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

Percentage Accurate: 74.0% → 84.7%

Time: 26.4s

Alternatives: 25

Speedup: 0.5×

• 57.6% 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: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(j * N[(a * c + N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $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 92.0%

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

      1. sub-neg 92.0%

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

      2. *-commutative 92.0%

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

      3. sub-neg 92.0%

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

      4. *-commutative 92.0%

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

      5. *-commutative 92.0%

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

      6. sub-neg 92.0%

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

      7. *-commutative 92.0%

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

      8. fma-define 92.0%

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

   3. Simplified 92.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 25.5%

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

   5. Simplified 29.4%

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

   6. Taylor expanded in t around inf 51.1%

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

      1. associate-/l* 57.0%

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

      2. +-commutative 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 85.1%

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

Alternative 2: 84.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $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[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $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 92.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 25.5%

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

   5. Simplified 29.4%

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

   6. Taylor expanded in t around inf 51.1%

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

      1. associate-/l* 57.0%

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

      2. +-commutative 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 85.1%

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

Alternative 3: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.72 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -9.5e+34)
     (* j (- (* a c) (* y i)))
     (if (<= j -2.1e-38)
       t_2
       (if (<= j -6.6e-99)
         (* x (- (* y z) (* t a)))
         (if (<= j -3.6e-213)
           t_2
           (if (<= j -1.72e-301)
             (* (* x y) (- z (* a (/ t y))))
             (if (<= j 3.1e-203)
               t_1
               (if (<= j 1.7e-95)
                 (* z (* c (- (* x (/ y c)) b)))
                 (if (<= j 5.2e-56)
                   t_1
                   (if (<= j 7.5e-45)
                     (* z (- (* x y) (* b c)))
                     (if (<= j 1.1e+38)
                       t_2
                       (* (* y j) (- (/ (* a c) y) i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -9.5e+34) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -2.1e-38) {
		tmp = t_2;
	} else if (j <= -6.6e-99) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -3.6e-213) {
		tmp = t_2;
	} else if (j <= -1.72e-301) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 3.1e-203) {
		tmp = t_1;
	} else if (j <= 1.7e-95) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 5.2e-56) {
		tmp = t_1;
	} else if (j <= 7.5e-45) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.1e+38) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-9.5d+34)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-2.1d-38)) then
        tmp = t_2
    else if (j <= (-6.6d-99)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= (-3.6d-213)) then
        tmp = t_2
    else if (j <= (-1.72d-301)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (j <= 3.1d-203) then
        tmp = t_1
    else if (j <= 1.7d-95) then
        tmp = z * (c * ((x * (y / c)) - b))
    else if (j <= 5.2d-56) then
        tmp = t_1
    else if (j <= 7.5d-45) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 1.1d+38) then
        tmp = t_2
    else
        tmp = (y * j) * (((a * c) / y) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -9.5e+34) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -2.1e-38) {
		tmp = t_2;
	} else if (j <= -6.6e-99) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -3.6e-213) {
		tmp = t_2;
	} else if (j <= -1.72e-301) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 3.1e-203) {
		tmp = t_1;
	} else if (j <= 1.7e-95) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 5.2e-56) {
		tmp = t_1;
	} else if (j <= 7.5e-45) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.1e+38) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -9.5e+34:
		tmp = j * ((a * c) - (y * i))
	elif j <= -2.1e-38:
		tmp = t_2
	elif j <= -6.6e-99:
		tmp = x * ((y * z) - (t * a))
	elif j <= -3.6e-213:
		tmp = t_2
	elif j <= -1.72e-301:
		tmp = (x * y) * (z - (a * (t / y)))
	elif j <= 3.1e-203:
		tmp = t_1
	elif j <= 1.7e-95:
		tmp = z * (c * ((x * (y / c)) - b))
	elif j <= 5.2e-56:
		tmp = t_1
	elif j <= 7.5e-45:
		tmp = z * ((x * y) - (b * c))
	elif j <= 1.1e+38:
		tmp = t_2
	else:
		tmp = (y * j) * (((a * c) / y) - i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -9.5e+34)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -2.1e-38)
		tmp = t_2;
	elseif (j <= -6.6e-99)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= -3.6e-213)
		tmp = t_2;
	elseif (j <= -1.72e-301)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (j <= 3.1e-203)
		tmp = t_1;
	elseif (j <= 1.7e-95)
		tmp = Float64(z * Float64(c * Float64(Float64(x * Float64(y / c)) - b)));
	elseif (j <= 5.2e-56)
		tmp = t_1;
	elseif (j <= 7.5e-45)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 1.1e+38)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(Float64(a * c) / y) - i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -9.5e+34)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -2.1e-38)
		tmp = t_2;
	elseif (j <= -6.6e-99)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= -3.6e-213)
		tmp = t_2;
	elseif (j <= -1.72e-301)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (j <= 3.1e-203)
		tmp = t_1;
	elseif (j <= 1.7e-95)
		tmp = z * (c * ((x * (y / c)) - b));
	elseif (j <= 5.2e-56)
		tmp = t_1;
	elseif (j <= 7.5e-45)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 1.1e+38)
		tmp = t_2;
	else
		tmp = (y * j) * (((a * c) / y) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+34], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-38], t$95$2, If[LessEqual[j, -6.6e-99], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-213], t$95$2, If[LessEqual[j, -1.72e-301], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-203], t$95$1, If[LessEqual[j, 1.7e-95], N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-56], t$95$1, If[LessEqual[j, 7.5e-45], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+38], t$95$2, N[(N[(y * j), $MachinePrecision] * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -9.4999999999999999e34

   1. Initial program 77.2%

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

   3. Taylor expanded in j around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -9.4999999999999999e34 < j < -2.10000000000000013e-38 or -6.59999999999999973e-99 < j < -3.6000000000000001e-213 or 7.5000000000000006e-45 < j < 1.10000000000000003e38

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf 68.9%

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

   if -2.10000000000000013e-38 < j < -6.59999999999999973e-99

   1. Initial program 64.7%

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

   3. Taylor expanded in x around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -3.6000000000000001e-213 < j < -1.72000000000000008e-301

   1. Initial program 70.5%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in x around 0 65.8%

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

       1. associate-*r* 70.4%

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

       2. *-commutative 70.4%

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

       3. associate-/l* 75.1%

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

   11. Simplified 75.1%

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

   if -1.72000000000000008e-301 < j < 3.09999999999999977e-203 or 1.69999999999999997e-95 < j < 5.19999999999999994e-56

   1. Initial program 72.8%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around inf 86.7%

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

      1. neg-mul-1 86.7%

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

      2. sub-neg 86.7%

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

      3. remove-double-neg 86.7%

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

      4. +-commutative 86.7%

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

      5. mul-1-neg 86.7%

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

      6. unsub-neg 86.7%

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

   8. Simplified 86.7%

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

   if 3.09999999999999977e-203 < j < 1.69999999999999997e-95

   1. Initial program 53.1%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in c around inf 54.8%

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

      1. associate-/l* 60.7%

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

   8. Simplified 60.7%

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

   if 5.19999999999999994e-56 < j < 7.5000000000000006e-45

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 1.10000000000000003e38 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 59.3%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in j around inf 71.9%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

