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

Percentage Accurate: 72.8% → 80.2%

Time: 22.4s

Alternatives: 23

Speedup: 0.5×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = 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 = z * ((x * y) + ((((t * ((b * i) - (x * a))) + t_1) / z) - (b * c)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = a * (j * (c - (y * (i / a))));
	}
	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 = z * ((x * y) + ((((t * ((b * i) - (x * a))) + t_1) / z) - (b * c)))
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = a * (j * (c - (y * (i / a))))
	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 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x * y) + Float64(Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + t_1) / z) - Float64(b * c))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(j * Float64(c - Float64(y * Float64(i / a)))));
	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 = z * ((x * y) + ((((t * ((b * i) - (x * a))) + t_1) / z) - (b * c)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = a * (j * (c - (y * (i / a))));
	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)], N[(z * N[(N[(x * y), $MachinePrecision] + N[(N[(N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / z), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(a * N[(j * N[(c - N[(y * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 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 80.4%

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

   3. Taylor expanded in z around -inf 87.4%

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

   5. Simplified 89.1%

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

   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)))) < +inf.0

   1. Initial program 96.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around -inf 22.7%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in j around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. *-commutative 66.1%

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

      4. associate-/l* 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 89.4%

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

Alternative 2: 81.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around -inf 22.7%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in j around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. *-commutative 66.1%

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

      4. associate-/l* 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 87.3%

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

Alternative 3: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+101} \lor \neg \left(b \leq 6.4 \cdot 10^{+174}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.5e+63)
     t_3
     (if (<= b -2.65e-98)
       t_2
       (if (<= b -4.7e-229)
         t_1
         (if (<= b 8.2e-212)
           t_2
           (if (<= b 6e-133)
             t_1
             (if (<= b 5.2e-76)
               (* j (- (* a c) (* y i)))
               (if (<= b 6.4e-63)
                 (* t (- (* b i) (* x a)))
                 (if (or (<= b 1.15e+101) (not (<= b 6.4e+174)))
                   t_3
                   (* i (- (* t b) (* y 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) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e+63) {
		tmp = t_3;
	} else if (b <= -2.65e-98) {
		tmp = t_2;
	} else if (b <= -4.7e-229) {
		tmp = t_1;
	} else if (b <= 8.2e-212) {
		tmp = t_2;
	} else if (b <= 6e-133) {
		tmp = t_1;
	} else if (b <= 5.2e-76) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 6.4e-63) {
		tmp = t * ((b * i) - (x * a));
	} else if ((b <= 1.15e+101) || !(b <= 6.4e+174)) {
		tmp = t_3;
	} else {
		tmp = i * ((t * b) - (y * 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) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = y * ((x * z) - (i * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.5d+63)) then
        tmp = t_3
    else if (b <= (-2.65d-98)) then
        tmp = t_2
    else if (b <= (-4.7d-229)) then
        tmp = t_1
    else if (b <= 8.2d-212) then
        tmp = t_2
    else if (b <= 6d-133) then
        tmp = t_1
    else if (b <= 5.2d-76) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 6.4d-63) then
        tmp = t * ((b * i) - (x * a))
    else if ((b <= 1.15d+101) .or. (.not. (b <= 6.4d+174))) then
        tmp = t_3
    else
        tmp = i * ((t * b) - (y * 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) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e+63) {
		tmp = t_3;
	} else if (b <= -2.65e-98) {
		tmp = t_2;
	} else if (b <= -4.7e-229) {
		tmp = t_1;
	} else if (b <= 8.2e-212) {
		tmp = t_2;
	} else if (b <= 6e-133) {
		tmp = t_1;
	} else if (b <= 5.2e-76) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 6.4e-63) {
		tmp = t * ((b * i) - (x * a));
	} else if ((b <= 1.15e+101) || !(b <= 6.4e+174)) {
		tmp = t_3;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = y * ((x * z) - (i * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.5e+63:
		tmp = t_3
	elif b <= -2.65e-98:
		tmp = t_2
	elif b <= -4.7e-229:
		tmp = t_1
	elif b <= 8.2e-212:
		tmp = t_2
	elif b <= 6e-133:
		tmp = t_1
	elif b <= 5.2e-76:
		tmp = j * ((a * c) - (y * i))
	elif b <= 6.4e-63:
		tmp = t * ((b * i) - (x * a))
	elif (b <= 1.15e+101) or not (b <= 6.4e+174):
		tmp = t_3
	else:
		tmp = i * ((t * b) - (y * j))
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.5e+63)
		tmp = t_3;
	elseif (b <= -2.65e-98)
		tmp = t_2;
	elseif (b <= -4.7e-229)
		tmp = t_1;
	elseif (b <= 8.2e-212)
		tmp = t_2;
	elseif (b <= 6e-133)
		tmp = t_1;
	elseif (b <= 5.2e-76)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 6.4e-63)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif ((b <= 1.15e+101) || !(b <= 6.4e+174))
		tmp = t_3;
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	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 = y * ((x * z) - (i * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.5e+63)
		tmp = t_3;
	elseif (b <= -2.65e-98)
		tmp = t_2;
	elseif (b <= -4.7e-229)
		tmp = t_1;
	elseif (b <= 8.2e-212)
		tmp = t_2;
	elseif (b <= 6e-133)
		tmp = t_1;
	elseif (b <= 5.2e-76)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 6.4e-63)
		tmp = t * ((b * i) - (x * a));
	elseif ((b <= 1.15e+101) || ~((b <= 6.4e+174)))
		tmp = t_3;
	else
		tmp = i * ((t * b) - (y * j));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+63], t$95$3, If[LessEqual[b, -2.65e-98], t$95$2, If[LessEqual[b, -4.7e-229], t$95$1, If[LessEqual[b, 8.2e-212], t$95$2, If[LessEqual[b, 6e-133], t$95$1, If[LessEqual[b, 5.2e-76], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e-63], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.15e+101], N[Not[LessEqual[b, 6.4e+174]], $MachinePrecision]], t$95$3, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.50000000000000017e63 or 6.39999999999999978e-63 < b < 1.1500000000000001e101 or 6.4000000000000001e174 < b

   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 b around inf 73.0%

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

   if -4.50000000000000017e63 < b < -2.65000000000000015e-98 or -4.70000000000000034e-229 < b < 8.20000000000000028e-212

   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 y around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

      5. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if -2.65000000000000015e-98 < b < -4.70000000000000034e-229 or 8.20000000000000028e-212 < b < 6.00000000000000038e-133

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

      4. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if 6.00000000000000038e-133 < b < 5.1999999999999999e-76

   1. Initial program 83.2%

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

   3. Taylor expanded in j around inf 83.6%

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

   if 5.1999999999999999e-76 < b < 6.39999999999999978e-63

   1. Initial program 50.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

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

      3. *-lft-identity 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 1.1500000000000001e101 < b < 6.4000000000000001e174

   1. Initial program 45.5%

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

   3. Taylor expanded in i around inf 72.7%

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

      1. sub-neg 72.7%

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

      2. mul-1-neg 72.7%

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

      3. remove-double-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. mul-1-neg 72.7%

