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

Percentage Accurate: 73.6% → 81.4%

Time: 20.3s

Alternatives: 25

Speedup: 0.5×

• 59.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.4% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* b (- (* t i) (* z c))) (* x (- (* y z) (* t a))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 (- INFINITY))
     (*
      a
      (-
       (* c j)
       (+
        (* x t)
        (/ (- (* b (- (* z c) (* t i))) (* y (- (* x z) (* i j)))) a))))
     (if (<= t_1 INFINITY) t_1 (* (* a c) (- j (* b (/ z 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 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = a * ((c * j) - ((x * t) + (((b * ((z * c) - (t * i))) - (y * ((x * z) - (i * j)))) / a)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * c) * (j - (b * (z / 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 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = a * ((c * j) - ((x * t) + (((b * ((z * c) - (t * i))) - (y * ((x * z) - (i * j)))) / a)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a * c) * (j - (b * (z / a)));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(a * N[(N[(c * j), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] + N[(N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * c), $MachinePrecision] * N[(j - N[(b * N[(z / a), $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 77.2%

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

   3. Taylor expanded in a around -inf 82.0%

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

   5. Simplified 85.5%

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

   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 91.9%

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

   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 34.8%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in c around inf 58.1%

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

      1. associate-*r* 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 83.8%

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

Alternative 2: 82.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* b (- (* t i) (* z c))) (* x (- (* y z) (* t a))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* (* a c) (- j (* b (/ z 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 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * c) * (j - (b * (z / 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 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a * c) * (j - (b * (z / a)));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.1%

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

   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 34.8%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in c around inf 58.1%

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

      1. associate-*r* 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 82.0%

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

Alternative 3: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 10^{-37}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(j - b \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(b \cdot \frac{t}{a} - j \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= i -8.5e+67)
     (* i (- (* t b) (* y j)))
     (if (<= i -9.5e-232)
       t_1
       (if (<= i 4e-289)
         (* c (- (* a j) (* z b)))
         (if (<= i 1.65e-80)
           t_1
           (if (<= i 1e-37)
             (* (* a c) (- j (* b (/ z a))))
             (* (* a i) (- (* b (/ t a)) (* j (/ y 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));
	double tmp;
	if (i <= -8.5e+67) {
		tmp = i * ((t * b) - (y * j));
	} else if (i <= -9.5e-232) {
		tmp = t_1;
	} else if (i <= 4e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.65e-80) {
		tmp = t_1;
	} else if (i <= 1e-37) {
		tmp = (a * c) * (j - (b * (z / a)));
	} else {
		tmp = (a * i) * ((b * (t / a)) - (j * (y / a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (i <= (-8.5d+67)) then
        tmp = i * ((t * b) - (y * j))
    else if (i <= (-9.5d-232)) then
        tmp = t_1
    else if (i <= 4d-289) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.65d-80) then
        tmp = t_1
    else if (i <= 1d-37) then
        tmp = (a * c) * (j - (b * (z / a)))
    else
        tmp = (a * i) * ((b * (t / a)) - (j * (y / a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -8.5e+67) {
		tmp = i * ((t * b) - (y * j));
	} else if (i <= -9.5e-232) {
		tmp = t_1;
	} else if (i <= 4e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.65e-80) {
		tmp = t_1;
	} else if (i <= 1e-37) {
		tmp = (a * c) * (j - (b * (z / a)));
	} else {
		tmp = (a * i) * ((b * (t / a)) - (j * (y / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if i <= -8.5e+67:
		tmp = i * ((t * b) - (y * j))
	elif i <= -9.5e-232:
		tmp = t_1
	elif i <= 4e-289:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.65e-80:
		tmp = t_1
	elif i <= 1e-37:
		tmp = (a * c) * (j - (b * (z / a)))
	else:
		tmp = (a * i) * ((b * (t / a)) - (j * (y / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (i <= -8.5e+67)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (i <= -9.5e-232)
		tmp = t_1;
	elseif (i <= 4e-289)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.65e-80)
		tmp = t_1;
	elseif (i <= 1e-37)
		tmp = Float64(Float64(a * c) * Float64(j - Float64(b * Float64(z / a))));
	else
		tmp = Float64(Float64(a * i) * Float64(Float64(b * Float64(t / a)) - Float64(j * Float64(y / 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));
	tmp = 0.0;
	if (i <= -8.5e+67)
		tmp = i * ((t * b) - (y * j));
	elseif (i <= -9.5e-232)
		tmp = t_1;
	elseif (i <= 4e-289)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.65e-80)
		tmp = t_1;
	elseif (i <= 1e-37)
		tmp = (a * c) * (j - (b * (z / a)));
	else
		tmp = (a * i) * ((b * (t / a)) - (j * (y / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e+67], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9.5e-232], t$95$1, If[LessEqual[i, 4e-289], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e-80], t$95$1, If[LessEqual[i, 1e-37], N[(N[(a * c), $MachinePrecision] * N[(j - N[(b * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * i), $MachinePrecision] * N[(N[(b * N[(t / a), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.50000000000000038e67

   1. Initial program 58.9%

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

   3. Taylor expanded in a around 0 72.2%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   if -8.50000000000000038e67 < i < -9.50000000000000033e-232 or 4e-289 < i < 1.65e-80

   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 b around 0 68.7%

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

   4. Taylor expanded in j around 0 64.3%

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

   if -9.50000000000000033e-232 < i < 4e-289

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 81.4%

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

   if 1.65e-80 < i < 1.00000000000000007e-37

   1. Initial program 78.3%

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

   3. Taylor expanded in a around -inf 67.0%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in c around inf 64.7%

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

      1. associate-*r* 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

   if 1.00000000000000007e-37 < i

   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 a around -inf 64.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in i around inf 60.8%

