

   1. Initial program 80.9%

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

   3. Taylor expanded in b around inf 51.2%

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

   if -7.9999999999999997e-234 < a < 1.19999999999999996e-231

   1. Initial program 70.3%

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

   3. Taylor expanded in a around 0 67.4%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. *-commutative 41.1%

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

      3. associate-*r* 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-234}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* i (* t b))))
   (if (<= i -7.2e-46)
     t_2
     (if (<= i -3.7e-291)
       t_1
       (if (<= i 6.5e-142) (* y (* x z)) (if (<= i 8e-16) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -7.2e-46) {
		tmp = t_2;
	} else if (i <= -3.7e-291) {
		tmp = t_1;
	} else if (i <= 6.5e-142) {
		tmp = y * (x * z);
	} else if (i <= 8e-16) {
		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)
    t_2 = i * (t * b)
    if (i <= (-7.2d-46)) then
        tmp = t_2
    else if (i <= (-3.7d-291)) then
        tmp = t_1
    else if (i <= 6.5d-142) then
        tmp = y * (x * z)
    else if (i <= 8d-16) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -7.2e-46) {
		tmp = t_2;
	} else if (i <= -3.7e-291) {
		tmp = t_1;
	} else if (i <= 6.5e-142) {
		tmp = y * (x * z);
	} else if (i <= 8e-16) {
		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)
	t_2 = i * (t * b)
	tmp = 0
	if i <= -7.2e-46:
		tmp = t_2
	elif i <= -3.7e-291:
		tmp = t_1
	elif i <= 6.5e-142:
		tmp = y * (x * z)
	elif i <= 8e-16:
		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(c * j))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -7.2e-46)
		tmp = t_2;
	elseif (i <= -3.7e-291)
		tmp = t_1;
	elseif (i <= 6.5e-142)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 8e-16)
		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);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (i <= -7.2e-46)
		tmp = t_2;
	elseif (i <= -3.7e-291)
		tmp = t_1;
	elseif (i <= 6.5e-142)
		tmp = y * (x * z);
	elseif (i <= 8e-16)
		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[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.2e-46], t$95$2, If[LessEqual[i, -3.7e-291], t$95$1, If[LessEqual[i, 6.5e-142], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -7.2e-46 or 7.9999999999999998e-16 < i

   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 t around inf 47.3%

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

      1. distribute-lft-out-- 47.3%

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

      2. *-commutative 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in a around 0 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-*r* 38.2%

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

   8. Simplified 38.2%

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

   if -7.2e-46 < i < -3.7000000000000001e-291 or 6.50000000000000027e-142 < i < 7.9999999999999998e-16

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around inf 39.7%

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

   if -3.7000000000000001e-291 < i < 6.50000000000000027e-142

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

      5. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in z around inf 39.9%

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

Alternative 22: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;i \leq -8 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* i (* t b))))
   (if (<= i -8e-46)
     t_2
     (if (<= i -5e-291)
       t_1
       (if (<= i 5.5e-140) (* x (* y z)) (if (<= i 1.05e-15) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -8e-46) {
		tmp = t_2;
	} else if (i <= -5e-291) {
		tmp = t_1;
	} else if (i <= 5.5e-140) {
		tmp = x * (y * z);
	} else if (i <= 1.05e-15) {
		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)
    t_2 = i * (t * b)
    if (i <= (-8d-46)) then
        tmp = t_2
    else if (i <= (-5d-291)) then
        tmp = t_1
    else if (i <= 5.5d-140) then
        tmp = x * (y * z)
    else if (i <= 1.05d-15) 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);
	double t_2 = i * (t * b);
	double tmp;
	if (i <= -8e-46) {
		tmp = t_2;
	} else if (i <= -5e-291) {
		tmp = t_1;
	} else if (i <= 5.5e-140) {
		tmp = x * (y * z);
	} else if (i <= 1.05e-15) {
		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)
	t_2 = i * (t * b)
	tmp = 0
	if i <= -8e-46:
		tmp = t_2
	elif i <= -5e-291:
		tmp = t_1
	elif i <= 5.5e-140:
		tmp = x * (y * z)
	elif i <= 1.05e-15:
		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(c * j))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (i <= -8e-46)
		tmp = t_2;
	elseif (i <= -5e-291)
		tmp = t_1;
	elseif (i <= 5.5e-140)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.05e-15)
		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);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (i <= -8e-46)
		tmp = t_2;
	elseif (i <= -5e-291)
		tmp = t_1;
	elseif (i <= 5.5e-140)
		tmp = x * (y * z);
	elseif (i <= 1.05e-15)
		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[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8e-46], t$95$2, If[LessEqual[i, -5e-291], t$95$1, If[LessEqual[i, 5.5e-140], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e-15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.00000000000000018e-46 or 1.0499999999999999e-15 < i

   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 t around inf 47.3%

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

      1. distribute-lft-out-- 47.3%

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

      2. *-commutative 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in a around 0 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-*r* 38.2%