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

      6. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+101} \lor \neg \left(b \leq 6.4 \cdot 10^{+174}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.9 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 120000000000:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 2.85 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* t i)) (* y (- (* i j) (* x z)))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -4.9e-17)
     t_2
     (if (<= c -2.2e-178)
       t_1
       (if (<= c -4.7e-265)
         (* i (- (* t b) (* y j)))
         (if (<= c 2.8e-44)
           t_1
           (if (<= c 120000000000.0)
             (* (* b i) (- t (* c (/ z i))))
             (if (<= c 1.25e+91)
               (* j (- (* a c) (* y i)))
               (if (<= c 2.85e+147) 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)) - (y * ((i * j) - (x * z)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.9e-17) {
		tmp = t_2;
	} else if (c <= -2.2e-178) {
		tmp = t_1;
	} else if (c <= -4.7e-265) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 2.8e-44) {
		tmp = t_1;
	} else if (c <= 120000000000.0) {
		tmp = (b * i) * (t - (c * (z / i)));
	} else if (c <= 1.25e+91) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= 2.85e+147) {
		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)) - (y * ((i * j) - (x * z)))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-4.9d-17)) then
        tmp = t_2
    else if (c <= (-2.2d-178)) then
        tmp = t_1
    else if (c <= (-4.7d-265)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 2.8d-44) then
        tmp = t_1
    else if (c <= 120000000000.0d0) then
        tmp = (b * i) * (t - (c * (z / i)))
    else if (c <= 1.25d+91) then
        tmp = j * ((a * c) - (y * i))
    else if (c <= 2.85d+147) 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)) - (y * ((i * j) - (x * z)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.9e-17) {
		tmp = t_2;
	} else if (c <= -2.2e-178) {
		tmp = t_1;
	} else if (c <= -4.7e-265) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 2.8e-44) {
		tmp = t_1;
	} else if (c <= 120000000000.0) {
		tmp = (b * i) * (t - (c * (z / i)));
	} else if (c <= 1.25e+91) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= 2.85e+147) {
		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)) - (y * ((i * j) - (x * z)))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -4.9e-17:
		tmp = t_2
	elif c <= -2.2e-178:
		tmp = t_1
	elif c <= -4.7e-265:
		tmp = i * ((t * b) - (y * j))
	elif c <= 2.8e-44:
		tmp = t_1
	elif c <= 120000000000.0:
		tmp = (b * i) * (t - (c * (z / i)))
	elif c <= 1.25e+91:
		tmp = j * ((a * c) - (y * i))
	elif c <= 2.85e+147:
		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(b * Float64(t * i)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.9e-17)
		tmp = t_2;
	elseif (c <= -2.2e-178)
		tmp = t_1;
	elseif (c <= -4.7e-265)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 2.8e-44)
		tmp = t_1;
	elseif (c <= 120000000000.0)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(c * Float64(z / i))));
	elseif (c <= 1.25e+91)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (c <= 2.85e+147)
		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)) - (y * ((i * j) - (x * z)));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.9e-17)
		tmp = t_2;
	elseif (c <= -2.2e-178)
		tmp = t_1;
	elseif (c <= -4.7e-265)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 2.8e-44)
		tmp = t_1;
	elseif (c <= 120000000000.0)
		tmp = (b * i) * (t - (c * (z / i)));
	elseif (c <= 1.25e+91)
		tmp = j * ((a * c) - (y * i));
	elseif (c <= 2.85e+147)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.9e-17], t$95$2, If[LessEqual[c, -2.2e-178], t$95$1, If[LessEqual[c, -4.7e-265], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e-44], t$95$1, If[LessEqual[c, 120000000000.0], N[(N[(b * i), $MachinePrecision] * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e+91], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.85e+147], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.90000000000000012e-17 or 2.84999999999999996e147 < c

   1. Initial program 62.5%

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

   3. Taylor expanded in c around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if -4.90000000000000012e-17 < c < -2.2000000000000001e-178 or -4.69999999999999986e-265 < c < 2.8e-44 or 1.2500000000000001e91 < c < 2.84999999999999996e147

   1. Initial program 83.6%

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

   3. Taylor expanded in a around 0 69.6%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in i around inf 67.7%

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

   if -2.2000000000000001e-178 < c < -4.69999999999999986e-265

   1. Initial program 72.3%

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

   3. Taylor expanded in i around inf 67.5%

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

      1. sub-neg 67.5%

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

      2. mul-1-neg 67.5%

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

      3. remove-double-neg 67.5%

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

      4. +-commutative 67.5%

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

      5. mul-1-neg 67.5%

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

      6. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

   if 2.8e-44 < c < 1.2e11

   1. Initial program 91.4%

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

   3. Taylor expanded in a around 0 75.0%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in i around -inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. *-commutative 75.6%

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

      3. distribute-rgt-neg-in 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in b around inf 75.8%

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

       1. associate-*r* 75.8%

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

       2. *-commutative 75.8%

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

       3. mul-1-neg 75.8%

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

       4. unsub-neg 75.8%

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

       5. associate-/l* 76.0%

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

   11. Simplified 76.0%

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

   if 1.2e11 < c < 1.2500000000000001e91

   1. Initial program 87.4%

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

   3. Taylor expanded in j around inf 75.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.9 \cdot 10^{-17}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-178}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 120000000000:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 2.85 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.4e+81)
     t_2
     (if (<= i -9.5e-96)
       t_1
       (if (<= i -1e-173)
         (* a (- (* c j) (* x t)))
         (if (<= i 5.5e-298)
           (* c (- (* a j) (* z b)))
           (if (<= i 4.4e-47)
             t_1
             (if (<= i 4.2e+33)
               (* y (- (* x z) (* i j)))
               (if (<= i 6e+110) (* b (* z (- (/ (* 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 = z * ((x * y) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+81) {
		tmp = t_2;
	} else if (i <= -9.5e-96) {
		tmp = t_1;
	} else if (i <= -1e-173) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.5e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.4e-47) {
		tmp = t_1;
	} else if (i <= 4.2e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 6e+110) {
		tmp = b * (z * (((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 = z * ((x * y) - (b * c))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.4d+81)) then
        tmp = t_2
    else if (i <= (-9.5d-96)) then
        tmp = t_1
    else if (i <= (-1d-173)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 5.5d-298) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 4.4d-47) then
        tmp = t_1
    else if (i <= 4.2d+33) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 6d+110) then
        tmp = b * (z * (((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 = z * ((x * y) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+81) {
		tmp = t_2;
	} else if (i <= -9.5e-96) {
		tmp = t_1;
	} else if (i <= -1e-173) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.5e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.4e-47) {
		tmp = t_1;
	} else if (i <= 4.2e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 6e+110) {
		tmp = b * (z * (((t * i) / z) - c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.4e+81:
		tmp = t_2
	elif i <= -9.5e-96:
		tmp = t_1
	elif i <= -1e-173:
		tmp = a * ((c * j) - (x * t))
	elif i <= 5.5e-298:
		tmp = c * ((a * j) - (z * b))
	elif i <= 4.4e-47:
		tmp = t_1
	elif i <= 4.2e+33:
		tmp = y * ((x * z) - (i * j))
	elif i <= 6e+110:
		tmp = b * (z * (((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(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.4e+81)
		tmp = t_2;
	elseif (i <= -9.5e-96)
		tmp = t_1;
	elseif (i <= -1e-173)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 5.5e-298)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 4.4e-47)
		tmp = t_1;
	elseif (i <= 4.2e+33)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 6e+110)
		tmp = Float64(b * Float64(z * Float64(Float64(Float64(t * i) / 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 = z * ((x * y) - (b * c));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.4e+81)
		tmp = t_2;
	elseif (i <= -9.5e-96)
		tmp = t_1;
	elseif (i <= -1e-173)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 5.5e-298)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 4.4e-47)
		tmp = t_1;
	elseif (i <= 4.2e+33)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 6e+110)
		tmp = b * (z * (((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[(z * N[(N[(x * y), $MachinePrecision] - 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, -2.4e+81], t$95$2, If[LessEqual[i, -9.5e-96], t$95$1, If[LessEqual[i, -1e-173], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e-298], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e-47], t$95$1, If[LessEqual[i, 4.2e+33], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+110], N[(b * N[(z * N[(N[(N[(t * i), $MachinePrecision] / z), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.3999999999999999e81 or 6.00000000000000014e110 < i

   1. Initial program 67.2%

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

   3. Taylor expanded in i around inf 77.3%

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

      1. sub-neg 77.3%

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

      2. mul-1-neg 77.3%

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

      3. remove-double-neg 77.3%

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

      4. +-commutative 77.3%

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

      5. mul-1-neg 77.3%

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

      6. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if -2.3999999999999999e81 < i < -9.4999999999999993e-96 or 5.4999999999999996e-298 < i < 4.40000000000000037e-47

   1. Initial program 76.0%

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

   3. Taylor expanded in z around inf 59.2%

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

   if -9.4999999999999993e-96 < i < -1e-173

   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 a around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -1e-173 < i < 5.4999999999999996e-298

   1. Initial program 87.3%

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

   3. Taylor expanded in c around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if 4.40000000000000037e-47 < i < 4.2000000000000001e33

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

      5. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   if 4.2000000000000001e33 < i < 6.00000000000000014e110