      \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(\frac{c \cdot a}{y} - i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.72 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.06 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -2e+35)
     (* j (- (* a c) (* y i)))
     (if (<= j -1.06e-37)
       t_2
       (if (<= j -7e-96)
         (- (* x (* y z)) (* a (* x t)))
         (if (<= j -4.7e-213)
           t_2
           (if (<= j -4e-301)
             (* (* x y) (- z (* a (/ t y))))
             (if (<= j 2.3e-199)
               t_1
               (if (<= j 1.05e-94)
                 (* z (* c (- (* x (/ y c)) b)))
                 (if (<= j 8.5e-53)
                   t_1
                   (if (<= j 3.7e-45)
                     (* z (- (* x y) (* b c)))
                     (if (<= j 9e+37)
                       t_2
                       (* (* y j) (- (/ (* a c) y) i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.06e-37) {
		tmp = t_2;
	} else if (j <= -7e-96) {
		tmp = (x * (y * z)) - (a * (x * t));
	} else if (j <= -4.7e-213) {
		tmp = t_2;
	} else if (j <= -4e-301) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.3e-199) {
		tmp = t_1;
	} else if (j <= 1.05e-94) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 8.5e-53) {
		tmp = t_1;
	} else if (j <= 3.7e-45) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 9e+37) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-2d+35)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-1.06d-37)) then
        tmp = t_2
    else if (j <= (-7d-96)) then
        tmp = (x * (y * z)) - (a * (x * t))
    else if (j <= (-4.7d-213)) then
        tmp = t_2
    else if (j <= (-4d-301)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (j <= 2.3d-199) then
        tmp = t_1
    else if (j <= 1.05d-94) then
        tmp = z * (c * ((x * (y / c)) - b))
    else if (j <= 8.5d-53) then
        tmp = t_1
    else if (j <= 3.7d-45) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 9d+37) then
        tmp = t_2
    else
        tmp = (y * j) * (((a * c) / y) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.06e-37) {
		tmp = t_2;
	} else if (j <= -7e-96) {
		tmp = (x * (y * z)) - (a * (x * t));
	} else if (j <= -4.7e-213) {
		tmp = t_2;
	} else if (j <= -4e-301) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.3e-199) {
		tmp = t_1;
	} else if (j <= 1.05e-94) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 8.5e-53) {
		tmp = t_1;
	} else if (j <= 3.7e-45) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 9e+37) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -2e+35:
		tmp = j * ((a * c) - (y * i))
	elif j <= -1.06e-37:
		tmp = t_2
	elif j <= -7e-96:
		tmp = (x * (y * z)) - (a * (x * t))
	elif j <= -4.7e-213:
		tmp = t_2
	elif j <= -4e-301:
		tmp = (x * y) * (z - (a * (t / y)))
	elif j <= 2.3e-199:
		tmp = t_1
	elif j <= 1.05e-94:
		tmp = z * (c * ((x * (y / c)) - b))
	elif j <= 8.5e-53:
		tmp = t_1
	elif j <= 3.7e-45:
		tmp = z * ((x * y) - (b * c))
	elif j <= 9e+37:
		tmp = t_2
	else:
		tmp = (y * j) * (((a * c) / y) - i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -2e+35)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -1.06e-37)
		tmp = t_2;
	elseif (j <= -7e-96)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(a * Float64(x * t)));
	elseif (j <= -4.7e-213)
		tmp = t_2;
	elseif (j <= -4e-301)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (j <= 2.3e-199)
		tmp = t_1;
	elseif (j <= 1.05e-94)
		tmp = Float64(z * Float64(c * Float64(Float64(x * Float64(y / c)) - b)));
	elseif (j <= 8.5e-53)
		tmp = t_1;
	elseif (j <= 3.7e-45)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 9e+37)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(Float64(a * c) / y) - i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -2e+35)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -1.06e-37)
		tmp = t_2;
	elseif (j <= -7e-96)
		tmp = (x * (y * z)) - (a * (x * t));
	elseif (j <= -4.7e-213)
		tmp = t_2;
	elseif (j <= -4e-301)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (j <= 2.3e-199)
		tmp = t_1;
	elseif (j <= 1.05e-94)
		tmp = z * (c * ((x * (y / c)) - b));
	elseif (j <= 8.5e-53)
		tmp = t_1;
	elseif (j <= 3.7e-45)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 9e+37)
		tmp = t_2;
	else
		tmp = (y * j) * (((a * c) / y) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+35], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.06e-37], t$95$2, If[LessEqual[j, -7e-96], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.7e-213], t$95$2, If[LessEqual[j, -4e-301], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-199], t$95$1, If[LessEqual[j, 1.05e-94], N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-53], t$95$1, If[LessEqual[j, 3.7e-45], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+37], t$95$2, N[(N[(y * j), $MachinePrecision] * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -1.9999999999999999e35

   1. Initial program 77.2%

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

   3. Taylor expanded in j around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -1.9999999999999999e35 < j < -1.06000000000000003e-37 or -6.9999999999999998e-96 < j < -4.7e-213 or 3.7e-45 < j < 8.99999999999999923e37

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf 68.9%

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

   if -1.06000000000000003e-37 < j < -6.9999999999999998e-96

   1. Initial program 64.7%

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

   3. Taylor expanded in x around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

      4. *-commutative 70.2%

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

   8. Simplified 70.2%

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

   if -4.7e-213 < j < -4.00000000000000027e-301

   1. Initial program 70.5%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in x around 0 65.8%

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

       1. associate-*r* 70.4%

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

       2. *-commutative 70.4%

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

       3. associate-/l* 75.1%

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

   11. Simplified 75.1%

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

   if -4.00000000000000027e-301 < j < 2.3000000000000001e-199 or 1.05e-94 < j < 8.50000000000000044e-53

   1. Initial program 72.8%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around inf 86.7%

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

      1. neg-mul-1 86.7%

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

      2. sub-neg 86.7%

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

      3. remove-double-neg 86.7%

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

      4. +-commutative 86.7%

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

      5. mul-1-neg 86.7%

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

      6. unsub-neg 86.7%

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

   8. Simplified 86.7%

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

   if 2.3000000000000001e-199 < j < 1.05e-94

   1. Initial program 53.1%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in c around inf 54.8%

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

      1. associate-/l* 60.7%

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

   8. Simplified 60.7%

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

   if 8.50000000000000044e-53 < j < 3.7e-45

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 8.99999999999999923e37 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 59.3%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in j around inf 71.9%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

      \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(\frac{c \cdot a}{y} - i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.06 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-199}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - \frac{a \cdot \left(x \cdot t\right)}{y}\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (/ (* a (* x t)) y))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -5.4e+35)
     (* j (- (* a c) (* y i)))
     (if (<= j -8e-38)
       t_2
       (if (<= j -1.05e-85)
         t_1
         (if (<= j -5.1e-213)
           t_2
           (if (<= j -4.8e-304)
             (* (* x y) (- z (* a (/ t y))))
             (if (<= j 2.6e-201)
               (* t (- (* b i) (* x a)))
               (if (<= j 4.8e-136)
                 t_1
                 (if (<= j 1.65e-84)
                   (* i (- (* t b) (* y j)))
                   (if (<= j 2.55e-45)
                     (* x (- (* y z) (* t a)))
                     (if (<= j 3.6e+37)
                       t_2
                       (* (* y j) (- (/ (* a c) y) i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - ((a * (x * t)) / y));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -5.4e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -8e-38) {
		tmp = t_2;
	} else if (j <= -1.05e-85) {
		tmp = t_1;
	} else if (j <= -5.1e-213) {
		tmp = t_2;
	} else if (j <= -4.8e-304) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.6e-201) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.8e-136) {
		tmp = t_1;
	} else if (j <= 1.65e-84) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2.55e-45) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 3.6e+37) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - ((a * (x * t)) / y))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-5.4d+35)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-8d-38)) then
        tmp = t_2
    else if (j <= (-1.05d-85)) then
        tmp = t_1
    else if (j <= (-5.1d-213)) then
        tmp = t_2
    else if (j <= (-4.8d-304)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (j <= 2.6d-201) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 4.8d-136) then
        tmp = t_1
    else if (j <= 1.65d-84) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= 2.55d-45) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 3.6d+37) then
        tmp = t_2
    else
        tmp = (y * j) * (((a * c) / y) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - ((a * (x * t)) / y));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -5.4e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -8e-38) {
		tmp = t_2;
	} else if (j <= -1.05e-85) {
		tmp = t_1;
	} else if (j <= -5.1e-213) {
		tmp = t_2;
	} else if (j <= -4.8e-304) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.6e-201) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.8e-136) {
		tmp = t_1;
	} else if (j <= 1.65e-84) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2.55e-45) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 3.6e+37) {
		tmp = t_2;
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - ((a * (x * t)) / y))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -5.4e+35:
		tmp = j * ((a * c) - (y * i))
	elif j <= -8e-38:
		tmp = t_2
	elif j <= -1.05e-85:
		tmp = t_1
	elif j <= -5.1e-213:
		tmp = t_2
	elif j <= -4.8e-304:
		tmp = (x * y) * (z - (a * (t / y)))
	elif j <= 2.6e-201:
		tmp = t * ((b * i) - (x * a))
	elif j <= 4.8e-136:
		tmp = t_1
	elif j <= 1.65e-84:
		tmp = i * ((t * b) - (y * j))
	elif j <= 2.55e-45:
		tmp = x * ((y * z) - (t * a))
	elif j <= 3.6e+37:
		tmp = t_2
	else:
		tmp = (y * j) * (((a * c) / y) - i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(Float64(a * Float64(x * t)) / y)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -5.4e+35)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -8e-38)
		tmp = t_2;
	elseif (j <= -1.05e-85)
		tmp = t_1;
	elseif (j <= -5.1e-213)
		tmp = t_2;
	elseif (j <= -4.8e-304)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (j <= 2.6e-201)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 4.8e-136)
		tmp = t_1;
	elseif (j <= 1.65e-84)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= 2.55e-45)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 3.6e+37)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(Float64(a * c) / y) - i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - ((a * (x * t)) / y));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -5.4e+35)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -8e-38)
		tmp = t_2;
	elseif (j <= -1.05e-85)
		tmp = t_1;
	elseif (j <= -5.1e-213)
		tmp = t_2;
	elseif (j <= -4.8e-304)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (j <= 2.6e-201)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 4.8e-136)
		tmp = t_1;
	elseif (j <= 1.65e-84)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= 2.55e-45)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 3.6e+37)
		tmp = t_2;
	else
		tmp = (y * j) * (((a * c) / y) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.4e+35], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8e-38], t$95$2, If[LessEqual[j, -1.05e-85], t$95$1, If[LessEqual[j, -5.1e-213], t$95$2, If[LessEqual[j, -4.8e-304], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e-201], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-136], t$95$1, If[LessEqual[j, 1.65e-84], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.55e-45], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+37], t$95$2, N[(N[(y * j), $MachinePrecision] * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -5.40000000000000005e35