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

      1. associate-*r* 64.7%

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

      2. +-commutative 64.7%

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

      3. mul-1-neg 64.7%

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

      4. unsub-neg 64.7%

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

      5. associate-/l* 64.7%

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

      6. associate-/l* 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 10^{-37}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(j - b \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(b \cdot \frac{t}{a} - j \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i \cdot \frac{t}{a} - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;b \leq -19:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-225}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* b (* t i)) (* y (* z (- x (* i (/ j z))))))))
   (if (<= b -1.95e+139)
     (* a (* b (- (* i (/ t a)) (* c (/ z a)))))
     (if (<= b -19.0)
       t_1
       (if (<= b 3.8e-225)
         (- (* j (- (* a c) (* y i))) (* t (* x a)))
         (if (<= b 2.7e+19)
           t_1
           (if (<= b 6.8e+162)
             (* a (- (* c j) (* x t)))
             (* b (- (* t i) (* z c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * (t * i)) + (y * (z * (x - (i * (j / z)))));
	double tmp;
	if (b <= -1.95e+139) {
		tmp = a * (b * ((i * (t / a)) - (c * (z / a))));
	} else if (b <= -19.0) {
		tmp = t_1;
	} else if (b <= 3.8e-225) {
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	} else if (b <= 2.7e+19) {
		tmp = t_1;
	} else if (b <= 6.8e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * (t * i)) + (y * (z * (x - (i * (j / z)))))
    if (b <= (-1.95d+139)) then
        tmp = a * (b * ((i * (t / a)) - (c * (z / a))))
    else if (b <= (-19.0d0)) then
        tmp = t_1
    else if (b <= 3.8d-225) then
        tmp = (j * ((a * c) - (y * i))) - (t * (x * a))
    else if (b <= 2.7d+19) then
        tmp = t_1
    else if (b <= 6.8d+162) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * (t * i)) + (y * (z * (x - (i * (j / z)))));
	double tmp;
	if (b <= -1.95e+139) {
		tmp = a * (b * ((i * (t / a)) - (c * (z / a))));
	} else if (b <= -19.0) {
		tmp = t_1;
	} else if (b <= 3.8e-225) {
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	} else if (b <= 2.7e+19) {
		tmp = t_1;
	} else if (b <= 6.8e+162) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * (t * i)) + (y * (z * (x - (i * (j / z)))))
	tmp = 0
	if b <= -1.95e+139:
		tmp = a * (b * ((i * (t / a)) - (c * (z / a))))
	elif b <= -19.0:
		tmp = t_1
	elif b <= 3.8e-225:
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a))
	elif b <= 2.7e+19:
		tmp = t_1
	elif b <= 6.8e+162:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(t * i)) + Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z))))))
	tmp = 0.0
	if (b <= -1.95e+139)
		tmp = Float64(a * Float64(b * Float64(Float64(i * Float64(t / a)) - Float64(c * Float64(z / a)))));
	elseif (b <= -19.0)
		tmp = t_1;
	elseif (b <= 3.8e-225)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(t * Float64(x * a)));
	elseif (b <= 2.7e+19)
		tmp = t_1;
	elseif (b <= 6.8e+162)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * (t * i)) + (y * (z * (x - (i * (j / z)))));
	tmp = 0.0;
	if (b <= -1.95e+139)
		tmp = a * (b * ((i * (t / a)) - (c * (z / a))));
	elseif (b <= -19.0)
		tmp = t_1;
	elseif (b <= 3.8e-225)
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	elseif (b <= 2.7e+19)
		tmp = t_1;
	elseif (b <= 6.8e+162)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.95e+139], N[(a * N[(b * N[(N[(i * N[(t / a), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -19.0], t$95$1, If[LessEqual[b, 3.8e-225], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+19], t$95$1, If[LessEqual[b, 6.8e+162], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.95000000000000003e139

   1. Initial program 60.4%

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

   3. Taylor expanded in a around -inf 63.9%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in b around inf 74.3%

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

      1. associate-*r* 74.3%

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

      2. neg-mul-1 74.3%

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

      3. associate-/l* 77.2%

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

      4. associate-/l* 78.0%

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

   8. Simplified 78.0%

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

   if -1.95000000000000003e139 < b < -19 or 3.8000000000000003e-225 < b < 2.7e19

   1. Initial program 72.1%

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

   3. Taylor expanded in a around 0 66.0%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in z around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in t around inf 67.5%

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

   if -19 < b < 3.8000000000000003e-225

   1. Initial program 74.0%

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

   3. Taylor expanded in b around 0 73.8%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-*r* 63.2%

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

   6. Simplified 63.2%

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

   if 2.7e19 < b < 6.80000000000000006e162

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   if 6.80000000000000006e162 < b

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i \cdot \frac{t}{a} - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;b \leq -19:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-225}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(j - b \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.3e+69)
     t_2
     (if (<= i -6e-233)
       t_1
       (if (<= i 8.5e-289)
         (* c (- (* a j) (* z b)))
         (if (<= i 3.9e-84)
           t_1
           (if (<= i 3.2e-34) (* (* a c) (- j (* b (/ z a)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.3e+69) {
		tmp = t_2;
	} else if (i <= -6e-233) {
		tmp = t_1;
	} else if (i <= 8.5e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.9e-84) {
		tmp = t_1;
	} else if (i <= 3.2e-34) {
		tmp = (a * c) * (j - (b * (z / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.3d+69)) then
        tmp = t_2
    else if (i <= (-6d-233)) then
        tmp = t_1
    else if (i <= 8.5d-289) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 3.9d-84) then
        tmp = t_1
    else if (i <= 3.2d-34) then
        tmp = (a * c) * (j - (b * (z / a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.3e+69) {
		tmp = t_2;
	} else if (i <= -6e-233) {
		tmp = t_1;
	} else if (i <= 8.5e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.9e-84) {
		tmp = t_1;
	} else if (i <= 3.2e-34) {
		tmp = (a * c) * (j - (b * (z / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.3e+69:
		tmp = t_2
	elif i <= -6e-233:
		tmp = t_1
	elif i <= 8.5e-289:
		tmp = c * ((a * j) - (z * b))
	elif i <= 3.9e-84:
		tmp = t_1
	elif i <= 3.2e-34:
		tmp = (a * c) * (j - (b * (z / a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.3e+69)
		tmp = t_2;
	elseif (i <= -6e-233)
		tmp = t_1;
	elseif (i <= 8.5e-289)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 3.9e-84)
		tmp = t_1;
	elseif (i <= 3.2e-34)
		tmp = Float64(Float64(a * c) * Float64(j - Float64(b * Float64(z / a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.3e+69)
		tmp = t_2;
	elseif (i <= -6e-233)
		tmp = t_1;
	elseif (i <= 8.5e-289)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 3.9e-84)
		tmp = t_1;
	elseif (i <= 3.2e-34)
		tmp = (a * c) * (j - (b * (z / a)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.3e+69], t$95$2, If[LessEqual[i, -6e-233], t$95$1, If[LessEqual[i, 8.5e-289], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.9e-84], t$95$1, If[LessEqual[i, 3.2e-34], N[(N[(a * c), $MachinePrecision] * N[(j - N[(b * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.3000000000000001e69 or 3.20000000000000003e-34 < i

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 0 72.0%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in i around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -1.3000000000000001e69 < i < -5.99999999999999997e-233 or 8.49999999999999931e-289 < i < 3.90000000000000023e-84