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in b around inf 70.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(z \cdot \left(c - \frac{i \cdot t}{z}\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.85 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* t i)) (* y (- (* i j) (* x z)))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.5e+92)
     t_2
     (if (<= i -7.2e-96)
       (* i (- (* t b) (/ (* z (- (* b c) (* x y))) i)))
       (if (<= i 3.4e-64)
         (* a (+ (* c j) (- (/ (* x (* y z)) a) (* x t))))
         (if (<= i 3.85e+34)
           t_1
           (if (<= i 4.8e+110)
             (* b (* z (- (/ (* t i) z) c)))
             (if (<= i 3.3e+150) 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)) - (y * ((i * j) - (x * z)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e+92) {
		tmp = t_2;
	} else if (i <= -7.2e-96) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} else if (i <= 3.4e-64) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 3.85e+34) {
		tmp = t_1;
	} else if (i <= 4.8e+110) {
		tmp = b * (z * (((t * i) / z) - c));
	} else if (i <= 3.3e+150) {
		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)) - (y * ((i * j) - (x * z)))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.5d+92)) then
        tmp = t_2
    else if (i <= (-7.2d-96)) then
        tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
    else if (i <= 3.4d-64) then
        tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
    else if (i <= 3.85d+34) then
        tmp = t_1
    else if (i <= 4.8d+110) then
        tmp = b * (z * (((t * i) / z) - c))
    else if (i <= 3.3d+150) 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)) - (y * ((i * j) - (x * z)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e+92) {
		tmp = t_2;
	} else if (i <= -7.2e-96) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} else if (i <= 3.4e-64) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 3.85e+34) {
		tmp = t_1;
	} else if (i <= 4.8e+110) {
		tmp = b * (z * (((t * i) / z) - c));
	} else if (i <= 3.3e+150) {
		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)) - (y * ((i * j) - (x * z)))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.5e+92:
		tmp = t_2
	elif i <= -7.2e-96:
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
	elif i <= 3.4e-64:
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
	elif i <= 3.85e+34:
		tmp = t_1
	elif i <= 4.8e+110:
		tmp = b * (z * (((t * i) / z) - c))
	elif i <= 3.3e+150:
		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(b * Float64(t * i)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.5e+92)
		tmp = t_2;
	elseif (i <= -7.2e-96)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	elseif (i <= 3.4e-64)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t))));
	elseif (i <= 3.85e+34)
		tmp = t_1;
	elseif (i <= 4.8e+110)
		tmp = Float64(b * Float64(z * Float64(Float64(Float64(t * i) / z) - c)));
	elseif (i <= 3.3e+150)
		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)) - (y * ((i * j) - (x * z)));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.5e+92)
		tmp = t_2;
	elseif (i <= -7.2e-96)
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	elseif (i <= 3.4e-64)
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	elseif (i <= 3.85e+34)
		tmp = t_1;
	elseif (i <= 4.8e+110)
		tmp = b * (z * (((t * i) / z) - c));
	elseif (i <= 3.3e+150)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $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+92], t$95$2, If[LessEqual[i, -7.2e-96], N[(i * N[(N[(t * b), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-64], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.85e+34], t$95$1, If[LessEqual[i, 4.8e+110], N[(b * N[(z * N[(N[(N[(t * i), $MachinePrecision] / z), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.3e+150], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.50000000000000007e92 or 3.29999999999999981e150 < i

   1. Initial program 64.4%

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

   3. Taylor expanded in i around inf 79.4%

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

      1. sub-neg 79.4%

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

      2. mul-1-neg 79.4%

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

      3. remove-double-neg 79.4%

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

      4. +-commutative 79.4%

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

      5. mul-1-neg 79.4%

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

      6. unsub-neg 79.4%

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

   5. Simplified 79.4%

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

   if -1.50000000000000007e92 < i < -7.20000000000000016e-96

   1. Initial program 70.0%

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

   3. Taylor expanded in a around 0 50.6%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in i around -inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. distribute-rgt-neg-in 50.6%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in j around 0 65.5%

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

   if -7.20000000000000016e-96 < i < 3.40000000000000012e-64

   1. Initial program 86.4%

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

   3. Taylor expanded in a around -inf 70.4%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in x around inf 64.2%

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

   if 3.40000000000000012e-64 < i < 3.8499999999999999e34 or 4.80000000000000025e110 < i < 3.29999999999999981e150

   1. Initial program 74.2%

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

   3. Taylor expanded in a around 0 67.9%

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

   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 i around inf 78.3%

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

   if 3.8499999999999999e34 < i < 4.80000000000000025e110

   1. Initial program 100.0%

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

   3. Taylor expanded in z around -inf 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in b around inf 70.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.85 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(z \cdot \left(\frac{t \cdot i}{z} - c\right)\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -5.5e+82)
     t_2
     (if (<= i -1.3e-94)
       t_1
       (if (<= i -5.5e-173)
         (* a (- (* c j) (* x t)))
         (if (<= i 3.7e-298)
           (* c (- (* a j) (* z b)))
           (if (<= i 5.8e-47)
             t_1
             (if (<= i 7.8e+33)
               (* y (- (* x z) (* i j)))
               (if (<= i 1.55e+111) (* 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 = z * ((x * y) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.5e+82) {
		tmp = t_2;
	} else if (i <= -1.3e-94) {
		tmp = t_1;
	} else if (i <= -5.5e-173) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3.7e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.8e-47) {
		tmp = t_1;
	} else if (i <= 7.8e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 1.55e+111) {
		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 = z * ((x * y) - (b * c))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-5.5d+82)) then
        tmp = t_2
    else if (i <= (-1.3d-94)) then
        tmp = t_1
    else if (i <= (-5.5d-173)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 3.7d-298) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 5.8d-47) then
        tmp = t_1
    else if (i <= 7.8d+33) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 1.55d+111) 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 = z * ((x * y) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.5e+82) {
		tmp = t_2;
	} else if (i <= -1.3e-94) {
		tmp = t_1;
	} else if (i <= -5.5e-173) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3.7e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.8e-47) {
		tmp = t_1;
	} else if (i <= 7.8e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 1.55e+111) {
		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 = z * ((x * y) - (b * c))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -5.5e+82:
		tmp = t_2
	elif i <= -1.3e-94:
		tmp = t_1
	elif i <= -5.5e-173:
		tmp = a * ((c * j) - (x * t))
	elif i <= 3.7e-298:
		tmp = c * ((a * j) - (z * b))
	elif i <= 5.8e-47:
		tmp = t_1
	elif i <= 7.8e+33:
		tmp = y * ((x * z) - (i * j))
	elif i <= 1.55e+111:
		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(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -5.5e+82)
		tmp = t_2;
	elseif (i <= -1.3e-94)
		tmp = t_1;
	elseif (i <= -5.5e-173)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 3.7e-298)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 5.8e-47)
		tmp = t_1;
	elseif (i <= 7.8e+33)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 1.55e+111)
		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 = z * ((x * y) - (b * c));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -5.5e+82)
		tmp = t_2;
	elseif (i <= -1.3e-94)
		tmp = t_1;
	elseif (i <= -5.5e-173)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 3.7e-298)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 5.8e-47)
		tmp = t_1;
	elseif (i <= 7.8e+33)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 1.55e+111)
		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[(z * N[(N[(x * y), $MachinePrecision] - 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, -5.5e+82], t$95$2, If[LessEqual[i, -1.3e-94], t$95$1, If[LessEqual[i, -5.5e-173], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e-298], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e-47], t$95$1, If[LessEqual[i, 7.8e+33], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.55e+111], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.49999999999999997e82 or 1.55e111 < i

   1. Initial program 67.2%

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

   3. Taylor expanded in i around inf 77.3%

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

      1. sub-neg 77.3%

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

      2. mul-1-neg 77.3%

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

      3. remove-double-neg 77.3%

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

      4. +-commutative 77.3%

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

      5. mul-1-neg 77.3%

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

      6. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if -5.49999999999999997e82 < i < -1.29999999999999997e-94 or 3.6999999999999998e-298 < i < 5.8000000000000001e-47

   1. Initial program 76.0%

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

   3. Taylor expanded in z around inf 59.2%

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

   if -1.29999999999999997e-94 < i < -5.50000000000000022e-173

   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 a around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -5.50000000000000022e-173 < i < 3.6999999999999998e-298