   1. Initial program 77.2%

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

   3. Taylor expanded in j around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -5.40000000000000005e35 < j < -7.9999999999999997e-38 or -1.05e-85 < j < -5.0999999999999997e-213 or 2.5499999999999999e-45 < j < 3.59999999999999998e37

   1. Initial program 84.0%

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

   3. Taylor expanded in b around inf 68.9%

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

   if -7.9999999999999997e-38 < j < -1.05e-85 or 2.59999999999999982e-201 < j < 4.7999999999999997e-136

   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 x around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in y around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. *-commutative 69.7%

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

   8. Simplified 69.7%

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

   if -5.0999999999999997e-213 < j < -4.8000000000000002e-304

   1. Initial program 70.5%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in x around 0 65.8%

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

       1. associate-*r* 70.4%

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

       2. *-commutative 70.4%

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

       3. associate-/l* 75.1%

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

   11. Simplified 75.1%

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

   if -4.8000000000000002e-304 < j < 2.59999999999999982e-201

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. associate-/l* 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in t around inf 90.3%

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

      1. neg-mul-1 90.3%

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

      2. sub-neg 90.3%

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

      3. remove-double-neg 90.3%

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

      4. +-commutative 90.3%

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

      5. mul-1-neg 90.3%

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

      6. unsub-neg 90.3%

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

   8. Simplified 90.3%

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

   if 4.7999999999999997e-136 < j < 1.64999999999999992e-84

   1. Initial program 44.5%

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

   3. Taylor expanded in i around inf 67.4%

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

      1. distribute-lft-out-- 67.4%

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

   5. Simplified 67.4%

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

   if 1.64999999999999992e-84 < j < 2.5499999999999999e-45

   1. Initial program 77.8%

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

   3. Taylor expanded in x around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   if 3.59999999999999998e37 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 59.3%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in j around inf 71.9%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

      \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(\frac{c \cdot a}{y} - i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.4 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z - \frac{a \cdot \left(x \cdot t\right)}{y}\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - \frac{a \cdot \left(x \cdot t\right)}{y}\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot i - x \cdot a\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;t\_3 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-206}:\\ \;\;\;\;t \cdot t\_2\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{t\_2}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+118}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (- (* b i) (* x a)))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= j -4.4e+33)
     (+ t_3 t_1)
     (if (<= j -1.6e-298)
       (- t_3 (* b (- (* z c) (* t i))))
       (if (<= j 2.7e-206)
         (* t t_2)
         (if (<= j 2.5e+37)
           (* y (+ (* x z) (- (* t (/ t_2 y)) (* i j))))
           (if (<= j 1.65e+118) (+ t_1 (* 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 = j * ((a * c) - (y * i));
	double t_2 = (b * i) - (x * a);
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -4.4e+33) {
		tmp = t_3 + t_1;
	} else if (j <= -1.6e-298) {
		tmp = t_3 - (b * ((z * c) - (t * i)));
	} else if (j <= 2.7e-206) {
		tmp = t * t_2;
	} else if (j <= 2.5e+37) {
		tmp = y * ((x * z) + ((t * (t_2 / y)) - (i * j)));
	} else if (j <= 1.65e+118) {
		tmp = t_1 + (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (b * i) - (x * a)
    t_3 = x * ((y * z) - (t * a))
    if (j <= (-4.4d+33)) then
        tmp = t_3 + t_1
    else if (j <= (-1.6d-298)) then
        tmp = t_3 - (b * ((z * c) - (t * i)))
    else if (j <= 2.7d-206) then
        tmp = t * t_2
    else if (j <= 2.5d+37) then
        tmp = y * ((x * z) + ((t * (t_2 / y)) - (i * j)))
    else if (j <= 1.65d+118) then
        tmp = t_1 + (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 = j * ((a * c) - (y * i));
	double t_2 = (b * i) - (x * a);
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -4.4e+33) {
		tmp = t_3 + t_1;
	} else if (j <= -1.6e-298) {
		tmp = t_3 - (b * ((z * c) - (t * i)));
	} else if (j <= 2.7e-206) {
		tmp = t * t_2;
	} else if (j <= 2.5e+37) {
		tmp = y * ((x * z) + ((t * (t_2 / y)) - (i * j)));
	} else if (j <= 1.65e+118) {
		tmp = t_1 + (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 = j * ((a * c) - (y * i))
	t_2 = (b * i) - (x * a)
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -4.4e+33:
		tmp = t_3 + t_1
	elif j <= -1.6e-298:
		tmp = t_3 - (b * ((z * c) - (t * i)))
	elif j <= 2.7e-206:
		tmp = t * t_2
	elif j <= 2.5e+37:
		tmp = y * ((x * z) + ((t * (t_2 / y)) - (i * j)))
	elif j <= 1.65e+118:
		tmp = t_1 + (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(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(b * i) - Float64(x * a))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -4.4e+33)
		tmp = Float64(t_3 + t_1);
	elseif (j <= -1.6e-298)
		tmp = Float64(t_3 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	elseif (j <= 2.7e-206)
		tmp = Float64(t * t_2);
	elseif (j <= 2.5e+37)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(t_2 / y)) - Float64(i * j))));
	elseif (j <= 1.65e+118)
		tmp = Float64(t_1 + 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 = j * ((a * c) - (y * i));
	t_2 = (b * i) - (x * a);
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -4.4e+33)
		tmp = t_3 + t_1;
	elseif (j <= -1.6e-298)
		tmp = t_3 - (b * ((z * c) - (t * i)));
	elseif (j <= 2.7e-206)
		tmp = t * t_2;
	elseif (j <= 2.5e+37)
		tmp = y * ((x * z) + ((t * (t_2 / y)) - (i * j)));
	elseif (j <= 1.65e+118)
		tmp = t_1 + (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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.4e+33], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[j, -1.6e-298], N[(t$95$3 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e-206], N[(t * t$95$2), $MachinePrecision], If[LessEqual[j, 2.5e+37], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e+118], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.39999999999999988e33

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 79.4%

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

   if -4.39999999999999988e33 < j < -1.59999999999999999e-298

   1. Initial program 77.6%

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

   3. Taylor expanded in j around 0 77.2%

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

   if -1.59999999999999999e-298 < j < 2.7000000000000001e-206

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. associate-/l* 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in t around inf 90.8%