   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 b around 0 68.7%

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

   4. Taylor expanded in j around 0 64.3%

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

   if -5.99999999999999997e-233 < i < 8.49999999999999931e-289

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 81.4%

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

   if 3.90000000000000023e-84 < i < 3.20000000000000003e-34

   1. Initial program 78.3%

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

   3. Taylor expanded in a around -inf 67.0%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in c around inf 64.7%

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

      1. associate-*r* 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+69}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(j - b \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;i \leq -3.1 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= i -3.1e+66)
     (* i (- (* t b) (* y j)))
     (if (<= i -2.5e-232)
       t_1
       (if (<= i 4e-289)
         (* c (- (* a j) (* z b)))
         (if (<= i 1.7e-77)
           t_1
           (- (* b (- (* t i) (* z c))) (* i (* 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 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -3.1e+66) {
		tmp = i * ((t * b) - (y * j));
	} else if (i <= -2.5e-232) {
		tmp = t_1;
	} else if (i <= 4e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.7e-77) {
		tmp = t_1;
	} else {
		tmp = (b * ((t * i) - (z * c))) - (i * (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) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (i <= (-3.1d+66)) then
        tmp = i * ((t * b) - (y * j))
    else if (i <= (-2.5d-232)) then
        tmp = t_1
    else if (i <= 4d-289) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.7d-77) then
        tmp = t_1
    else
        tmp = (b * ((t * i) - (z * c))) - (i * (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 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -3.1e+66) {
		tmp = i * ((t * b) - (y * j));
	} else if (i <= -2.5e-232) {
		tmp = t_1;
	} else if (i <= 4e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.7e-77) {
		tmp = t_1;
	} else {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if i <= -3.1e+66:
		tmp = i * ((t * b) - (y * j))
	elif i <= -2.5e-232:
		tmp = t_1
	elif i <= 4e-289:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.7e-77:
		tmp = t_1
	else:
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (i <= -3.1e+66)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (i <= -2.5e-232)
		tmp = t_1;
	elseif (i <= 4e-289)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.7e-77)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (i <= -3.1e+66)
		tmp = i * ((t * b) - (y * j));
	elseif (i <= -2.5e-232)
		tmp = t_1;
	elseif (i <= 4e-289)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.7e-77)
		tmp = t_1;
	else
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.1e+66], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.5e-232], t$95$1, If[LessEqual[i, 4e-289], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-77], t$95$1, N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.10000000000000019e66

   1. Initial program 58.9%

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

   3. Taylor expanded in a around 0 72.2%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   if -3.10000000000000019e66 < i < -2.5e-232 or 4e-289 < i < 1.69999999999999991e-77

   1. Initial program 73.7%

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

   3. Taylor expanded in b around 0 69.0%

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

   4. Taylor expanded in j around 0 63.7%

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

   if -2.5e-232 < i < 4e-289

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 81.4%

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

   if 1.69999999999999991e-77 < i

   1. Initial program 73.7%

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

   3. Taylor expanded in a around 0 69.6%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x around 0 61.5%

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

      1. +-commutative 61.5%

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

      2. cancel-sign-sub-inv 61.5%

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

      3. fma-undefine 61.5%

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

      4. mul-1-neg 61.5%

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

      5. unsub-neg 61.5%

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

      6. fma-undefine 61.5%

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

      7. cancel-sign-sub-inv 61.5%

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

   8. Simplified 61.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -30000:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(b \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -30000.0)
     (+ t_3 t_1)
     (if (<= j -3.8e-29)
       (* i (* b (- t (* c (/ z i)))))
       (if (<= j 4.6e+32) (+ t_2 t_1) (+ t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -30000.0) {
		tmp = t_3 + t_1;
	} else if (j <= -3.8e-29) {
		tmp = i * (b * (t - (c * (z / i))));
	} else if (j <= 4.6e+32) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-30000.0d0)) then
        tmp = t_3 + t_1
    else if (j <= (-3.8d-29)) then
        tmp = i * (b * (t - (c * (z / i))))
    else if (j <= 4.6d+32) then
        tmp = t_2 + t_1
    else
        tmp = t_2 + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -30000.0) {
		tmp = t_3 + t_1;
	} else if (j <= -3.8e-29) {
		tmp = i * (b * (t - (c * (z / i))));
	} else if (j <= 4.6e+32) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -30000.0:
		tmp = t_3 + t_1
	elif j <= -3.8e-29:
		tmp = i * (b * (t - (c * (z / i))))
	elif j <= 4.6e+32:
		tmp = t_2 + t_1
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -30000.0)
		tmp = Float64(t_3 + t_1);
	elseif (j <= -3.8e-29)
		tmp = Float64(i * Float64(b * Float64(t - Float64(c * Float64(z / i)))));
	elseif (j <= 4.6e+32)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -30000.0)
		tmp = t_3 + t_1;
	elseif (j <= -3.8e-29)
		tmp = i * (b * (t - (c * (z / i))));
	elseif (j <= 4.6e+32)
		tmp = t_2 + t_1;
	else
		tmp = t_2 + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -30000.0], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[j, -3.8e-29], N[(i * N[(b * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e+32], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3e4

   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 76.8%

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

   if -3e4 < j < -3.79999999999999976e-29

   1. Initial program 13.0%

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

   3. Taylor expanded in b around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in i around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. mul-1-neg 87.3%

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

      3. unsub-neg 87.3%

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

      4. *-commutative 87.3%

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

      5. associate-*r* 74.8%

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

      6. *-commutative 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in t around 0 87.3%

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

       1. associate-/l* 87.3%

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

       2. distribute-lft-out-- 99.8%

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

       3. associate-/l* 99.8%

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

   11. Simplified 99.8%

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

   if -3.79999999999999976e-29 < j < 4.5999999999999999e32

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if 4.5999999999999999e32 < j