   1. Initial program 87.3%

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

   3. Taylor expanded in c around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if 5.8000000000000001e-47 < i < 7.8000000000000004e33

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

      5. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   if 7.8000000000000004e33 < i < 1.55e111

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 70.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_2 := a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* t i)) (* y (- (* i j) (* x z)))))
        (t_2 (* a (* j (- c (* y (/ i a)))))))
   (if (<= j -3.2e+180)
     t_2
     (if (<= j -6.4e+74)
       t_1
       (if (<= j -5.2e+16)
         (* j (- (* a c) (* y i)))
         (if (<= j -2.05e-148)
           t_1
           (if (<= j 3e+92)
             (* i (- (* t b) (/ (* z (- (* b c) (* x y))) i)))
             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)) - (y * ((i * j) - (x * z)));
	double t_2 = a * (j * (c - (y * (i / a))));
	double tmp;
	if (j <= -3.2e+180) {
		tmp = t_2;
	} else if (j <= -6.4e+74) {
		tmp = t_1;
	} else if (j <= -5.2e+16) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -2.05e-148) {
		tmp = t_1;
	} else if (j <= 3e+92) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} 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)) - (y * ((i * j) - (x * z)))
    t_2 = a * (j * (c - (y * (i / a))))
    if (j <= (-3.2d+180)) then
        tmp = t_2
    else if (j <= (-6.4d+74)) then
        tmp = t_1
    else if (j <= (-5.2d+16)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-2.05d-148)) then
        tmp = t_1
    else if (j <= 3d+92) then
        tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
    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)) - (y * ((i * j) - (x * z)));
	double t_2 = a * (j * (c - (y * (i / a))));
	double tmp;
	if (j <= -3.2e+180) {
		tmp = t_2;
	} else if (j <= -6.4e+74) {
		tmp = t_1;
	} else if (j <= -5.2e+16) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -2.05e-148) {
		tmp = t_1;
	} else if (j <= 3e+92) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * (t * i)) - (y * ((i * j) - (x * z)))
	t_2 = a * (j * (c - (y * (i / a))))
	tmp = 0
	if j <= -3.2e+180:
		tmp = t_2
	elif j <= -6.4e+74:
		tmp = t_1
	elif j <= -5.2e+16:
		tmp = j * ((a * c) - (y * i))
	elif j <= -2.05e-148:
		tmp = t_1
	elif j <= 3e+92:
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(t * i)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_2 = Float64(a * Float64(j * Float64(c - Float64(y * Float64(i / a)))))
	tmp = 0.0
	if (j <= -3.2e+180)
		tmp = t_2;
	elseif (j <= -6.4e+74)
		tmp = t_1;
	elseif (j <= -5.2e+16)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -2.05e-148)
		tmp = t_1;
	elseif (j <= 3e+92)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	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)) - (y * ((i * j) - (x * z)));
	t_2 = a * (j * (c - (y * (i / a))));
	tmp = 0.0;
	if (j <= -3.2e+180)
		tmp = t_2;
	elseif (j <= -6.4e+74)
		tmp = t_1;
	elseif (j <= -5.2e+16)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -2.05e-148)
		tmp = t_1;
	elseif (j <= 3e+92)
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(j * N[(c - N[(y * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+180], t$95$2, If[LessEqual[j, -6.4e+74], t$95$1, If[LessEqual[j, -5.2e+16], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.05e-148], t$95$1, If[LessEqual[j, 3e+92], N[(i * N[(N[(t * b), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.19999999999999994e180 or 3.00000000000000013e92 < j

   1. Initial program 67.7%

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

   3. Taylor expanded in a around -inf 63.5%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in j around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

      3. *-commutative 76.8%

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

      4. associate-/l* 76.8%

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

   8. Simplified 76.8%

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

   if -3.19999999999999994e180 < j < -6.39999999999999989e74 or -5.2e16 < j < -2.0500000000000001e-148

   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 0 60.2%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in i around inf 58.6%

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

   if -6.39999999999999989e74 < j < -5.2e16

   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 j around inf 71.7%

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

   if -2.0500000000000001e-148 < j < 3.00000000000000013e92

   1. Initial program 79.4%

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

   3. Taylor expanded in a around 0 71.8%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in i around -inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in j around 0 66.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= z -1.35e+14)
     (* b (* z (- c)))
     (if (<= z -1.85e-300)
       t_1
       (if (<= z 2.45e-288)
         (* b (* t i))
         (if (<= z 5.4e-180)
           t_1
           (if (<= z 2.1e-104)
             (* j (* y (- i)))
             (if (<= z 4.9e+39) t_1 (* x (* y z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -1.35e+14) {
		tmp = b * (z * -c);
	} else if (z <= -1.85e-300) {
		tmp = t_1;
	} else if (z <= 2.45e-288) {
		tmp = b * (t * i);
	} else if (z <= 5.4e-180) {
		tmp = t_1;
	} else if (z <= 2.1e-104) {
		tmp = j * (y * -i);
	} else if (z <= 4.9e+39) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	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 (z <= (-1.35d+14)) then
        tmp = b * (z * -c)
    else if (z <= (-1.85d-300)) then
        tmp = t_1
    else if (z <= 2.45d-288) then
        tmp = b * (t * i)
    else if (z <= 5.4d-180) then
        tmp = t_1
    else if (z <= 2.1d-104) then
        tmp = j * (y * -i)
    else if (z <= 4.9d+39) then
        tmp = t_1
    else
        tmp = x * (y * z)
    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 (z <= -1.35e+14) {
		tmp = b * (z * -c);
	} else if (z <= -1.85e-300) {
		tmp = t_1;
	} else if (z <= 2.45e-288) {
		tmp = b * (t * i);
	} else if (z <= 5.4e-180) {
		tmp = t_1;
	} else if (z <= 2.1e-104) {
		tmp = j * (y * -i);
	} else if (z <= 4.9e+39) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if z <= -1.35e+14:
		tmp = b * (z * -c)
	elif z <= -1.85e-300:
		tmp = t_1
	elif z <= 2.45e-288:
		tmp = b * (t * i)
	elif z <= 5.4e-180:
		tmp = t_1
	elif z <= 2.1e-104:
		tmp = j * (y * -i)
	elif z <= 4.9e+39:
		tmp = t_1
	else:
		tmp = x * (y * z)
	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 (z <= -1.35e+14)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= -1.85e-300)
		tmp = t_1;
	elseif (z <= 2.45e-288)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 5.4e-180)
		tmp = t_1;
	elseif (z <= 2.1e-104)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (z <= 4.9e+39)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	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 (z <= -1.35e+14)
		tmp = b * (z * -c);
	elseif (z <= -1.85e-300)
		tmp = t_1;
	elseif (z <= 2.45e-288)
		tmp = b * (t * i);
	elseif (z <= 5.4e-180)
		tmp = t_1;
	elseif (z <= 2.1e-104)
		tmp = j * (y * -i);
	elseif (z <= 4.9e+39)
		tmp = t_1;
	else
		tmp = x * (y * z);
	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[z, -1.35e+14], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-300], t$95$1, If[LessEqual[z, 2.45e-288], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-180], t$95$1, If[LessEqual[z, 2.1e-104], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+39], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.35e14

   1. Initial program 65.8%

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

   3. Taylor expanded in a around 0 66.1%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in i around 0 60.9%

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

   7. Taylor expanded in b around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. *-commutative 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-lft-neg-in 51.2%

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

      5. distribute-rgt-neg-in 51.2%

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

      6. *-commutative 51.2%

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

      7. distribute-rgt-neg-in 51.2%

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

   9. Simplified 51.2%

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

   if -1.35e14 < z < -1.8500000000000001e-300 or 2.45000000000000013e-288 < z < 5.40000000000000028e-180 or 2.09999999999999999e-104 < z < 4.89999999999999987e39

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   if -1.8500000000000001e-300 < z < 2.45000000000000013e-288

   1. Initial program 100.0%

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

   3. Taylor expanded in i around inf 73.1%

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

      1. sub-neg 73.1%

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

      2. mul-1-neg 73.1%

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

      3. remove-double-neg 73.1%

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

      4. +-commutative 73.1%

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

      5. mul-1-neg 73.1%

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

      6. unsub-neg 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in b around inf 87.4%