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

      1. neg-mul-1 90.8%

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

      2. sub-neg 90.8%

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

      3. remove-double-neg 90.8%

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

      4. +-commutative 90.8%

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

      5. mul-1-neg 90.8%

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

      6. unsub-neg 90.8%

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

   8. Simplified 90.8%

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

   if 2.7000000000000001e-206 < j < 2.49999999999999994e37

   1. Initial program 70.7%

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

   3. Taylor expanded in y around -inf 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in t around inf 66.9%

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

      1. associate-/l* 69.3%

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

      2. +-commutative 69.3%

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

      3. mul-1-neg 69.3%

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

      4. unsub-neg 69.3%

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

   8. Simplified 69.3%

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

   if 2.49999999999999994e37 < j < 1.65e118

   1. Initial program 90.3%

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

   3. Taylor expanded in t around inf 76.2%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in t around 0 85.9%

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

   if 1.65e118 < j

   1. Initial program 62.4%

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

   3. Taylor expanded in j around inf 76.1%

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

      1. *-commutative 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.25e+122)
   (* c (- (* a j) (* z b)))
   (if (<= c -1.65e+77)
     (* (* x y) (- z (* a (/ t y))))
     (if (<= c -1.02e+27)
       (* b (- (* t i) (* z c)))
       (if (<= c -6.8e-137)
         (* y (- (* x z) (* i j)))
         (if (<= c 1.25e+60)
           (* y (- (* t (/ (- (* b i) (* x a)) y)) (* i j)))
           (* j (- (* a c) (* y 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 (c <= -1.25e+122) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -1.65e+77) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (c <= -1.02e+27) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -6.8e-137) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.25e+60) {
		tmp = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.25d+122)) then
        tmp = c * ((a * j) - (z * b))
    else if (c <= (-1.65d+77)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (c <= (-1.02d+27)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= (-6.8d-137)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.25d+60) then
        tmp = y * ((t * (((b * i) - (x * a)) / y)) - (i * j))
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.25e+122) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -1.65e+77) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (c <= -1.02e+27) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -6.8e-137) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.25e+60) {
		tmp = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.25e+122:
		tmp = c * ((a * j) - (z * b))
	elif c <= -1.65e+77:
		tmp = (x * y) * (z - (a * (t / y)))
	elif c <= -1.02e+27:
		tmp = b * ((t * i) - (z * c))
	elif c <= -6.8e-137:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.25e+60:
		tmp = y * ((t * (((b * i) - (x * a)) / y)) - (i * j))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.25e+122)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (c <= -1.65e+77)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (c <= -1.02e+27)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= -6.8e-137)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.25e+60)
		tmp = Float64(y * Float64(Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / y)) - Float64(i * j)));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.25e+122)
		tmp = c * ((a * j) - (z * b));
	elseif (c <= -1.65e+77)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (c <= -1.02e+27)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= -6.8e-137)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.25e+60)
		tmp = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.25e+122], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.65e+77], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.02e+27], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e-137], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e+60], N[(y * N[(N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.24999999999999997e122

   1. Initial program 65.2%

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

   3. Taylor expanded in c around inf 70.9%

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

      1. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -1.24999999999999997e122 < c < -1.6499999999999999e77

   1. Initial program 80.3%

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

   3. Taylor expanded in x around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

      4. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in x around 0 70.6%

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

       1. associate-*r* 70.7%

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

       2. *-commutative 70.7%

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

       3. associate-/l* 80.4%

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

   11. Simplified 80.4%

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

   if -1.6499999999999999e77 < c < -1.0199999999999999e27

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   if -1.0199999999999999e27 < c < -6.80000000000000028e-137

   1. Initial program 72.0%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   if -6.80000000000000028e-137 < c < 1.24999999999999994e60

   1. Initial program 82.5%

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

   3. Taylor expanded in y around -inf 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. associate-/l* 74.4%

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

      2. +-commutative 74.4%

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

      3. mul-1-neg 74.4%

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

      4. unsub-neg 74.4%

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

   8. Simplified 74.4%

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

   9. Taylor expanded in z around 0 67.2%

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

       1. associate-/l* 69.1%

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

   11. Simplified 69.1%

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

   if 1.24999999999999994e60 < c

   1. Initial program 58.2%

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

   3. Taylor expanded in j around inf 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+290}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* t (/ (- (* b i) (* x a)) y)) (* i j)))))
   (if (<= t -8.8e+20)
     t_1
     (if (<= t -3.9e-66)
       (* c (- (* a j) (* z b)))
       (if (<= t -4.1e-97)
         (* z (- (* x y) (* b c)))
         (if (<= t 7e-67)
           (* y (+ (* x z) (- (/ (* a (* c j)) y) (* i j))))
           (if (<= t 6.5e+209)
             t_1
             (if (<= t 1.5e+290)
               (* a (- (* c j) (* x t)))
               (* y (* x z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	double tmp;
	if (t <= -8.8e+20) {
		tmp = t_1;
	} else if (t <= -3.9e-66) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -4.1e-97) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7e-67) {
		tmp = y * ((x * z) + (((a * (c * j)) / y) - (i * j)));
	} else if (t <= 6.5e+209) {
		tmp = t_1;
	} else if (t <= 1.5e+290) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t * (((b * i) - (x * a)) / y)) - (i * j))
    if (t <= (-8.8d+20)) then
        tmp = t_1
    else if (t <= (-3.9d-66)) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= (-4.1d-97)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 7d-67) then
        tmp = y * ((x * z) + (((a * (c * j)) / y) - (i * j)))
    else if (t <= 6.5d+209) then
        tmp = t_1
    else if (t <= 1.5d+290) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	double tmp;
	if (t <= -8.8e+20) {
		tmp = t_1;
	} else if (t <= -3.9e-66) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -4.1e-97) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7e-67) {
		tmp = y * ((x * z) + (((a * (c * j)) / y) - (i * j)));
	} else if (t <= 6.5e+209) {
		tmp = t_1;
	} else if (t <= 1.5e+290) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((t * (((b * i) - (x * a)) / y)) - (i * j))
	tmp = 0
	if t <= -8.8e+20:
		tmp = t_1
	elif t <= -3.9e-66:
		tmp = c * ((a * j) - (z * b))
	elif t <= -4.1e-97:
		tmp = z * ((x * y) - (b * c))
	elif t <= 7e-67:
		tmp = y * ((x * z) + (((a * (c * j)) / y) - (i * j)))
	elif t <= 6.5e+209:
		tmp = t_1
	elif t <= 1.5e+290:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / y)) - Float64(i * j)))
	tmp = 0.0
	if (t <= -8.8e+20)
		tmp = t_1;
	elseif (t <= -3.9e-66)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= -4.1e-97)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 7e-67)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(c * j)) / y) - Float64(i * j))));
	elseif (t <= 6.5e+209)
		tmp = t_1;
	elseif (t <= 1.5e+290)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((t * (((b * i) - (x * a)) / y)) - (i * j));
	tmp = 0.0;
	if (t <= -8.8e+20)
		tmp = t_1;
	elseif (t <= -3.9e-66)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= -4.1e-97)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 7e-67)
		tmp = y * ((x * z) + (((a * (c * j)) / y) - (i * j)));
	elseif (t <= 6.5e+209)
		tmp = t_1;
	elseif (t <= 1.5e+290)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+20], t$95$1, If[LessEqual[t, -3.9e-66], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-97], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-67], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+209], t$95$1, If[LessEqual[t, 1.5e+290], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8.8e20 or 7.0000000000000001e-67 < t < 6.49999999999999975e209

   1. Initial program 70.4%

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

   3. Taylor expanded in y around -inf 59.0%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in t around inf 70.1%

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

      1. associate-/l* 72.3%

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

      2. +-commutative 72.3%

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

      3. mul-1-neg 72.3%

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

      4. unsub-neg 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in z around 0 66.7%

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

       1. associate-/l* 68.8%

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

   11. Simplified 68.8%

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

   if -8.8e20 < t < -3.89999999999999983e-66

   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 c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -3.89999999999999983e-66 < t < -4.09999999999999993e-97

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   if -4.09999999999999993e-97 < t < 7.0000000000000001e-67