   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 x around 0 75.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -30000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(b \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t - \frac{t\_1}{a}\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 0.315:\\ \;\;\;\;t\_1 + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t + \frac{b \cdot \left(z \cdot c\right)}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= a -2.6e-28)
     (* a (- (* c j) (- (* x t) (/ t_1 a))))
     (if (<= a 7.5e-254)
       (* z (- (* x y) (* b c)))
       (if (<= a 0.315)
         (+ t_1 (* y (* z (- x (* i (/ j z))))))
         (* a (- (* c j) (+ (* x t) (/ (* b (* z c)) 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 = b * (t * i);
	double tmp;
	if (a <= -2.6e-28) {
		tmp = a * ((c * j) - ((x * t) - (t_1 / a)));
	} else if (a <= 7.5e-254) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 0.315) {
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	} else {
		tmp = a * ((c * j) - ((x * t) + ((b * (z * c)) / a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (a <= (-2.6d-28)) then
        tmp = a * ((c * j) - ((x * t) - (t_1 / a)))
    else if (a <= 7.5d-254) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 0.315d0) then
        tmp = t_1 + (y * (z * (x - (i * (j / z)))))
    else
        tmp = a * ((c * j) - ((x * t) + ((b * (z * c)) / a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (a <= -2.6e-28) {
		tmp = a * ((c * j) - ((x * t) - (t_1 / a)));
	} else if (a <= 7.5e-254) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 0.315) {
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	} else {
		tmp = a * ((c * j) - ((x * t) + ((b * (z * c)) / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if a <= -2.6e-28:
		tmp = a * ((c * j) - ((x * t) - (t_1 / a)))
	elif a <= 7.5e-254:
		tmp = z * ((x * y) - (b * c))
	elif a <= 0.315:
		tmp = t_1 + (y * (z * (x - (i * (j / z)))))
	else:
		tmp = a * ((c * j) - ((x * t) + ((b * (z * c)) / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (a <= -2.6e-28)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(Float64(x * t) - Float64(t_1 / a))));
	elseif (a <= 7.5e-254)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 0.315)
		tmp = Float64(t_1 + Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z))))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(Float64(x * t) + Float64(Float64(b * Float64(z * c)) / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (a <= -2.6e-28)
		tmp = a * ((c * j) - ((x * t) - (t_1 / a)));
	elseif (a <= 7.5e-254)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 0.315)
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	else
		tmp = a * ((c * j) - ((x * t) + ((b * (z * c)) / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e-28], N[(a * N[(N[(c * j), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-254], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.315], N[(t$95$1 + N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] + N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6e-28

   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 -inf 78.1%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around inf 72.6%

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

   if -2.6e-28 < a < 7.5000000000000005e-254

   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 z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if 7.5000000000000005e-254 < a < 0.315000000000000002

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 73.1%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

      3. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in t around inf 68.6%

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

   if 0.315000000000000002 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in a around -inf 83.8%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in c around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-*r* 66.0%

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

      3. neg-mul-1 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t - \frac{b \cdot \left(t \cdot i\right)}{a}\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 0.315:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t + \frac{b \cdot \left(z \cdot c\right)}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - \left(x \cdot t - \frac{t\_1}{a}\right)\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+30}:\\ \;\;\;\;t\_1 + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (- (* c j) (- (* x t) (/ t_1 a))))))
   (if (<= a -4.8e-29)
     t_2
     (if (<= a 1.92e-252)
       (* z (- (* x y) (* b c)))
       (if (<= a 8e+30) (+ t_1 (* y (* z (- x (* i (/ j z)))))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * ((c * j) - ((x * t) - (t_1 / a)));
	double tmp;
	if (a <= -4.8e-29) {
		tmp = t_2;
	} else if (a <= 1.92e-252) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8e+30) {
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = a * ((c * j) - ((x * t) - (t_1 / a)))
    if (a <= (-4.8d-29)) then
        tmp = t_2
    else if (a <= 1.92d-252) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 8d+30) then
        tmp = t_1 + (y * (z * (x - (i * (j / z)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * ((c * j) - ((x * t) - (t_1 / a)));
	double tmp;
	if (a <= -4.8e-29) {
		tmp = t_2;
	} else if (a <= 1.92e-252) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8e+30) {
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * ((c * j) - ((x * t) - (t_1 / a)))
	tmp = 0
	if a <= -4.8e-29:
		tmp = t_2
	elif a <= 1.92e-252:
		tmp = z * ((x * y) - (b * c))
	elif a <= 8e+30:
		tmp = t_1 + (y * (z * (x - (i * (j / z)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(Float64(x * t) - Float64(t_1 / a))))
	tmp = 0.0
	if (a <= -4.8e-29)
		tmp = t_2;
	elseif (a <= 1.92e-252)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 8e+30)
		tmp = Float64(t_1 + Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = a * ((c * j) - ((x * t) - (t_1 / a)));
	tmp = 0.0;
	if (a <= -4.8e-29)
		tmp = t_2;
	elseif (a <= 1.92e-252)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 8e+30)
		tmp = t_1 + (y * (z * (x - (i * (j / z)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e-29], t$95$2, If[LessEqual[a, 1.92e-252], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+30], N[(t$95$1 + N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.79999999999999984e-29 or 8.0000000000000002e30 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in a around -inf 80.6%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in t around inf 70.4%

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

   if -4.79999999999999984e-29 < a < 1.92000000000000007e-252

   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 z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if 1.92000000000000007e-252 < a < 8.0000000000000002e30

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 72.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. associate-/l* 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in t around inf 66.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t - \frac{b \cdot \left(t \cdot i\right)}{a}\right)\right)\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - \left(x \cdot t - \frac{b \cdot \left(t \cdot i\right)}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= i -1.05e+125)
     (* i (* t b))
     (if (<= i -6.1e-111)
       t_1
       (if (<= i -1.45e-232)
         (* z (* x y))
         (if (<= i 1.95e-171)
           (* z (* c (- b)))
           (if (<= i 5.6e-78) t_1 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (i <= -1.05e+125) {
		tmp = i * (t * b);
	} else if (i <= -6.1e-111) {
		tmp = t_1;
	} else if (i <= -1.45e-232) {
		tmp = z * (x * y);
	} else if (i <= 1.95e-171) {
		tmp = z * (c * -b);
	} else if (i <= 5.6e-78) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (i <= (-1.05d+125)) then
        tmp = i * (t * b)
    else if (i <= (-6.1d-111)) then
        tmp = t_1
    else if (i <= (-1.45d-232)) then
        tmp = z * (x * y)
    else if (i <= 1.95d-171) then
        tmp = z * (c * -b)
    else if (i <= 5.6d-78) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (i <= -1.05e+125) {
		tmp = i * (t * b);
	} else if (i <= -6.1e-111) {
		tmp = t_1;
	} else if (i <= -1.45e-232) {
		tmp = z * (x * y);
	} else if (i <= 1.95e-171) {
		tmp = z * (c * -b);
	} else if (i <= 5.6e-78) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if i <= -1.05e+125:
		tmp = i * (t * b)
	elif i <= -6.1e-111:
		tmp = t_1
	elif i <= -1.45e-232:
		tmp = z * (x * y)
	elif i <= 1.95e-171:
		tmp = z * (c * -b)
	elif i <= 5.6e-78:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (i <= -1.05e+125)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -6.1e-111)
		tmp = t_1;
	elseif (i <= -1.45e-232)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.95e-171)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 5.6e-78)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (i <= -1.05e+125)
		tmp = i * (t * b);
	elseif (i <= -6.1e-111)
		tmp = t_1;
	elseif (i <= -1.45e-232)
		tmp = z * (x * y);
	elseif (i <= 1.95e-171)
		tmp = z * (c * -b);
	elseif (i <= 5.6e-78)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+125], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.1e-111], t$95$1, If[LessEqual[i, -1.45e-232], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.95e-171], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.6e-78], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.05e125