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

   if 5.40000000000000028e-180 < z < 2.09999999999999999e-104

   1. Initial program 73.2%

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

   3. Taylor expanded in j around inf 61.3%

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

   4. Taylor expanded in a around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. distribute-rgt-neg-in 54.9%

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

   6. Simplified 54.9%

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

   if 4.89999999999999987e39 < z

   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 y around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

      5. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf 48.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))))
   (if (<= b -1.12e-10)
     t_1
     (if (<= b 4e-109)
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (if (<= b 7.5e+125)
         t_1
         (if (<= b 6.4e+174)
           (* a (* j (- c (* y (/ i a)))))
           (* (* b i) (- t (* c (/ z 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 = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -1.12e-10) {
		tmp = t_1;
	} else if (b <= 4e-109) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (b <= 7.5e+125) {
		tmp = t_1;
	} else if (b <= 6.4e+174) {
		tmp = a * (j * (c - (y * (i / a))));
	} else {
		tmp = (b * i) * (t - (c * (z / i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    if (b <= (-1.12d-10)) then
        tmp = t_1
    else if (b <= 4d-109) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (b <= 7.5d+125) then
        tmp = t_1
    else if (b <= 6.4d+174) then
        tmp = a * (j * (c - (y * (i / a))))
    else
        tmp = (b * i) * (t - (c * (z / 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 = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -1.12e-10) {
		tmp = t_1;
	} else if (b <= 4e-109) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (b <= 7.5e+125) {
		tmp = t_1;
	} else if (b <= 6.4e+174) {
		tmp = a * (j * (c - (y * (i / a))));
	} else {
		tmp = (b * i) * (t - (c * (z / i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -1.12e-10:
		tmp = t_1
	elif b <= 4e-109:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif b <= 7.5e+125:
		tmp = t_1
	elif b <= 6.4e+174:
		tmp = a * (j * (c - (y * (i / a))))
	else:
		tmp = (b * i) * (t - (c * (z / i)))
	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(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -1.12e-10)
		tmp = t_1;
	elseif (b <= 4e-109)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (b <= 7.5e+125)
		tmp = t_1;
	elseif (b <= 6.4e+174)
		tmp = Float64(a * Float64(j * Float64(c - Float64(y * Float64(i / a)))));
	else
		tmp = Float64(Float64(b * i) * Float64(t - Float64(c * Float64(z / i))));
	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))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -1.12e-10)
		tmp = t_1;
	elseif (b <= 4e-109)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (b <= 7.5e+125)
		tmp = t_1;
	elseif (b <= 6.4e+174)
		tmp = a * (j * (c - (y * (i / a))));
	else
		tmp = (b * i) * (t - (c * (z / i)));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.12e-10], t$95$1, If[LessEqual[b, 4e-109], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+125], t$95$1, If[LessEqual[b, 6.4e+174], N[(a * N[(j * N[(c - N[(y * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * i), $MachinePrecision] * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.12e-10 or 4e-109 < b < 7.5000000000000006e125

   1. Initial program 78.7%

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

   3. Taylor expanded in a around 0 72.5%

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

   5. Simplified 77.6%

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

   if -1.12e-10 < b < 4e-109

   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 b around 0 78.9%

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

   if 7.5000000000000006e125 < b < 6.4000000000000001e174

   1. Initial program 38.5%

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

   3. Taylor expanded in a around -inf 32.0%

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

   5. Simplified 32.0%

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

   6. Taylor expanded in j around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-/l* 84.7%

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

   8. Simplified 84.7%

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

   if 6.4000000000000001e174 < b

   1. Initial program 85.7%

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

   3. Taylor expanded in a around 0 86.1%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in i around -inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. *-commutative 82.1%

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

      3. distribute-rgt-neg-in 82.1%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in b around inf 86.1%

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

       1. associate-*r* 86.1%

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

       2. *-commutative 86.1%

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

       3. mul-1-neg 86.1%

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

       4. unsub-neg 86.1%

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

       5. associate-/l* 89.4%

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

   11. Simplified 89.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b i) (- t (* c (/ z i))))))
   (if (<= b -1.15e+66)
     t_1
     (if (<= b 5.5e-109)
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (if (<= b 7.5e+125)
         (* i (- (* t b) (/ (* z (- (* b c) (* x y))) i)))
         (if (<= b 6.4e+174) (* a (* j (- c (* y (/ i a))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - (c * (z / i)));
	double tmp;
	if (b <= -1.15e+66) {
		tmp = t_1;
	} else if (b <= 5.5e-109) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (b <= 7.5e+125) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 6.4e+174) {
		tmp = a * (j * (c - (y * (i / a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * i) * (t - (c * (z / i)))
    if (b <= (-1.15d+66)) then
        tmp = t_1
    else if (b <= 5.5d-109) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (b <= 7.5d+125) then
        tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
    else if (b <= 6.4d+174) then
        tmp = a * (j * (c - (y * (i / a))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - (c * (z / i)));
	double tmp;
	if (b <= -1.15e+66) {
		tmp = t_1;
	} else if (b <= 5.5e-109) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (b <= 7.5e+125) {
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	} else if (b <= 6.4e+174) {
		tmp = a * (j * (c - (y * (i / a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * i) * (t - (c * (z / i)))
	tmp = 0
	if b <= -1.15e+66:
		tmp = t_1
	elif b <= 5.5e-109:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif b <= 7.5e+125:
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i))
	elif b <= 6.4e+174:
		tmp = a * (j * (c - (y * (i / a))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * i) * Float64(t - Float64(c * Float64(z / i))))
	tmp = 0.0
	if (b <= -1.15e+66)
		tmp = t_1;
	elseif (b <= 5.5e-109)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (b <= 7.5e+125)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i)));
	elseif (b <= 6.4e+174)
		tmp = Float64(a * Float64(j * Float64(c - Float64(y * Float64(i / a)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * i) * (t - (c * (z / i)));
	tmp = 0.0;
	if (b <= -1.15e+66)
		tmp = t_1;
	elseif (b <= 5.5e-109)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (b <= 7.5e+125)
		tmp = i * ((t * b) - ((z * ((b * c) - (x * y))) / i));
	elseif (b <= 6.4e+174)
		tmp = a * (j * (c - (y * (i / a))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * i), $MachinePrecision] * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+66], t$95$1, If[LessEqual[b, 5.5e-109], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+125], N[(i * N[(N[(t * b), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+174], N[(a * N[(j * N[(c - N[(y * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e66 or 6.4000000000000001e174 < b

   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 78.5%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in i around -inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. *-commutative 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in b around inf 77.9%

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

       1. associate-*r* 76.7%

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

       2. *-commutative 76.7%

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

       3. mul-1-neg 76.7%

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

       4. unsub-neg 76.7%

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

       5. associate-/l* 80.0%

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

   11. Simplified 80.0%

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

   if -1.15e66 < b < 5.5000000000000003e-109

   1. Initial program 75.5%

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

   3. Taylor expanded in b around 0 78.2%

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

   if 5.5000000000000003e-109 < b < 7.5000000000000006e125

   1. Initial program 80.7%

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

   3. Taylor expanded in a around 0 68.1%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in i around -inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. *-commutative 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in j around 0 59.8%