   1. Initial program 85.5%

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

   3. Taylor expanded in y around -inf 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in j around inf 64.1%

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

   if 6.49999999999999975e209 < t < 1.5e290

   1. Initial program 60.0%

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

   3. Taylor expanded in a around inf 87.0%

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

      1. +-commutative 87.0%

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

      2. mul-1-neg 87.0%

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

      3. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

   if 1.5e290 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in x around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+290}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_3 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+238}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* i (* y (- j)))) (t_3 (* j (* a c))))
   (if (<= a -2.15e+238)
     t_3
     (if (<= a -2.6e+105)
       t_1
       (if (<= a -8e+15)
         t_3
         (if (<= a -7e-239)
           (* z (* x y))
           (if (<= a 1.65e-292)
             t_2
             (if (<= a 1.72e-152)
               (* t (* b i))
               (if (<= a 3.7e+111) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = i * (y * -j);
	double t_3 = j * (a * c);
	double tmp;
	if (a <= -2.15e+238) {
		tmp = t_3;
	} else if (a <= -2.6e+105) {
		tmp = t_1;
	} else if (a <= -8e+15) {
		tmp = t_3;
	} else if (a <= -7e-239) {
		tmp = z * (x * y);
	} else if (a <= 1.65e-292) {
		tmp = t_2;
	} else if (a <= 1.72e-152) {
		tmp = t * (b * i);
	} else if (a <= 3.7e+111) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = i * (y * -j)
    t_3 = j * (a * c)
    if (a <= (-2.15d+238)) then
        tmp = t_3
    else if (a <= (-2.6d+105)) then
        tmp = t_1
    else if (a <= (-8d+15)) then
        tmp = t_3
    else if (a <= (-7d-239)) then
        tmp = z * (x * y)
    else if (a <= 1.65d-292) then
        tmp = t_2
    else if (a <= 1.72d-152) then
        tmp = t * (b * i)
    else if (a <= 3.7d+111) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = i * (y * -j);
	double t_3 = j * (a * c);
	double tmp;
	if (a <= -2.15e+238) {
		tmp = t_3;
	} else if (a <= -2.6e+105) {
		tmp = t_1;
	} else if (a <= -8e+15) {
		tmp = t_3;
	} else if (a <= -7e-239) {
		tmp = z * (x * y);
	} else if (a <= 1.65e-292) {
		tmp = t_2;
	} else if (a <= 1.72e-152) {
		tmp = t * (b * i);
	} else if (a <= 3.7e+111) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = i * (y * -j)
	t_3 = j * (a * c)
	tmp = 0
	if a <= -2.15e+238:
		tmp = t_3
	elif a <= -2.6e+105:
		tmp = t_1
	elif a <= -8e+15:
		tmp = t_3
	elif a <= -7e-239:
		tmp = z * (x * y)
	elif a <= 1.65e-292:
		tmp = t_2
	elif a <= 1.72e-152:
		tmp = t * (b * i)
	elif a <= 3.7e+111:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	t_3 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -2.15e+238)
		tmp = t_3;
	elseif (a <= -2.6e+105)
		tmp = t_1;
	elseif (a <= -8e+15)
		tmp = t_3;
	elseif (a <= -7e-239)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.65e-292)
		tmp = t_2;
	elseif (a <= 1.72e-152)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 3.7e+111)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	t_2 = i * (y * -j);
	t_3 = j * (a * c);
	tmp = 0.0;
	if (a <= -2.15e+238)
		tmp = t_3;
	elseif (a <= -2.6e+105)
		tmp = t_1;
	elseif (a <= -8e+15)
		tmp = t_3;
	elseif (a <= -7e-239)
		tmp = z * (x * y);
	elseif (a <= 1.65e-292)
		tmp = t_2;
	elseif (a <= 1.72e-152)
		tmp = t * (b * i);
	elseif (a <= 3.7e+111)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+238], t$95$3, If[LessEqual[a, -2.6e+105], t$95$1, If[LessEqual[a, -8e+15], t$95$3, If[LessEqual[a, -7e-239], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-292], t$95$2, If[LessEqual[a, 1.72e-152], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+111], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.14999999999999992e238 or -2.6000000000000002e105 < a < -8e15

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in c around inf 49.2%

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

      1. pow1 49.2%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 54.0%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 54.0%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 54.0%

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

      2. *-commutative 54.0%

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

   10. Simplified 54.0%

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

   if -2.14999999999999992e238 < a < -2.6000000000000002e105 or 3.7000000000000003e111 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. *-commutative 56.6%

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

      3. distribute-rgt-neg-in 56.6%

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

   8. Simplified 56.6%

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

   if -8e15 < a < -7.00000000000000011e-239

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in y around inf 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

   if -7.00000000000000011e-239 < a < 1.64999999999999997e-292 or 1.72e-152 < a < 3.7000000000000003e111

   1. Initial program 82.7%

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

   3. Taylor expanded in y around -inf 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around inf 67.0%

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

      1. associate-/l* 68.5%

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

      2. +-commutative 68.5%

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

      3. mul-1-neg 68.5%

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

      4. unsub-neg 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in j around inf 40.1%

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

       1. mul-1-neg 40.1%

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

       2. *-commutative 40.1%

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

       3. distribute-rgt-neg-in 40.1%

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

       4. *-commutative 40.1%

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

   11. Simplified 40.1%

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

   if 1.64999999999999997e-292 < a < 1.72e-152

   1. Initial program 75.9%

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

   3. Taylor expanded in t around inf 49.7%

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

      1. distribute-lft-out-- 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in a around 0 41.0%

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

      1. neg-mul-1 41.0%

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

      2. distribute-rgt-neg-in 41.0%

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

   8. Simplified 41.0%

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

   9. Taylor expanded in t around 0 38.1%

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

       1. associate-*r* 41.0%

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

       2. *-commutative 41.0%

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

   11. Simplified 41.0%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+238}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -7e+35)
     (* j (- (* a c) (* y i)))
     (if (<= j -6.8e-39)
       t_2
       (if (<= j -1.52e-89)
         t_1
         (if (<= j -5.5e-213)
           t_2
           (if (<= j -1.16e-303)
             t_1
             (if (<= j 2.6e+37)
               (* t (- (* b i) (* x a)))
               (* (* y j) (- (/ (* a c) y) i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -7e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -6.8e-39) {
		tmp = t_2;
	} else if (j <= -1.52e-89) {
		tmp = t_1;
	} else if (j <= -5.5e-213) {
		tmp = t_2;
	} else if (j <= -1.16e-303) {
		tmp = t_1;
	} else if (j <= 2.6e+37) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-7d+35)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-6.8d-39)) then
        tmp = t_2
    else if (j <= (-1.52d-89)) then
        tmp = t_1
    else if (j <= (-5.5d-213)) then
        tmp = t_2
    else if (j <= (-1.16d-303)) then
        tmp = t_1
    else if (j <= 2.6d+37) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (y * j) * (((a * c) / y) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -7e+35) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -6.8e-39) {
		tmp = t_2;
	} else if (j <= -1.52e-89) {
		tmp = t_1;
	} else if (j <= -5.5e-213) {
		tmp = t_2;
	} else if (j <= -1.16e-303) {
		tmp = t_1;
	} else if (j <= 2.6e+37) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (y * j) * (((a * c) / y) - i);
	}
	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))
	tmp = 0
	if j <= -7e+35:
		tmp = j * ((a * c) - (y * i))
	elif j <= -6.8e-39:
		tmp = t_2
	elif j <= -1.52e-89:
		tmp = t_1
	elif j <= -5.5e-213:
		tmp = t_2
	elif j <= -1.16e-303:
		tmp = t_1
	elif j <= 2.6e+37:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (y * j) * (((a * c) / y) - i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -7e+35)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -6.8e-39)
		tmp = t_2;
	elseif (j <= -1.52e-89)
		tmp = t_1;
	elseif (j <= -5.5e-213)
		tmp = t_2;
	elseif (j <= -1.16e-303)
		tmp = t_1;
	elseif (j <= 2.6e+37)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(Float64(a * c) / y) - i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -7e+35)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -6.8e-39)
		tmp = t_2;
	elseif (j <= -1.52e-89)
		tmp = t_1;
	elseif (j <= -5.5e-213)
		tmp = t_2;
	elseif (j <= -1.16e-303)
		tmp = t_1;
	elseif (j <= 2.6e+37)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (y * j) * (((a * c) / y) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+35], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.8e-39], t$95$2, If[LessEqual[j, -1.52e-89], t$95$1, If[LessEqual[j, -5.5e-213], t$95$2, If[LessEqual[j, -1.16e-303], t$95$1, If[LessEqual[j, 2.6e+37], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.0000000000000001e35

   1. Initial program 77.2%

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

   3. Taylor expanded in j around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -7.0000000000000001e35 < j < -6.7999999999999998e-39 or -1.52e-89 < j < -5.50000000000000008e-213

   1. Initial program 83.7%

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

   3. Taylor expanded in b around inf 68.4%

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

   if -6.7999999999999998e-39 < j < -1.52e-89 or -5.50000000000000008e-213 < j < -1.16e-303

   1. Initial program 68.1%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -1.16e-303 < j < 2.5999999999999999e37

   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 z around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