   1. Initial program 57.9%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*r* 51.9%

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

      6. *-commutative 51.9%

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

   8. Simplified 51.9%

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

   9. Taylor expanded in t around inf 51.0%

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

       1. *-commutative 51.0%

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

   11. Simplified 51.0%

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

   if -1.05e125 < i < -6.1000000000000002e-111 or 1.9499999999999999e-171 < i < 5.60000000000000047e-78

   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 inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in c around 0 49.5%

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

      1. associate-*r* 49.5%

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

      2. neg-mul-1 49.5%

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

   8. Simplified 49.5%

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

   if -6.1000000000000002e-111 < i < -1.45e-232

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -1.45e-232 < i < 1.9499999999999999e-171

   1. Initial program 72.9%

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

   3. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-lft-neg-out 43.3%

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

      3. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   if 5.60000000000000047e-78 < i

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 44.2%

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

      1. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in t around inf 36.3%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-111}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= i -4.5e+125)
     (* i (* t b))
     (if (<= i -7e-104)
       t_1
       (if (<= i -3e-233)
         (* z (* x y))
         (if (<= i 2.3e-171)
           (* z (* c (- b)))
           (if (<= i 5.8e-78) t_1 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (i <= -4.5e+125) {
		tmp = i * (t * b);
	} else if (i <= -7e-104) {
		tmp = t_1;
	} else if (i <= -3e-233) {
		tmp = z * (x * y);
	} else if (i <= 2.3e-171) {
		tmp = z * (c * -b);
	} else if (i <= 5.8e-78) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (i <= (-4.5d+125)) then
        tmp = i * (t * b)
    else if (i <= (-7d-104)) then
        tmp = t_1
    else if (i <= (-3d-233)) then
        tmp = z * (x * y)
    else if (i <= 2.3d-171) then
        tmp = z * (c * -b)
    else if (i <= 5.8d-78) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (i <= -4.5e+125) {
		tmp = i * (t * b);
	} else if (i <= -7e-104) {
		tmp = t_1;
	} else if (i <= -3e-233) {
		tmp = z * (x * y);
	} else if (i <= 2.3e-171) {
		tmp = z * (c * -b);
	} else if (i <= 5.8e-78) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if i <= -4.5e+125:
		tmp = i * (t * b)
	elif i <= -7e-104:
		tmp = t_1
	elif i <= -3e-233:
		tmp = z * (x * y)
	elif i <= 2.3e-171:
		tmp = z * (c * -b)
	elif i <= 5.8e-78:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (i <= -4.5e+125)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -7e-104)
		tmp = t_1;
	elseif (i <= -3e-233)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.3e-171)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 5.8e-78)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (i <= -4.5e+125)
		tmp = i * (t * b);
	elseif (i <= -7e-104)
		tmp = t_1;
	elseif (i <= -3e-233)
		tmp = z * (x * y);
	elseif (i <= 2.3e-171)
		tmp = z * (c * -b);
	elseif (i <= 5.8e-78)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+125], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e-104], t$95$1, If[LessEqual[i, -3e-233], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e-171], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e-78], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.5e125

   1. Initial program 57.9%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*r* 51.9%

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

      6. *-commutative 51.9%

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

   8. Simplified 51.9%

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

   9. Taylor expanded in t around inf 51.0%

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

       1. *-commutative 51.0%

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

   11. Simplified 51.0%

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

   if -4.5e125 < i < -7.00000000000000057e-104 or 2.29999999999999978e-171 < i < 5.8000000000000001e-78

   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 inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in c around 0 49.5%

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

      1. associate-*r* 49.5%

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

      2. neg-mul-1 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in a around 0 49.5%

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

       1. neg-mul-1 49.5%

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

       2. distribute-lft-neg-in 49.5%

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

       3. associate-*l* 48.1%

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

       4. *-commutative 48.1%

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

       5. *-commutative 48.1%

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

   11. Simplified 48.1%

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

   if -7.00000000000000057e-104 < i < -2.99999999999999999e-233

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -2.99999999999999999e-233 < i < 2.29999999999999978e-171

   1. Initial program 72.9%

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

   3. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-lft-neg-out 43.3%

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

      3. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   if 5.8000000000000001e-78 < i

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 44.2%

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

      1. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in t around inf 36.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -7.1 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= i -1.25e+125)
     (* i (* t b))
     (if (<= i -7.1e-109)
       t_1
       (if (<= i -2.8e-233)
         (* z (* x y))
         (if (<= i 2.45e-171)
           (* c (* z (- b)))
           (if (<= i 1.75e-77) t_1 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (i <= -1.25e+125) {
		tmp = i * (t * b);
	} else if (i <= -7.1e-109) {
		tmp = t_1;
	} else if (i <= -2.8e-233) {
		tmp = z * (x * y);
	} else if (i <= 2.45e-171) {
		tmp = c * (z * -b);
	} else if (i <= 1.75e-77) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (i <= (-1.25d+125)) then
        tmp = i * (t * b)
    else if (i <= (-7.1d-109)) then
        tmp = t_1
    else if (i <= (-2.8d-233)) then
        tmp = z * (x * y)
    else if (i <= 2.45d-171) then
        tmp = c * (z * -b)
    else if (i <= 1.75d-77) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (i <= -1.25e+125) {
		tmp = i * (t * b);
	} else if (i <= -7.1e-109) {
		tmp = t_1;
	} else if (i <= -2.8e-233) {
		tmp = z * (x * y);
	} else if (i <= 2.45e-171) {
		tmp = c * (z * -b);
	} else if (i <= 1.75e-77) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if i <= -1.25e+125:
		tmp = i * (t * b)
	elif i <= -7.1e-109:
		tmp = t_1
	elif i <= -2.8e-233:
		tmp = z * (x * y)
	elif i <= 2.45e-171:
		tmp = c * (z * -b)
	elif i <= 1.75e-77:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (i <= -1.25e+125)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -7.1e-109)
		tmp = t_1;
	elseif (i <= -2.8e-233)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.45e-171)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 1.75e-77)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (i <= -1.25e+125)
		tmp = i * (t * b);
	elseif (i <= -7.1e-109)
		tmp = t_1;
	elseif (i <= -2.8e-233)
		tmp = z * (x * y);
	elseif (i <= 2.45e-171)
		tmp = c * (z * -b);
	elseif (i <= 1.75e-77)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+125], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.1e-109], t$95$1, If[LessEqual[i, -2.8e-233], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.45e-171], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e-77], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.24999999999999991e125

   1. Initial program 57.9%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*r* 51.9%

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

      6. *-commutative 51.9%

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

   8. Simplified 51.9%

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

   9. Taylor expanded in t around inf 51.0%

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

       1. *-commutative 51.0%

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

   11. Simplified 51.0%

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

   if -1.24999999999999991e125 < i < -7.0999999999999999e-109 or 2.44999999999999991e-171 < i < 1.75000000000000006e-77