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

   if 7.5000000000000006e125 < b < 6.4000000000000001e174

   1. Initial program 38.5%

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

   3. Taylor expanded in a around -inf 32.0%

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

   5. Simplified 32.0%

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

   6. Taylor expanded in j around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-/l* 84.7%

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

   8. Simplified 84.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+66}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - y \cdot \frac{i}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - c \cdot \frac{z}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -880000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.06 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -880000000000.0)
     t_2
     (if (<= i -1.06e-39)
       t_1
       (if (<= i -8e-113)
         (* b (- (* t i) (* z c)))
         (if (<= i 3e+112) 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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -880000000000.0) {
		tmp = t_2;
	} else if (i <= -1.06e-39) {
		tmp = t_1;
	} else if (i <= -8e-113) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 3e+112) {
		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 = c * ((a * j) - (z * b))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-880000000000.0d0)) then
        tmp = t_2
    else if (i <= (-1.06d-39)) then
        tmp = t_1
    else if (i <= (-8d-113)) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 3d+112) 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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -880000000000.0) {
		tmp = t_2;
	} else if (i <= -1.06e-39) {
		tmp = t_1;
	} else if (i <= -8e-113) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 3e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -880000000000.0:
		tmp = t_2
	elif i <= -1.06e-39:
		tmp = t_1
	elif i <= -8e-113:
		tmp = b * ((t * i) - (z * c))
	elif i <= 3e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -880000000000.0)
		tmp = t_2;
	elseif (i <= -1.06e-39)
		tmp = t_1;
	elseif (i <= -8e-113)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 3e+112)
		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 = c * ((a * j) - (z * b));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -880000000000.0)
		tmp = t_2;
	elseif (i <= -1.06e-39)
		tmp = t_1;
	elseif (i <= -8e-113)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 3e+112)
		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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -880000000000.0], t$95$2, If[LessEqual[i, -1.06e-39], t$95$1, If[LessEqual[i, -8e-113], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.8e11 or 2.99999999999999979e112 < i

   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 i around inf 73.7%

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

      1. sub-neg 73.7%

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

      2. mul-1-neg 73.7%

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

      3. remove-double-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. mul-1-neg 73.7%

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

      6. unsub-neg 73.7%

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

   5. Simplified 73.7%

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

   if -8.8e11 < i < -1.06000000000000004e-39 or -7.99999999999999983e-113 < i < 2.99999999999999979e112

   1. Initial program 82.5%

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

   3. Taylor expanded in c around inf 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   if -1.06000000000000004e-39 < i < -7.99999999999999983e-113

   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 b around inf 48.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -880000000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.06 \cdot 10^{-39}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.15e-10)
     t_2
     (if (<= b -7.4e-230)
       t_1
       (if (<= b 1.2e-213) (* z (* x y)) (if (<= b 1.05e-100) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.15e-10) {
		tmp = t_2;
	} else if (b <= -7.4e-230) {
		tmp = t_1;
	} else if (b <= 1.2e-213) {
		tmp = z * (x * y);
	} else if (b <= 1.05e-100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.15d-10)) then
        tmp = t_2
    else if (b <= (-7.4d-230)) then
        tmp = t_1
    else if (b <= 1.2d-213) then
        tmp = z * (x * y)
    else if (b <= 1.05d-100) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.15e-10) {
		tmp = t_2;
	} else if (b <= -7.4e-230) {
		tmp = t_1;
	} else if (b <= 1.2e-213) {
		tmp = z * (x * y);
	} else if (b <= 1.05e-100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.15e-10:
		tmp = t_2
	elif b <= -7.4e-230:
		tmp = t_1
	elif b <= 1.2e-213:
		tmp = z * (x * y)
	elif b <= 1.05e-100:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.15e-10)
		tmp = t_2;
	elseif (b <= -7.4e-230)
		tmp = t_1;
	elseif (b <= 1.2e-213)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.05e-100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.15e-10)
		tmp = t_2;
	elseif (b <= -7.4e-230)
		tmp = t_1;
	elseif (b <= 1.2e-213)
		tmp = z * (x * y);
	elseif (b <= 1.05e-100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e-10], t$95$2, If[LessEqual[b, -7.4e-230], t$95$1, If[LessEqual[b, 1.2e-213], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15000000000000004e-10 or 1.05000000000000005e-100 < b

   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 b around inf 64.1%

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

   if -1.15000000000000004e-10 < b < -7.39999999999999963e-230 or 1.19999999999999998e-213 < b < 1.05000000000000005e-100

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -7.39999999999999963e-230 < b < 1.19999999999999998e-213

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around inf 38.9%

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

      1. associate-*r* 44.4%

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

      2. *-commutative 44.4%

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

   8. Simplified 44.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* y (- i)))))
   (if (<= z -3.4e-17)
     (* b (* z (- c)))
     (if (<= z 9.5e-254)
       t_1
       (if (<= z 5.1e-180)
         (* x (* a (- t)))
         (if (<= z 8e-68) t_1 (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (z <= -3.4e-17) {
		tmp = b * (z * -c);
	} else if (z <= 9.5e-254) {
		tmp = t_1;
	} else if (z <= 5.1e-180) {
		tmp = x * (a * -t);
	} else if (z <= 8e-68) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y * -i)
    if (z <= (-3.4d-17)) then
        tmp = b * (z * -c)
    else if (z <= 9.5d-254) then
        tmp = t_1
    else if (z <= 5.1d-180) then
        tmp = x * (a * -t)
    else if (z <= 8d-68) then
        tmp = t_1
    else
        tmp = x * (y * z)
    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 * (y * -i);
	double tmp;
	if (z <= -3.4e-17) {
		tmp = b * (z * -c);
	} else if (z <= 9.5e-254) {
		tmp = t_1;
	} else if (z <= 5.1e-180) {
		tmp = x * (a * -t);
	} else if (z <= 8e-68) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (y * -i)
	tmp = 0
	if z <= -3.4e-17:
		tmp = b * (z * -c)
	elif z <= 9.5e-254:
		tmp = t_1
	elif z <= 5.1e-180:
		tmp = x * (a * -t)
	elif z <= 8e-68:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (z <= -3.4e-17)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= 9.5e-254)
		tmp = t_1;
	elseif (z <= 5.1e-180)
		tmp = Float64(x * Float64(a * Float64(-t)));
	elseif (z <= 8e-68)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (y * -i);
	tmp = 0.0;
	if (z <= -3.4e-17)
		tmp = b * (z * -c);
	elseif (z <= 9.5e-254)
		tmp = t_1;
	elseif (z <= 5.1e-180)
		tmp = x * (a * -t);
	elseif (z <= 8e-68)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-17], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-254], t$95$1, If[LessEqual[z, 5.1e-180], N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-68], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e-17

   1. Initial program 66.4%

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

   3. Taylor expanded in a around 0 66.7%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in i around 0 59.6%

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

   7. Taylor expanded in b around inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. *-commutative 49.5%

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

      3. mul-1-neg 49.5%

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

      4. distribute-lft-neg-in 49.5%

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

      5. distribute-rgt-neg-in 49.5%

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

      6. *-commutative 49.5%

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

      7. distribute-rgt-neg-in 49.5%

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

   9. Simplified 49.5%

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

   if -3.3999999999999998e-17 < z < 9.5000000000000003e-254 or 5.0999999999999999e-180 < z < 8.00000000000000053e-68

   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 inf 54.2%

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

   4. Taylor expanded in a around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-rgt-neg-in 36.3%

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

   6. Simplified 36.3%

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

   if 9.5000000000000003e-254 < z < 5.0999999999999999e-180

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in j around 0 44.6%

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

      1. neg-mul-1 44.6%

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

      2. distribute-lft-neg-in 44.6%

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

      3. *-commutative 44.6%

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

   8. Simplified 44.6%

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

      1. associate-*r* 44.8%

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

      2. neg-sub0 44.8%

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

   10. Applied egg-rr 44.8%

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

   11. Taylor expanded in a around 0 44.6%

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

       1. mul-1-neg 44.6%

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

       2. *-commutative 44.6%

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

       3. associate-*r* 44.8%

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

       4. *-commutative 44.8%

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

       5. associate-*l* 44.8%

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

       6. distribute-rgt-neg-in 44.8%

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

   13. Simplified 44.8%

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

   if 8.00000000000000053e-68 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. *-commutative 52.8%