      4. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in t around inf 59.7%

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

      1. neg-mul-1 59.7%

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

      2. sub-neg 59.7%

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

      3. remove-double-neg 59.7%

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

      4. +-commutative 59.7%

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

      5. mul-1-neg 59.7%

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

      6. unsub-neg 59.7%

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

   8. Simplified 59.7%

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

   if 2.5999999999999999e37 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 59.3%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in j around inf 71.9%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(\frac{a \cdot c}{y} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.6 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -9.6e+34)
     t_2
     (if (<= j -1.35e-36)
       t_1
       (if (<= j -2.8e-87)
         (* t (* x (- a)))
         (if (<= j -2.35e-266)
           t_1
           (if (<= j 3.4e-208)
             (* a (- (* c j) (* x t)))
             (if (<= j 7e+37) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.6e+34) {
		tmp = t_2;
	} else if (j <= -1.35e-36) {
		tmp = t_1;
	} else if (j <= -2.8e-87) {
		tmp = t * (x * -a);
	} else if (j <= -2.35e-266) {
		tmp = t_1;
	} else if (j <= 3.4e-208) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 7e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-9.6d+34)) then
        tmp = t_2
    else if (j <= (-1.35d-36)) then
        tmp = t_1
    else if (j <= (-2.8d-87)) then
        tmp = t * (x * -a)
    else if (j <= (-2.35d-266)) then
        tmp = t_1
    else if (j <= 3.4d-208) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= 7d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.6e+34) {
		tmp = t_2;
	} else if (j <= -1.35e-36) {
		tmp = t_1;
	} else if (j <= -2.8e-87) {
		tmp = t * (x * -a);
	} else if (j <= -2.35e-266) {
		tmp = t_1;
	} else if (j <= 3.4e-208) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 7e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -9.6e+34:
		tmp = t_2
	elif j <= -1.35e-36:
		tmp = t_1
	elif j <= -2.8e-87:
		tmp = t * (x * -a)
	elif j <= -2.35e-266:
		tmp = t_1
	elif j <= 3.4e-208:
		tmp = a * ((c * j) - (x * t))
	elif j <= 7e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.6e+34)
		tmp = t_2;
	elseif (j <= -1.35e-36)
		tmp = t_1;
	elseif (j <= -2.8e-87)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (j <= -2.35e-266)
		tmp = t_1;
	elseif (j <= 3.4e-208)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= 7e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.6e+34)
		tmp = t_2;
	elseif (j <= -1.35e-36)
		tmp = t_1;
	elseif (j <= -2.8e-87)
		tmp = t * (x * -a);
	elseif (j <= -2.35e-266)
		tmp = t_1;
	elseif (j <= 3.4e-208)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= 7e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.6e+34], t$95$2, If[LessEqual[j, -1.35e-36], t$95$1, If[LessEqual[j, -2.8e-87], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.35e-266], t$95$1, If[LessEqual[j, 3.4e-208], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+37], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.59999999999999948e34 or 7e37 < j

   1. Initial program 74.1%

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

   3. Taylor expanded in j around inf 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -9.59999999999999948e34 < j < -1.35000000000000004e-36 or -2.8000000000000001e-87 < j < -2.35000000000000014e-266 or 3.4e-208 < j < 7e37

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 54.7%

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

   if -1.35000000000000004e-36 < j < -2.8000000000000001e-87

   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 t around inf 60.9%

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

      1. distribute-lft-out-- 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in a around inf 54.6%

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

   if -2.35000000000000014e-266 < j < 3.4e-208

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.38 \cdot 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -1.38e+35)
     t_3
     (if (<= j -7.2e-38)
       t_2
       (if (<= j -1.95e-90)
         t_1
         (if (<= j -4.8e-213)
           t_2
           (if (<= j -1.16e-301)
             t_1
             (if (<= j 1.75e+37) (* t (- (* b i) (* x a))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.38e+35) {
		tmp = t_3;
	} else if (j <= -7.2e-38) {
		tmp = t_2;
	} else if (j <= -1.95e-90) {
		tmp = t_1;
	} else if (j <= -4.8e-213) {
		tmp = t_2;
	} else if (j <= -1.16e-301) {
		tmp = t_1;
	} else if (j <= 1.75e+37) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-1.38d+35)) then
        tmp = t_3
    else if (j <= (-7.2d-38)) then
        tmp = t_2
    else if (j <= (-1.95d-90)) then
        tmp = t_1
    else if (j <= (-4.8d-213)) then
        tmp = t_2
    else if (j <= (-1.16d-301)) then
        tmp = t_1
    else if (j <= 1.75d+37) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.38e+35) {
		tmp = t_3;
	} else if (j <= -7.2e-38) {
		tmp = t_2;
	} else if (j <= -1.95e-90) {
		tmp = t_1;
	} else if (j <= -4.8e-213) {
		tmp = t_2;
	} else if (j <= -1.16e-301) {
		tmp = t_1;
	} else if (j <= 1.75e+37) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.38e+35:
		tmp = t_3
	elif j <= -7.2e-38:
		tmp = t_2
	elif j <= -1.95e-90:
		tmp = t_1
	elif j <= -4.8e-213:
		tmp = t_2
	elif j <= -1.16e-301:
		tmp = t_1
	elif j <= 1.75e+37:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.38e+35)
		tmp = t_3;
	elseif (j <= -7.2e-38)
		tmp = t_2;
	elseif (j <= -1.95e-90)
		tmp = t_1;
	elseif (j <= -4.8e-213)
		tmp = t_2;
	elseif (j <= -1.16e-301)
		tmp = t_1;
	elseif (j <= 1.75e+37)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.38e+35)
		tmp = t_3;
	elseif (j <= -7.2e-38)
		tmp = t_2;
	elseif (j <= -1.95e-90)
		tmp = t_1;
	elseif (j <= -4.8e-213)
		tmp = t_2;
	elseif (j <= -1.16e-301)
		tmp = t_1;
	elseif (j <= 1.75e+37)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(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, -1.38e+35], t$95$3, If[LessEqual[j, -7.2e-38], t$95$2, If[LessEqual[j, -1.95e-90], t$95$1, If[LessEqual[j, -4.8e-213], t$95$2, If[LessEqual[j, -1.16e-301], t$95$1, If[LessEqual[j, 1.75e+37], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.38000000000000007e35 or 1.75e37 < j

   1. Initial program 74.1%

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

   3. Taylor expanded in j around inf 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -1.38000000000000007e35 < j < -7.2000000000000001e-38 or -1.95000000000000002e-90 < j < -4.79999999999999991e-213

   1. Initial program 83.7%

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

   3. Taylor expanded in b around inf 68.4%

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

   if -7.2000000000000001e-38 < j < -1.95000000000000002e-90 or -4.79999999999999991e-213 < j < -1.15999999999999998e-301

   1. Initial program 68.1%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -1.15999999999999998e-301 < j < 1.75e37

   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 z around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

      4. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in t around inf 59.7%

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

      1. neg-mul-1 59.7%

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

      2. sub-neg 59.7%

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

      3. remove-double-neg 59.7%

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

      4. +-commutative 59.7%

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

      5. mul-1-neg 59.7%

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

      6. unsub-neg 59.7%

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

   8. Simplified 59.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.38 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+47} \lor \neg \left(b \leq 4.85 \cdot 10^{+55}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= b -1.7e+47) (not (<= b 4.85e+55)))
     (+ (- (* z (* x y)) (* b (- (* z c) (* t i)))) t_1)
     (+ (* 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 = j * ((a * c) - (y * i));
	double tmp;
	if ((b <= -1.7e+47) || !(b <= 4.85e+55)) {
		tmp = ((z * (x * y)) - (b * ((z * c) - (t * i)))) + t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + 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) - (y * i))
    if ((b <= (-1.7d+47)) .or. (.not. (b <= 4.85d+55))) then
        tmp = ((z * (x * y)) - (b * ((z * c) - (t * i)))) + t_1
    else
        tmp = (x * ((y * z) - (t * a))) + 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) - (y * i));
	double tmp;
	if ((b <= -1.7e+47) || !(b <= 4.85e+55)) {
		tmp = ((z * (x * y)) - (b * ((z * c) - (t * i)))) + t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (b <= -1.7e+47) or not (b <= 4.85e+55):
		tmp = ((z * (x * y)) - (b * ((z * c) - (t * i)))) + t_1
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if ((b <= -1.7e+47) || !(b <= 4.85e+55))
		tmp = Float64(Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(t * i)))) + t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((b <= -1.7e+47) || ~((b <= 4.85e+55)))
		tmp = ((z * (x * y)) - (b * ((z * c) - (t * i)))) + t_1;
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.7e+47], N[Not[LessEqual[b, 4.85e+55]], $MachinePrecision]], N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6999999999999999e47 or 4.8500000000000003e55 < b