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

   8. Simplified 38.2%

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

   if -8.00000000000000018e-46 < i < -5.0000000000000003e-291 or 5.50000000000000026e-140 < i < 1.0499999999999999e-15

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around inf 39.7%

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

   if -5.0000000000000003e-291 < i < 5.50000000000000026e-140

   1. Initial program 86.1%

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

   3. Taylor expanded in a around 0 54.8%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in x around inf 36.2%

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

      1. *-commutative 36.2%

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

   8. Simplified 36.2%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 43.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-225}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1e-70)
     t_1
     (if (<= a -4.9e-225)
       (* (* z c) (- b))
       (if (<= a 4.5e-27) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1e-70) {
		tmp = t_1;
	} else if (a <= -4.9e-225) {
		tmp = (z * c) * -b;
	} else if (a <= 4.5e-27) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1d-70)) then
        tmp = t_1
    else if (a <= (-4.9d-225)) then
        tmp = (z * c) * -b
    else if (a <= 4.5d-27) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1e-70) {
		tmp = t_1;
	} else if (a <= -4.9e-225) {
		tmp = (z * c) * -b;
	} else if (a <= 4.5e-27) {
		tmp = z * (x * y);
	} 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 <= -1e-70:
		tmp = t_1
	elif a <= -4.9e-225:
		tmp = (z * c) * -b
	elif a <= 4.5e-27:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1e-70)
		tmp = t_1;
	elseif (a <= -4.9e-225)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (a <= 4.5e-27)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1e-70)
		tmp = t_1;
	elseif (a <= -4.9e-225)
		tmp = (z * c) * -b;
	elseif (a <= 4.5e-27)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-70], t$95$1, If[LessEqual[a, -4.9e-225], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[a, 4.5e-27], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.99999999999999996e-71 or 4.5000000000000002e-27 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in a around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if -9.99999999999999996e-71 < a < -4.89999999999999971e-225

   1. Initial program 79.2%

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

   3. Taylor expanded in j around 0 67.9%

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

   4. Taylor expanded in c around inf 40.2%

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

      1. associate-*r* 40.2%

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

      2. neg-mul-1 40.2%

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

      3. *-commutative 40.2%

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

   6. Simplified 40.2%

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

   if -4.89999999999999971e-225 < a < 4.5000000000000002e-27

   1. Initial program 78.0%

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

   3. Taylor expanded in a around 0 74.4%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around inf 35.6%

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

      1. *-commutative 35.6%

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

      2. *-commutative 35.6%

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

      3. associate-*r* 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-225}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{-46} \lor \neg \left(i \leq 9 \cdot 10^{-16}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6.5e-46) (not (<= i 9e-16))) (* i (* t b)) (* 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 ((i <= -6.5e-46) || !(i <= 9e-16)) {
		tmp = i * (t * b);
	} 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 ((i <= (-6.5d-46)) .or. (.not. (i <= 9d-16))) then
        tmp = i * (t * b)
    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 ((i <= -6.5e-46) || !(i <= 9e-16)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -6.5e-46) or not (i <= 9e-16):
		tmp = i * (t * b)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -6.5e-46) || !(i <= 9e-16))
		tmp = Float64(i * Float64(t * b));
	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 ((i <= -6.5e-46) || ~((i <= 9e-16)))
		tmp = i * (t * b);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6.5e-46], N[Not[LessEqual[i, 9e-16]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.49999999999999966e-46 or 9.0000000000000003e-16 < i

   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 t around inf 47.3%

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

      1. distribute-lft-out-- 47.3%

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

      2. *-commutative 47.3%

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

   5. Simplified 47.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 35.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. associate-*r* 38.2%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -6.49999999999999966e-46 < i < 9.0000000000000003e-16

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 33.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{-46} \lor \neg \left(i \leq 9 \cdot 10^{-16}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-46} \lor \neg \left(i \leq 1.02 \cdot 10^{-15}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.5e-46) (not (<= i 1.02e-15))) (* b (* t i)) (* 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 ((i <= -2.5e-46) || !(i <= 1.02e-15)) {
		tmp = b * (t * i);
	} 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 ((i <= (-2.5d-46)) .or. (.not. (i <= 1.02d-15))) then
        tmp = b * (t * i)
    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 ((i <= -2.5e-46) || !(i <= 1.02e-15)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.5e-46) or not (i <= 1.02e-15):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.5e-46) || !(i <= 1.02e-15))
		tmp = Float64(b * Float64(t * i));
	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 ((i <= -2.5e-46) || ~((i <= 1.02e-15)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.5e-46], N[Not[LessEqual[i, 1.02e-15]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.49999999999999996e-46 or 1.02e-15 < i

   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 t around inf 47.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 47.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 47.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 35.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 35.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -2.49999999999999996e-46 < i < 1.02e-15

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 33.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-46} \lor \neg \left(i \leq 1.02 \cdot 10^{-15}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 a around inf 37.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 37.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 37.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 37.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 37.0%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 37.0%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 23.6%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Add Preprocessing

Developer target: 58.7% 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 2024100 
(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)))))