   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 inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in c around 0 49.5%

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

      1. associate-*r* 49.5%

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

      2. neg-mul-1 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in a around 0 49.5%

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

       1. neg-mul-1 49.5%

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

       2. distribute-lft-neg-in 49.5%

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

       3. associate-*l* 48.1%

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

       4. *-commutative 48.1%

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

       5. *-commutative 48.1%

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

   11. Simplified 48.1%

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

   if -7.0999999999999999e-109 < i < -2.8000000000000001e-233

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -2.8000000000000001e-233 < i < 2.44999999999999991e-171

   1. Initial program 72.9%

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

   3. Taylor expanded in a around -inf 61.4%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in c around inf 58.3%

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

      1. associate-*r* 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   9. Taylor expanded in a around 0 37.2%

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

       1. mul-1-neg 37.2%

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

       2. *-commutative 37.2%

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

       3. associate-*r* 43.2%

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

       4. *-commutative 43.2%

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

       5. distribute-rgt-neg-out 43.2%

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

       6. distribute-rgt-neg-in 43.2%

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

   11. Simplified 43.2%

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

   if 1.75000000000000006e-77 < i

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 44.2%

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

      1. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in t around inf 36.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -7.1 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1800000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -3.1e+60)
     t_1
     (if (<= i -1.25e-233)
       (* x (- (* y z) (* t a)))
       (if (<= i 2.9e-288)
         (* c (- (* a j) (* z b)))
         (if (<= i 1800000.0) (* z (- (* x y) (* b c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.1e+60) {
		tmp = t_1;
	} else if (i <= -1.25e-233) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2.9e-288) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1800000.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-3.1d+60)) then
        tmp = t_1
    else if (i <= (-1.25d-233)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 2.9d-288) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1800000.0d0) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.1e+60) {
		tmp = t_1;
	} else if (i <= -1.25e-233) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2.9e-288) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1800000.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.1e+60:
		tmp = t_1
	elif i <= -1.25e-233:
		tmp = x * ((y * z) - (t * a))
	elif i <= 2.9e-288:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1800000.0:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.1e+60)
		tmp = t_1;
	elseif (i <= -1.25e-233)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 2.9e-288)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1800000.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.1e+60)
		tmp = t_1;
	elseif (i <= -1.25e-233)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 2.9e-288)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1800000.0)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.1e+60], t$95$1, If[LessEqual[i, -1.25e-233], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.9e-288], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1800000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.1000000000000001e60 or 1.8e6 < i

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 70.5%

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

   6. Taylor expanded in i around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

   8. Simplified 70.0%

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

   if -3.1000000000000001e60 < i < -1.25000000000000003e-233

   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 b around 0 71.6%

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

   4. Taylor expanded in j around 0 64.2%

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

   if -1.25000000000000003e-233 < i < 2.90000000000000015e-288

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 81.4%

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

   if 2.90000000000000015e-288 < i < 1.8e6

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1800000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -3e+69)
     t_2
     (if (<= i -6e-233)
       t_1
       (if (<= i 6.2e-289)
         (* c (- (* a j) (* z b)))
         (if (<= i 4.4e-57) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3e+69) {
		tmp = t_2;
	} else if (i <= -6e-233) {
		tmp = t_1;
	} else if (i <= 6.2e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.4e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-3d+69)) then
        tmp = t_2
    else if (i <= (-6d-233)) then
        tmp = t_1
    else if (i <= 6.2d-289) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 4.4d-57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3e+69) {
		tmp = t_2;
	} else if (i <= -6e-233) {
		tmp = t_1;
	} else if (i <= 6.2e-289) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.4e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3e+69:
		tmp = t_2
	elif i <= -6e-233:
		tmp = t_1
	elif i <= 6.2e-289:
		tmp = c * ((a * j) - (z * b))
	elif i <= 4.4e-57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3e+69)
		tmp = t_2;
	elseif (i <= -6e-233)
		tmp = t_1;
	elseif (i <= 6.2e-289)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 4.4e-57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3e+69)
		tmp = t_2;
	elseif (i <= -6e-233)
		tmp = t_1;
	elseif (i <= 6.2e-289)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 4.4e-57)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3e+69], t$95$2, If[LessEqual[i, -6e-233], t$95$1, If[LessEqual[i, 6.2e-289], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e-57], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.99999999999999983e69 or 4.39999999999999997e-57 < 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 a around 0 70.6%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in i around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

   8. Simplified 65.7%

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

   if -2.99999999999999983e69 < i < -5.99999999999999997e-233 or 6.2e-289 < i < 4.39999999999999997e-57

   1. Initial program 73.7%

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

   3. Taylor expanded in b around 0 67.5%

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

   4. Taylor expanded in j around 0 62.4%

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

   if -5.99999999999999997e-233 < i < 6.2e-289

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 81.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+69}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -3.8e+65)
     t_2
     (if (<= i -1.05e-236)
       t_1
       (if (<= i 3.3e-171)
         (* c (- (* a j) (* z b)))
         (if (<= i 3.4e-38) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.8e+65) {
		tmp = t_2;
	} else if (i <= -1.05e-236) {
		tmp = t_1;
	} else if (i <= 3.3e-171) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.4e-38) {
		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 = i * ((t * b) - (y * j))
    if (i <= (-3.8d+65)) then
        tmp = t_2
    else if (i <= (-1.05d-236)) then
        tmp = t_1
    else if (i <= 3.3d-171) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 3.4d-38) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.8e+65) {
		tmp = t_2;
	} else if (i <= -1.05e-236) {
		tmp = t_1;
	} else if (i <= 3.3e-171) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.4e-38) {
		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 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.8e+65:
		tmp = t_2
	elif i <= -1.05e-236:
		tmp = t_1
	elif i <= 3.3e-171:
		tmp = c * ((a * j) - (z * b))
	elif i <= 3.4e-38:
		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(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.8e+65)
		tmp = t_2;
	elseif (i <= -1.05e-236)
		tmp = t_1;
	elseif (i <= 3.3e-171)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 3.4e-38)
		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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.8e+65)
		tmp = t_2;
	elseif (i <= -1.05e-236)
		tmp = t_1;
	elseif (i <= 3.3e-171)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 3.4e-38)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.8e+65], t$95$2, If[LessEqual[i, -1.05e-236], t$95$1, If[LessEqual[i, 3.3e-171], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.80000000000000011e65 or 3.4000000000000002e-38 < i

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 0 72.0%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in i around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -3.80000000000000011e65 < i < -1.04999999999999989e-236 or 3.3000000000000002e-171 < i < 3.4000000000000002e-38