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l* 77.0%

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

   5. Simplified 77.0%

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

   if -1.6999999999999999e47 < b < 4.8500000000000003e55

   1. Initial program 69.4%

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

   3. Taylor expanded in b around 0 74.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+47} \lor \neg \left(b \leq 4.85 \cdot 10^{+55}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -4.7e+148)
     t_2
     (if (<= b 9.2e-28)
       t_1
       (if (<= b 5.8e+42) (* i (* y (- j))) (if (<= b 5.8e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.7e+148) {
		tmp = t_2;
	} else if (b <= 9.2e-28) {
		tmp = t_1;
	} else if (b <= 5.8e+42) {
		tmp = i * (y * -j);
	} else if (b <= 5.8e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-4.7d+148)) then
        tmp = t_2
    else if (b <= 9.2d-28) then
        tmp = t_1
    else if (b <= 5.8d+42) then
        tmp = i * (y * -j)
    else if (b <= 5.8d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.7e+148) {
		tmp = t_2;
	} else if (b <= 9.2e-28) {
		tmp = t_1;
	} else if (b <= 5.8e+42) {
		tmp = i * (y * -j);
	} else if (b <= 5.8e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.7e+148:
		tmp = t_2
	elif b <= 9.2e-28:
		tmp = t_1
	elif b <= 5.8e+42:
		tmp = i * (y * -j)
	elif b <= 5.8e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.7e+148)
		tmp = t_2;
	elseif (b <= 9.2e-28)
		tmp = t_1;
	elseif (b <= 5.8e+42)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 5.8e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.7e+148)
		tmp = t_2;
	elseif (b <= 9.2e-28)
		tmp = t_1;
	elseif (b <= 5.8e+42)
		tmp = i * (y * -j);
	elseif (b <= 5.8e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+148], t$95$2, If[LessEqual[b, 9.2e-28], t$95$1, If[LessEqual[b, 5.8e+42], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.6999999999999997e148 or 5.7999999999999997e69 < b

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 68.8%

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

   if -4.6999999999999997e148 < b < 9.19999999999999942e-28 or 5.79999999999999961e42 < b < 5.7999999999999997e69

   1. Initial program 71.6%

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

   3. Taylor expanded in a around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   if 9.19999999999999942e-28 < b < 5.79999999999999961e42

   1. Initial program 75.5%

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

   3. Taylor expanded in y around -inf 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in t around inf 69.2%

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

      1. associate-/l* 69.7%

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

      2. +-commutative 69.7%

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

      3. mul-1-neg 69.7%

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

      4. unsub-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in j around inf 45.0%

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

       1. mul-1-neg 45.0%

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

       2. *-commutative 45.0%

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

       3. distribute-rgt-neg-in 45.0%

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

       4. *-commutative 45.0%

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

   11. Simplified 45.0%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+116} \lor \neg \left(b \leq 6 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.4e+116) (not (<= b 6e+136)))
   (* b (- (* t i) (* z c)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+116) || !(b <= 6e+136)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.4d+116)) .or. (.not. (b <= 6d+136))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+116) || !(b <= 6e+136)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.4e+116) or not (b <= 6e+136):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.4e+116) || !(b <= 6e+136))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.4e+116) || ~((b <= 6e+136)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.4e+116], N[Not[LessEqual[b, 6e+136]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.40000000000000023e116 or 5.99999999999999958e136 < b

   1. Initial program 74.9%

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

   3. Taylor expanded in b around inf 68.5%

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

   if -3.40000000000000023e116 < b < 5.99999999999999958e136

   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 b around 0 74.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+116} \lor \neg \left(b \leq 6 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+132}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= b -1.02e+120)
     (* b (- (* t i) (* z c)))
     (if (<= b 1.05e+132)
       (+ t_1 (* j (- (* a c) (* y i))))
       (- t_1 (* b (- (* z c) (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -1.02e+120) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= 1.05e+132) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (b <= (-1.02d+120)) then
        tmp = b * ((t * i) - (z * c))
    else if (b <= 1.05d+132) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = t_1 - (b * ((z * c) - (t * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -1.02e+120) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= 1.05e+132) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -1.02e+120:
		tmp = b * ((t * i) - (z * c))
	elif b <= 1.05e+132:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.02e+120)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (b <= 1.05e+132)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -1.02e+120)
		tmp = b * ((t * i) - (z * c));
	elseif (b <= 1.05e+132)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = t_1 - (b * ((z * c) - (t * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+120], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+132], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.01999999999999997e120

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf 67.9%

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

   if -1.01999999999999997e120 < b < 1.04999999999999997e132

   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 b around 0 74.5%

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

   if 1.04999999999999997e132 < b

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 0 71.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= t -1.65e+207)
     (* t (* b i))
     (if (<= t -1.25e+158)
       t_1
       (if (<= t -1.1e+119)
         (* b (* t i))
         (if (<= t 1.75e-29) (* j (* a 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 = x * (t * -a);
	double tmp;
	if (t <= -1.65e+207) {
		tmp = t * (b * i);
	} else if (t <= -1.25e+158) {
		tmp = t_1;
	} else if (t <= -1.1e+119) {
		tmp = b * (t * i);
	} else if (t <= 1.75e-29) {
		tmp = j * (a * 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 = x * (t * -a)
    if (t <= (-1.65d+207)) then
        tmp = t * (b * i)
    else if (t <= (-1.25d+158)) then
        tmp = t_1
    else if (t <= (-1.1d+119)) then
        tmp = b * (t * i)
    else if (t <= 1.75d-29) then
        tmp = j * (a * 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 = x * (t * -a);
	double tmp;
	if (t <= -1.65e+207) {
		tmp = t * (b * i);
	} else if (t <= -1.25e+158) {
		tmp = t_1;
	} else if (t <= -1.1e+119) {
		tmp = b * (t * i);
	} else if (t <= 1.75e-29) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if t <= -1.65e+207:
		tmp = t * (b * i)
	elif t <= -1.25e+158:
		tmp = t_1
	elif t <= -1.1e+119:
		tmp = b * (t * i)
	elif t <= 1.75e-29:
		tmp = j * (a * c)
	else:
		tmp = t_1
	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 (t <= -1.65e+207)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -1.25e+158)
		tmp = t_1;
	elseif (t <= -1.1e+119)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 1.75e-29)
		tmp = Float64(j * Float64(a * 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 = x * (t * -a);
	tmp = 0.0;
	if (t <= -1.65e+207)
		tmp = t * (b * i);
	elseif (t <= -1.25e+158)
		tmp = t_1;
	elseif (t <= -1.1e+119)
		tmp = b * (t * i);
	elseif (t <= 1.75e-29)
		tmp = j * (a * 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[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+207], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e+158], t$95$1, If[LessEqual[t, -1.1e+119], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-29], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65e207

   1. Initial program 47.6%

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

   3. Taylor expanded in t around inf 74.3%

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

      1. distribute-lft-out-- 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in a around 0 60.8%

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

      1. neg-mul-1 60.8%

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

      2. distribute-rgt-neg-in 60.8%

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

   8. Simplified 60.8%

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

   9. Taylor expanded in t around 0 57.7%

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

       1. associate-*r* 60.8%

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

       2. *-commutative 60.8%

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

   11. Simplified 60.8%

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

   if -1.65e207 < t < -1.2499999999999999e158 or 1.7499999999999999e-29 < t

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in z around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. *-commutative 43.1%

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

      3. distribute-rgt-neg-in 43.1%

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

   8. Simplified 43.1%

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

   if -1.2499999999999999e158 < t < -1.1000000000000001e119

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in a around 0 70.7%

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

   if -1.1000000000000001e119 < t < 1.7499999999999999e-29

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 39.0%

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

      1. +-commutative 39.0%

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

      2. mul-1-neg 39.0%

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

      3. unsub-neg 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in c around inf 30.3%

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

      1. pow1 30.3%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 32.4%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 32.4%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 32.4%