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

      5. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in z around inf 43.9%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* y (- i)))))
   (if (<= z -1e-17)
     (* b (* z (- c)))
     (if (<= z 1.6e-253)
       t_1
       (if (<= z 3.5e-180)
         (* a (* x (- t)))
         (if (<= z 2.9e-61) t_1 (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (z <= -1e-17) {
		tmp = b * (z * -c);
	} else if (z <= 1.6e-253) {
		tmp = t_1;
	} else if (z <= 3.5e-180) {
		tmp = a * (x * -t);
	} else if (z <= 2.9e-61) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y * -i)
    if (z <= (-1d-17)) then
        tmp = b * (z * -c)
    else if (z <= 1.6d-253) then
        tmp = t_1
    else if (z <= 3.5d-180) then
        tmp = a * (x * -t)
    else if (z <= 2.9d-61) then
        tmp = t_1
    else
        tmp = x * (y * z)
    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 * (y * -i);
	double tmp;
	if (z <= -1e-17) {
		tmp = b * (z * -c);
	} else if (z <= 1.6e-253) {
		tmp = t_1;
	} else if (z <= 3.5e-180) {
		tmp = a * (x * -t);
	} else if (z <= 2.9e-61) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (y * -i)
	tmp = 0
	if z <= -1e-17:
		tmp = b * (z * -c)
	elif z <= 1.6e-253:
		tmp = t_1
	elif z <= 3.5e-180:
		tmp = a * (x * -t)
	elif z <= 2.9e-61:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (z <= -1e-17)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= 1.6e-253)
		tmp = t_1;
	elseif (z <= 3.5e-180)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 2.9e-61)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (y * -i);
	tmp = 0.0;
	if (z <= -1e-17)
		tmp = b * (z * -c);
	elseif (z <= 1.6e-253)
		tmp = t_1;
	elseif (z <= 3.5e-180)
		tmp = a * (x * -t);
	elseif (z <= 2.9e-61)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-17], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-253], t$95$1, If[LessEqual[z, 3.5e-180], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-61], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000007e-17

   1. Initial program 66.4%

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

   3. Taylor expanded in a around 0 66.7%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in i around 0 59.6%

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

   7. Taylor expanded in b around inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. *-commutative 49.5%

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

      3. mul-1-neg 49.5%

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

      4. distribute-lft-neg-in 49.5%

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

      5. distribute-rgt-neg-in 49.5%

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

      6. *-commutative 49.5%

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

      7. distribute-rgt-neg-in 49.5%

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

   9. Simplified 49.5%

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

   if -1.00000000000000007e-17 < z < 1.5999999999999999e-253 or 3.5000000000000001e-180 < z < 2.8999999999999999e-61

   1. Initial program 84.8%

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

   3. Taylor expanded in j around inf 54.6%

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

   4. Taylor expanded in a around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. distribute-rgt-neg-in 36.0%

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

   6. Simplified 36.0%

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

   if 1.5999999999999999e-253 < z < 3.5000000000000001e-180

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in j around 0 44.6%

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

      1. neg-mul-1 44.6%

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

      2. distribute-lft-neg-in 44.6%

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

      3. *-commutative 44.6%

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

   8. Simplified 44.6%

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

   if 2.8999999999999999e-61 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. *-commutative 53.4%

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

      5. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around inf 44.4%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-253}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-61}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1400000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.3e-7)
   (* b (* z (- c)))
   (if (<= z 3.2e-277)
     (* t (* b i))
     (if (<= z 7e-199)
       (* a (* c j))
       (if (<= z 1400000.0) (* b (* t i)) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e-7) {
		tmp = b * (z * -c);
	} else if (z <= 3.2e-277) {
		tmp = t * (b * i);
	} else if (z <= 7e-199) {
		tmp = a * (c * j);
	} else if (z <= 1400000.0) {
		tmp = b * (t * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.3d-7)) then
        tmp = b * (z * -c)
    else if (z <= 3.2d-277) then
        tmp = t * (b * i)
    else if (z <= 7d-199) then
        tmp = a * (c * j)
    else if (z <= 1400000.0d0) then
        tmp = b * (t * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e-7) {
		tmp = b * (z * -c);
	} else if (z <= 3.2e-277) {
		tmp = t * (b * i);
	} else if (z <= 7e-199) {
		tmp = a * (c * j);
	} else if (z <= 1400000.0) {
		tmp = b * (t * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.3e-7:
		tmp = b * (z * -c)
	elif z <= 3.2e-277:
		tmp = t * (b * i)
	elif z <= 7e-199:
		tmp = a * (c * j)
	elif z <= 1400000.0:
		tmp = b * (t * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.3e-7)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= 3.2e-277)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 7e-199)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1400000.0)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.3e-7)
		tmp = b * (z * -c);
	elseif (z <= 3.2e-277)
		tmp = t * (b * i);
	elseif (z <= 7e-199)
		tmp = a * (c * j);
	elseif (z <= 1400000.0)
		tmp = b * (t * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.3e-7], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-277], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-199], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1400000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.29999999999999995e-7

   1. Initial program 67.5%

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

   3. Taylor expanded in a around 0 66.1%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in i around 0 60.6%

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

   7. Taylor expanded in b around inf 50.3%

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

      1. associate-*r* 50.3%

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

      2. *-commutative 50.3%

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

      3. mul-1-neg 50.3%

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

      4. distribute-lft-neg-in 50.3%

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

      5. distribute-rgt-neg-in 50.3%

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

      6. *-commutative 50.3%

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

      7. distribute-rgt-neg-in 50.3%

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

   9. Simplified 50.3%

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

   if -2.29999999999999995e-7 < z < 3.1999999999999998e-277

   1. Initial program 85.2%

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

   3. Taylor expanded in i around inf 49.3%

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

      1. sub-neg 49.3%

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

      2. mul-1-neg 49.3%

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

      3. remove-double-neg 49.3%

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

      4. +-commutative 49.3%

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

      5. mul-1-neg 49.3%

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

      6. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in b around inf 30.9%

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

      1. associate-*r* 31.0%

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

   8. Applied egg-rr 31.0%

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

   if 3.1999999999999998e-277 < z < 6.9999999999999998e-199

   1. Initial program 75.2%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in j around inf 51.5%

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

      1. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if 6.9999999999999998e-199 < z < 1.4e6

   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 i around inf 57.4%

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

      1. sub-neg 57.4%

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

      2. mul-1-neg 57.4%

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

      3. remove-double-neg 57.4%

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

      4. +-commutative 57.4%

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

      5. mul-1-neg 57.4%

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

      6. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf 38.0%

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

   if 1.4e6 < z

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in z around inf 45.5%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1400000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.5e+66)
   (* b (* t i))
   (if (<= b -1.6e-198)
     (* c (* a j))
     (if (<= b 6.5e-108) (* z (* x y)) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.5e+66) {
		tmp = b * (t * i);
	} else if (b <= -1.6e-198) {
		tmp = c * (a * j);
	} else if (b <= 6.5e-108) {
		tmp = z * (x * y);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.5d+66)) then
        tmp = b * (t * i)
    else if (b <= (-1.6d-198)) then
        tmp = c * (a * j)
    else if (b <= 6.5d-108) then
        tmp = z * (x * y)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.5e+66) {
		tmp = b * (t * i);
	} else if (b <= -1.6e-198) {
		tmp = c * (a * j);
	} else if (b <= 6.5e-108) {
		tmp = z * (x * y);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.5e+66:
		tmp = b * (t * i)
	elif b <= -1.6e-198:
		tmp = c * (a * j)
	elif b <= 6.5e-108:
		tmp = z * (x * y)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.5e+66)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -1.6e-198)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 6.5e-108)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.5e+66)
		tmp = b * (t * i);
	elseif (b <= -1.6e-198)
		tmp = c * (a * j);
	elseif (b <= 6.5e-108)
		tmp = z * (x * y);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.5e+66], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-198], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-108], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.4999999999999998e66

   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 i around inf 44.5%

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

      1. sub-neg 44.5%

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

      2. mul-1-neg 44.5%

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

      3. remove-double-neg 44.5%

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

      4. +-commutative 44.5%

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

      5. mul-1-neg 44.5%

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

      6. unsub-neg 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in b around inf 41.2%

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

   if -4.4999999999999998e66 < b < -1.59999999999999997e-198

   1. Initial program 73.4%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in j around inf 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

      1. associate-*r* 34.9%

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

   10. Applied egg-rr 34.9%

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

   if -1.59999999999999997e-198 < b < 6.5000000000000002e-108

   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 y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in z around inf 33.4%

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

      1. associate-*r* 38.1%

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

      2. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if 6.5000000000000002e-108 < b

   1. Initial program 76.9%

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

   3. Taylor expanded in i around inf 54.8%

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

      1. sub-neg 54.8%

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

      2. mul-1-neg 54.8%

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

      3. remove-double-neg 54.8%

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

      4. +-commutative 54.8%

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

      5. mul-1-neg 54.8%

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

      6. unsub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in b around inf 35.4%