   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 a around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   if -1.04999999999999989e-236 < i < 3.3000000000000002e-171

   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 c around inf 66.0%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -118:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -118.0)
     (+ (* y (- (* x z) (* i j))) t_1)
     (if (<= b 6.8e+162)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -118.0) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (b <= 6.8e+162) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-118.0d0)) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else if (b <= 6.8d+162) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -118.0) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (b <= 6.8e+162) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -118.0:
		tmp = (y * ((x * z) - (i * j))) + t_1
	elif b <= 6.8e+162:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -118.0)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	elseif (b <= 6.8e+162)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * 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 * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -118.0)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	elseif (b <= 6.8e+162)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -118.0], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 6.8e+162], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -118

   1. Initial program 66.1%

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

   3. Taylor expanded in a around 0 73.7%

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

   5. Simplified 80.6%

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

   if -118 < b < 6.80000000000000006e162

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 68.8%

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

   if 6.80000000000000006e162 < b

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -118:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.1 \cdot 10^{+117}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -9.1e+117)
     (- t_1 (* i (* y j)))
     (if (<= b 6.8e+162)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.1e+117) {
		tmp = t_1 - (i * (y * j));
	} else if (b <= 6.8e+162) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-9.1d+117)) then
        tmp = t_1 - (i * (y * j))
    else if (b <= 6.8d+162) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.1e+117) {
		tmp = t_1 - (i * (y * j));
	} else if (b <= 6.8e+162) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -9.1e+117:
		tmp = t_1 - (i * (y * j))
	elif b <= 6.8e+162:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.1e+117)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (b <= 6.8e+162)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * 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 * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.1e+117)
		tmp = t_1 - (i * (y * j));
	elseif (b <= 6.8e+162)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.1e+117], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+162], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.1000000000000003e117

   1. Initial program 57.6%

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

   3. Taylor expanded in a around 0 75.1%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. cancel-sign-sub-inv 75.1%

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

      3. fma-undefine 75.1%

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

      4. mul-1-neg 75.1%

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

      5. unsub-neg 75.1%

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

      6. fma-undefine 75.1%

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

      7. cancel-sign-sub-inv 75.1%

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

   8. Simplified 75.1%

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

   if -9.1000000000000003e117 < b < 6.80000000000000006e162

   1. Initial program 73.1%

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

   3. Taylor expanded in b around 0 68.6%

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

   if 6.80000000000000006e162 < b

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.1 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+162}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+61} \lor \neg \left(z \leq 1.1 \cdot 10^{+94}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -4.6e+61) (not (<= z 1.1e+94)))
   (* z (- (* x y) (* b c)))
   (- (* j (- (* a c) (* y i))) (* t (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.6e+61) || !(z <= 1.1e+94)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-4.6d+61)) .or. (.not. (z <= 1.1d+94))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (j * ((a * c) - (y * i))) - (t * (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.6e+61) || !(z <= 1.1e+94)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -4.6e+61) or not (z <= 1.1e+94):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -4.6e+61) || !(z <= 1.1e+94))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(t * Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -4.6e+61) || ~((z <= 1.1e+94)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (j * ((a * c) - (y * i))) - (t * (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -4.6e+61], N[Not[LessEqual[z, 1.1e+94]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999999e61 or 1.10000000000000006e94 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -4.5999999999999999e61 < z < 1.10000000000000006e94

   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 b around 0 64.9%

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

   4. Taylor expanded in z around 0 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

      4. associate-*r* 57.9%

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

      5. *-commutative 57.9%

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

      6. associate-*r* 57.9%

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

   6. Simplified 57.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+61} \lor \neg \left(z \leq 1.1 \cdot 10^{+94}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.1e+132)
   (* i (* t b))
   (if (<= b -1.35e+46)
     (* x (* y z))
     (if (<= b 3.2e+183) (* a (- (* c j) (* x t))) (* z (* c (- 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 <= -1.1e+132) {
		tmp = i * (t * b);
	} else if (b <= -1.35e+46) {
		tmp = x * (y * z);
	} else if (b <= 3.2e+183) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (c * -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 <= (-1.1d+132)) then
        tmp = i * (t * b)
    else if (b <= (-1.35d+46)) then
        tmp = x * (y * z)
    else if (b <= 3.2d+183) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = z * (c * -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 <= -1.1e+132) {
		tmp = i * (t * b);
	} else if (b <= -1.35e+46) {
		tmp = x * (y * z);
	} else if (b <= 3.2e+183) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.1e+132:
		tmp = i * (t * b)
	elif b <= -1.35e+46:
		tmp = x * (y * z)
	elif b <= 3.2e+183:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.1e+132)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -1.35e+46)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 3.2e+183)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.1e+132)
		tmp = i * (t * b);
	elseif (b <= -1.35e+46)
		tmp = x * (y * z);
	elseif (b <= 3.2e+183)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.1e+132], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e+46], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+183], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.09999999999999994e132

   1. Initial program 59.7%

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

   3. Taylor expanded in b around inf 72.8%

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

      1. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in i around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

      5. associate-*r* 65.0%

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

      6. *-commutative 65.0%

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

   8. Simplified 65.0%

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

   9. Taylor expanded in t around inf 52.5%

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

       1. *-commutative 52.5%

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

   11. Simplified 52.5%

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

   if -1.09999999999999994e132 < b < -1.3500000000000001e46

   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 z around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 48.3%

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

   if -1.3500000000000001e46 < b < 3.2000000000000002e183

   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 a around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

   5. Simplified 51.0%

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

   if 3.2000000000000002e183 < b

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in y around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-lft-neg-out 60.2%

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

      3. *-commutative 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -6.1 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -6.1e+58)
     t_1
     (if (<= a -2.7e-29)
       (* b (* t i))
       (if (<= a 1.85e+169) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -6.1e+58) {
		tmp = t_1;
	} else if (a <= -2.7e-29) {
		tmp = b * (t * i);
	} else if (a <= 1.85e+169) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-6.1d+58)) then
        tmp = t_1
    else if (a <= (-2.7d-29)) then
        tmp = b * (t * i)
    else if (a <= 1.85d+169) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -6.1e+58) {
		tmp = t_1;
	} else if (a <= -2.7e-29) {
		tmp = b * (t * i);
	} else if (a <= 1.85e+169) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -6.1e+58:
		tmp = t_1
	elif a <= -2.7e-29:
		tmp = b * (t * i)
	elif a <= 1.85e+169:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -6.1e+58)
		tmp = t_1;
	elseif (a <= -2.7e-29)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.85e+169)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -6.1e+58)
		tmp = t_1;
	elseif (a <= -2.7e-29)
		tmp = b * (t * i);
	elseif (a <= 1.85e+169)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.1e+58], t$95$1, If[LessEqual[a, -2.7e-29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+169], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.1000000000000002e58 or 1.85e169 < a

   1. Initial program 59.8%

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

   3. Taylor expanded in a around -inf 77.6%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in c around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. associate-/l* 55.3%

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

   8. Simplified 55.3%

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

   9. Taylor expanded in j around inf 47.4%

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

   if -6.1000000000000002e58 < a < -2.70000000000000023e-29

   1. Initial program 79.8%

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

   3. Taylor expanded in b around inf 43.5%

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

      1. *-commutative 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in t around inf 37.2%

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

   if -2.70000000000000023e-29 < a < 1.85e169

   1. Initial program 76.2%

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

   3. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 31.2%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+192}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= a -4.7e-28)
     t_1
     (if (<= a 3.2e-109)
       (* x (* y z))
       (if (<= a 1.15e+192) (* i (* t b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (a <= -4.7e-28) {
		tmp = t_1;
	} else if (a <= 3.2e-109) {
		tmp = x * (y * z);
	} else if (a <= 1.15e+192) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (a <= (-4.7d-28)) then
        tmp = t_1
    else if (a <= 3.2d-109) then
        tmp = x * (y * z)
    else if (a <= 1.15d+192) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (a <= -4.7e-28) {
		tmp = t_1;
	} else if (a <= 3.2e-109) {
		tmp = x * (y * z);
	} else if (a <= 1.15e+192) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if a <= -4.7e-28:
		tmp = t_1
	elif a <= 3.2e-109:
		tmp = x * (y * z)
	elif a <= 1.15e+192:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (a <= -4.7e-28)
		tmp = t_1;
	elseif (a <= 3.2e-109)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.15e+192)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (a <= -4.7e-28)
		tmp = t_1;
	elseif (a <= 3.2e-109)
		tmp = x * (y * z);
	elseif (a <= 1.15e+192)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e-28], t$95$1, If[LessEqual[a, 3.2e-109], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+192], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6999999999999996e-28 or 1.15e192 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in a around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in c around inf 42.2%

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

      1. *-commutative 42.2%

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

   8. Simplified 42.2%

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

   if -4.6999999999999996e-28 < a < 3.2000000000000002e-109

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in y around inf 35.9%

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

   if 3.2000000000000002e-109 < a < 1.15e192

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf 42.7%

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

      1. *-commutative 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in i around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. mul-1-neg 40.5%

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

      3. unsub-neg 40.5%

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

      4. *-commutative 40.5%

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

      5. associate-*r* 38.3%

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

      6. *-commutative 38.3%

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

   8. Simplified 38.3%

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

   9. Taylor expanded in t around inf 29.6%

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

       1. *-commutative 29.6%

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

   11. Simplified 29.6%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+192}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+32} \lor \neg \left(b \leq 6.8 \cdot 10^{+162}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.3e+32) (not (<= b 6.8e+162)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.3e+32) || !(b <= 6.8e+162)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.3d+32)) .or. (.not. (b <= 6.8d+162))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.3e+32) || !(b <= 6.8e+162)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.3e+32) or not (b <= 6.8e+162):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.3e+32) || !(b <= 6.8e+162))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.3e+32) || ~((b <= 6.8e+162)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.3e+32], N[Not[LessEqual[b, 6.8e+162]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3000000000000002e32 or 6.80000000000000006e162 < b

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -3.3000000000000002e32 < b < 6.80000000000000006e162

   1. Initial program 72.2%

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

   3. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   5. Simplified 51.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+32} \lor \neg \left(b \leq 6.8 \cdot 10^{+162}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+58} \lor \neg \left(a \leq 2.2 \cdot 10^{+193}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -9.2e+58) (not (<= a 2.2e+193))) (* 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 ((a <= -9.2e+58) || !(a <= 2.2e+193)) {
		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 ((a <= (-9.2d+58)) .or. (.not. (a <= 2.2d+193))) 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 ((a <= -9.2e+58) || !(a <= 2.2e+193)) {
		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 (a <= -9.2e+58) or not (a <= 2.2e+193):
		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 ((a <= -9.2e+58) || !(a <= 2.2e+193))
		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 ((a <= -9.2e+58) || ~((a <= 2.2e+193)))
		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[Or[LessEqual[a, -9.2e+58], N[Not[LessEqual[a, 2.2e+193]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.2000000000000001e58 or 2.19999999999999986e193 < a

   1. Initial program 60.3%

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

   3. Taylor expanded in a around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in c around inf 47.2%

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

      1. *-commutative 47.2%

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

   8. Simplified 47.2%

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

   if -9.2000000000000001e58 < a < 2.19999999999999986e193

   1. Initial program 75.7%

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

   3. Taylor expanded in b around inf 42.0%

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

      1. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in i around inf 37.0%

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

      1. +-commutative 37.0%

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

      2. mul-1-neg 37.0%

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

      3. unsub-neg 37.0%

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

      4. *-commutative 37.0%

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

      5. associate-*r* 37.0%

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

      6. *-commutative 37.0%

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

   8. Simplified 37.0%

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

   9. Taylor expanded in t around inf 26.8%

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

       1. *-commutative 26.8%

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

   11. Simplified 26.8%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+58} \lor \neg \left(a \leq 2.2 \cdot 10^{+193}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 27.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+59} \lor \neg \left(a \leq 1.15 \cdot 10^{+192}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.05e+59) (not (<= a 1.15e+192))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.05e+59) || !(a <= 1.15e+192)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.05d+59)) .or. (.not. (a <= 1.15d+192))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.05e+59) || !(a <= 1.15e+192)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.05e+59) or not (a <= 1.15e+192):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.05e+59) || !(a <= 1.15e+192))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.05e+59) || ~((a <= 1.15e+192)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.05e+59], N[Not[LessEqual[a, 1.15e+192]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04999999999999992e59 or 1.15e192 < a

   1. Initial program 60.3%

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

   3. Taylor expanded in a around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in c around inf 47.2%

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

      1. *-commutative 47.2%

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

   8. Simplified 47.2%

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

   if -1.04999999999999992e59 < a < 1.15e192

   1. Initial program 75.7%

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

   3. Taylor expanded in b around inf 42.0%

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

      1. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in t around inf 26.5%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+59} \lor \neg \left(a \leq 1.15 \cdot 10^{+192}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 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 70.2%

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

3. Taylor expanded in a around inf 41.6%

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

   1. +-commutative 41.6%

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

   2. mul-1-neg 41.6%

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

   3. unsub-neg 41.6%

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

5. Simplified 41.6%

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

6. Taylor expanded in c around inf 23.2%

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

   1. *-commutative 23.2%

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

8. Simplified 23.2%

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

9. Final simplification 23.2%

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

Developer Target 1: 60.0% 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 2024170 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

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