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

      1. associate-*r* 38.7%

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

   8. Applied egg-rr 38.7%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+145} \lor \neg \left(b \leq 2.9 \cdot 10^{-74}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5.8e+145) (not (<= b 2.9e-74))) (* i (* t b)) (* x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.8e+145) || !(b <= 2.9e-74)) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-5.8d+145)) .or. (.not. (b <= 2.9d-74))) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.8e+145) || !(b <= 2.9e-74)) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -5.8e+145) or not (b <= 2.9e-74):
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -5.8e+145) || !(b <= 2.9e-74))
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -5.8e+145) || ~((b <= 2.9e-74)))
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -5.8e+145], N[Not[LessEqual[b, 2.9e-74]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.8000000000000001e145 or 2.9e-74 < b

   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 i around inf 53.8%

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

      1. sub-neg 53.8%

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

      2. mul-1-neg 53.8%

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

      3. remove-double-neg 53.8%

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

      4. +-commutative 53.8%

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

      5. mul-1-neg 53.8%

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

      6. unsub-neg 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in b around inf 42.5%

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

      1. *-commutative 42.5%

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

   8. Simplified 42.5%

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

   if -5.8000000000000001e145 < b < 2.9e-74

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

      5. *-commutative 45.1%

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

   5. Simplified 45.1%

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

   6. Taylor expanded in z around inf 29.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+145} \lor \neg \left(b \leq 2.9 \cdot 10^{-74}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-104} \lor \neg \left(t \leq 2.1 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.9e-104) (not (<= t 2.1e+84))) (* 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 ((t <= -1.9e-104) || !(t <= 2.1e+84)) {
		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 ((t <= (-1.9d-104)) .or. (.not. (t <= 2.1d+84))) 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 ((t <= -1.9e-104) || !(t <= 2.1e+84)) {
		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 (t <= -1.9e-104) or not (t <= 2.1e+84):
		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 ((t <= -1.9e-104) || !(t <= 2.1e+84))
		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 ((t <= -1.9e-104) || ~((t <= 2.1e+84)))
		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[t, -1.9e-104], N[Not[LessEqual[t, 2.1e+84]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9e-104 or 2.10000000000000019e84 < t

   1. Initial program 71.5%

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

   3. Taylor expanded in i around inf 48.6%

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

      1. sub-neg 48.6%

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

      2. mul-1-neg 48.6%

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

      3. remove-double-neg 48.6%

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

      4. +-commutative 48.6%

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

      5. mul-1-neg 48.6%

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

      6. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in b around inf 38.5%

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

   if -1.9e-104 < t < 2.10000000000000019e84

   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 a around inf 33.8%

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

      1. +-commutative 33.8%

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

      2. mul-1-neg 33.8%

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

      3. unsub-neg 33.8%

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

      4. *-commutative 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in j around inf 28.8%

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

      1. *-commutative 28.8%

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

   8. Simplified 28.8%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-104} \lor \neg \left(t \leq 2.1 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3e+142)
   (* i (* t b))
   (if (<= b 3e-74) (* x (* y z)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3e+142) {
		tmp = i * (t * b);
	} else if (b <= 3e-74) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3d+142)) then
        tmp = i * (t * b)
    else if (b <= 3d-74) then
        tmp = x * (y * z)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3e+142) {
		tmp = i * (t * b);
	} else if (b <= 3e-74) {
		tmp = x * (y * z);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3e+142:
		tmp = i * (t * b)
	elif b <= 3e-74:
		tmp = x * (y * z)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3e+142)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= 3e-74)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3e+142)
		tmp = i * (t * b);
	elseif (b <= 3e-74)
		tmp = x * (y * z);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3e+142], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-74], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999975e142

   1. Initial program 75.6%

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

   3. Taylor expanded in i around inf 52.7%

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

      1. sub-neg 52.7%

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

      2. mul-1-neg 52.7%

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

      3. remove-double-neg 52.7%

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

      4. +-commutative 52.7%

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

      5. mul-1-neg 52.7%

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

      6. unsub-neg 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in b around inf 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -2.99999999999999975e142 < b < 3.00000000000000007e-74

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

      5. *-commutative 45.1%

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

   5. Simplified 45.1%

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

   6. Taylor expanded in z around inf 29.3%

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

   if 3.00000000000000007e-74 < b

   1. Initial program 76.7%

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

   3. Taylor expanded in i around inf 54.4%

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

      1. sub-neg 54.4%

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

      2. mul-1-neg 54.4%

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

      3. remove-double-neg 54.4%

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

      4. +-commutative 54.4%

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

      5. mul-1-neg 54.4%

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

      6. unsub-neg 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in b around inf 36.3%

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

      1. associate-*r* 39.8%

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

   8. Applied egg-rr 39.8%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.4e-12)
   (* b (* t i))
   (if (<= b 6.2e-101) (* a (* c j)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.4e-12) {
		tmp = b * (t * i);
	} else if (b <= 6.2e-101) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.4d-12)) then
        tmp = b * (t * i)
    else if (b <= 6.2d-101) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.4e-12) {
		tmp = b * (t * i);
	} else if (b <= 6.2e-101) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.4e-12:
		tmp = b * (t * i)
	elif b <= 6.2e-101:
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.4e-12)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 6.2e-101)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.4e-12)
		tmp = b * (t * i);
	elseif (b <= 6.2e-101)
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.4e-12], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-101], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4000000000000001e-12

   1. Initial program 77.3%

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

   3. Taylor expanded in i around inf 49.3%

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

      1. sub-neg 49.3%

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

      2. mul-1-neg 49.3%

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

      3. remove-double-neg 49.3%

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

      4. +-commutative 49.3%

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

      5. mul-1-neg 49.3%

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

      6. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in b around inf 37.8%

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

   if -3.4000000000000001e-12 < b < 6.19999999999999946e-101

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in j around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

   if 6.19999999999999946e-101 < b

   1. Initial program 77.8%

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

   3. Taylor expanded in i around inf 54.3%

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

      1. sub-neg 54.3%

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

      2. mul-1-neg 54.3%

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

      3. remove-double-neg 54.3%

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

      4. +-commutative 54.3%

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

      5. mul-1-neg 54.3%

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

      6. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in b around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 9.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 9.2e+133) (* a (* c j)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 9.2e+133) {
		tmp = a * (c * j);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= 9.2d+133) then
        tmp = a * (c * j)
    else
        tmp = a * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 9.2e+133) {
		tmp = a * (c * j);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= 9.2e+133:
		tmp = a * (c * j)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 9.2e+133)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= 9.2e+133)
		tmp = a * (c * j);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 9.2e+133], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.1999999999999996e133

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 36.5%

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

      1. +-commutative 36.5%

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

      2. mul-1-neg 36.5%

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

      3. unsub-neg 36.5%

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

      4. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in j around inf 23.8%

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

      1. *-commutative 23.8%

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

   8. Simplified 23.8%

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

   if 9.1999999999999996e133 < t

   1. Initial program 59.1%

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

   3. Taylor expanded in a around inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in j around 0 34.7%

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

      1. neg-mul-1 34.7%

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

      2. distribute-lft-neg-in 34.7%

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

      3. *-commutative 34.7%

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

   8. Simplified 34.7%

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

      1. associate-*r* 27.6%

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

      2. neg-sub0 27.6%

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

   10. Applied egg-rr 27.6%

       \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(0 - t\right)} \]
   11. Step-by-step derivation

       1. associate-*l* 34.7%

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

       2. add-sqr-sqrt 0.0%

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

       3. sqrt-unprod 37.5%

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

       4. sub0-neg 37.5%

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

       5. sub0-neg 37.5%

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

       6. sqr-neg 37.5%

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

       7. sqrt-unprod 26.9%

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

       8. add-sqr-sqrt 26.9%

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

   12. Applied egg-rr 26.9%

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

4. Final simplification 24.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.9% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.9%

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

3. Taylor expanded in a around inf 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 22.2%

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

   1. *-commutative 22.2%

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

8. Simplified 22.2%

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

9. Final simplification 22.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. 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 2024097 
(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)))))