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

      2. *-commutative 32.4%

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

   10. Simplified 32.4%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.95e+207)
   (* t (* b i))
   (if (<= t -1.3e+158)
     (* x (* t (- a)))
     (if (<= t -4.6e+118)
       (* b (* t i))
       (if (<= t 4.6e-33) (* j (* a c)) (* a (* x (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.95e+207) {
		tmp = t * (b * i);
	} else if (t <= -1.3e+158) {
		tmp = x * (t * -a);
	} else if (t <= -4.6e+118) {
		tmp = b * (t * i);
	} else if (t <= 4.6e-33) {
		tmp = j * (a * c);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.95d+207)) then
        tmp = t * (b * i)
    else if (t <= (-1.3d+158)) then
        tmp = x * (t * -a)
    else if (t <= (-4.6d+118)) then
        tmp = b * (t * i)
    else if (t <= 4.6d-33) then
        tmp = j * (a * c)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.95e+207) {
		tmp = t * (b * i);
	} else if (t <= -1.3e+158) {
		tmp = x * (t * -a);
	} else if (t <= -4.6e+118) {
		tmp = b * (t * i);
	} else if (t <= 4.6e-33) {
		tmp = j * (a * c);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.95e+207:
		tmp = t * (b * i)
	elif t <= -1.3e+158:
		tmp = x * (t * -a)
	elif t <= -4.6e+118:
		tmp = b * (t * i)
	elif t <= 4.6e-33:
		tmp = j * (a * c)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.95e+207)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -1.3e+158)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -4.6e+118)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 4.6e-33)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.95e+207)
		tmp = t * (b * i);
	elseif (t <= -1.3e+158)
		tmp = x * (t * -a);
	elseif (t <= -4.6e+118)
		tmp = b * (t * i);
	elseif (t <= 4.6e-33)
		tmp = j * (a * c);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.95e+207], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e+158], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e+118], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-33], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.94999999999999986e207

   1. Initial program 47.6%

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

   3. Taylor expanded in t around inf 74.3%

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

      1. distribute-lft-out-- 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in a around 0 60.8%

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

      1. neg-mul-1 60.8%

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

      2. distribute-rgt-neg-in 60.8%

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

   8. Simplified 60.8%

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

   9. Taylor expanded in t around 0 57.7%

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

       1. associate-*r* 60.8%

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

       2. *-commutative 60.8%

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

   11. Simplified 60.8%

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

   if -1.94999999999999986e207 < t < -1.3e158

   1. Initial program 76.8%

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

   3. Taylor expanded in x around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. *-commutative 54.1%

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

      3. distribute-rgt-neg-in 54.1%

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

   8. Simplified 54.1%

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

   if -1.3e158 < t < -4.60000000000000032e118

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in a around 0 70.7%

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

   if -4.60000000000000032e118 < t < 4.59999999999999971e-33

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 39.0%

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

      1. +-commutative 39.0%

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

      2. mul-1-neg 39.0%

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

      3. unsub-neg 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in c around inf 30.3%

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

      1. pow1 30.3%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 32.4%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 32.4%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 32.4%

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

      2. *-commutative 32.4%

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

   10. Simplified 32.4%

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

   if 4.59999999999999971e-33 < t

   1. Initial program 76.4%

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

   3. Taylor expanded in a around inf 51.7%

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

      1. +-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in c around 0 42.5%

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

      1. associate-*r* 42.5%

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

      2. neg-mul-1 42.5%

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

   8. Simplified 42.5%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+199}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -6e+217)
   (* x (* y z))
   (if (<= y 6.4e+74)
     (* a (- (* c j) (* x t)))
     (if (<= y 1.75e+199) (* i (* y (- j))) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6e+217) {
		tmp = x * (y * z);
	} else if (y <= 6.4e+74) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.75e+199) {
		tmp = i * (y * -j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-6d+217)) then
        tmp = x * (y * z)
    else if (y <= 6.4d+74) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 1.75d+199) then
        tmp = i * (y * -j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6e+217) {
		tmp = x * (y * z);
	} else if (y <= 6.4e+74) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.75e+199) {
		tmp = i * (y * -j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -6e+217:
		tmp = x * (y * z)
	elif y <= 6.4e+74:
		tmp = a * ((c * j) - (x * t))
	elif y <= 1.75e+199:
		tmp = i * (y * -j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -6e+217)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 6.4e+74)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 1.75e+199)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -6e+217)
		tmp = x * (y * z);
	elseif (y <= 6.4e+74)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 1.75e+199)
		tmp = i * (y * -j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -6e+217], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+74], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+199], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999952e217

   1. Initial program 52.7%

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

   3. Taylor expanded in x around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. *-commutative 57.5%

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

   8. Simplified 57.5%

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

   if -5.99999999999999952e217 < y < 6.39999999999999989e74

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

   5. Simplified 50.3%

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

   if 6.39999999999999989e74 < y < 1.7499999999999999e199

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. associate-/l* 85.1%

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

      2. +-commutative 85.1%

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

      3. mul-1-neg 85.1%

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

      4. unsub-neg 85.1%

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

   8. Simplified 85.1%

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

   9. Taylor expanded in j around inf 49.1%

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

       1. mul-1-neg 49.1%

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

       2. *-commutative 49.1%

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

       3. distribute-rgt-neg-in 49.1%

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

       4. *-commutative 49.1%

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

   11. Simplified 49.1%

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

   if 1.7499999999999999e199 < y

   1. Initial program 43.8%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+199}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -225000 \lor \neg \left(j \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -225000.0) (not (<= j 1.56e+38)))
   (* j (- (* a c) (* y i)))
   (* t (- (* b i) (* 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 ((j <= -225000.0) || !(j <= 1.56e+38)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t * ((b * i) - (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 ((j <= (-225000.0d0)) .or. (.not. (j <= 1.56d+38))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t * ((b * i) - (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 ((j <= -225000.0) || !(j <= 1.56e+38)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -225000.0) or not (j <= 1.56e+38):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -225000.0) || !(j <= 1.56e+38))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - 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 ((j <= -225000.0) || ~((j <= 1.56e+38)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -225000.0], N[Not[LessEqual[j, 1.56e+38]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -225000 or 1.5599999999999999e38 < j

   1. Initial program 74.9%

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

   3. Taylor expanded in j around inf 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if -225000 < j < 1.5599999999999999e38

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around inf 56.6%

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

      1. neg-mul-1 56.6%

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

      2. sub-neg 56.6%

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

      3. remove-double-neg 56.6%

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

      4. +-commutative 56.6%

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

      5. mul-1-neg 56.6%

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

      6. unsub-neg 56.6%

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

   8. Simplified 56.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -225000 \lor \neg \left(j \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+33} \lor \neg \left(j \leq 7.8 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4e+33) (not (<= j 7.8e+37))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4e+33) || !(j <= 7.8e+37)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-4d+33)) .or. (.not. (j <= 7.8d+37))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4e+33) || !(j <= 7.8e+37)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4e+33) or not (j <= 7.8e+37):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4e+33) || !(j <= 7.8e+37))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -4e+33) || ~((j <= 7.8e+37)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -4e+33], N[Not[LessEqual[j, 7.8e+37]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.9999999999999998e33 or 7.7999999999999997e37 < j

   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 inf 46.9%

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

      1. +-commutative 46.9%

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

      2. mul-1-neg 46.9%

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

      3. unsub-neg 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in c around inf 39.1%

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

   if -3.9999999999999998e33 < j < 7.7999999999999997e37

   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 t around inf 55.5%

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

      1. distribute-lft-out-- 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in a around 0 31.0%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+33} \lor \neg \left(j \leq 7.8 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -18500000000000 \lor \neg \left(y \leq 10^{+50}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -18500000000000.0) (not (<= y 1e+50)))
   (* x (* y z))
   (* j (* a c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -18500000000000.0) || !(y <= 1e+50)) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-18500000000000.0d0)) .or. (.not. (y <= 1d+50))) then
        tmp = x * (y * z)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -18500000000000.0) || !(y <= 1e+50)) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -18500000000000.0) or not (y <= 1e+50):
		tmp = x * (y * z)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -18500000000000.0) || !(y <= 1e+50))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -18500000000000.0) || ~((y <= 1e+50)))
		tmp = x * (y * z);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -18500000000000.0], N[Not[LessEqual[y, 1e+50]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e13 or 1.0000000000000001e50 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in x around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in z around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   if -1.85e13 < y < 1.0000000000000001e50

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in c around inf 30.4%

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

      1. pow1 30.4%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 32.2%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 32.2%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 32.2%

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

      2. *-commutative 32.2%

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

   10. Simplified 32.2%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18500000000000 \lor \neg \left(y \leq 10^{+50}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.9e+33)
   (* a (* c j))
   (if (<= j 8.5e+37) (* b (* t i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.9e+33) {
		tmp = a * (c * j);
	} else if (j <= 8.5e+37) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.9d+33)) then
        tmp = a * (c * j)
    else if (j <= 8.5d+37) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.9e+33) {
		tmp = a * (c * j);
	} else if (j <= 8.5e+37) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.9e+33:
		tmp = a * (c * j)
	elif j <= 8.5e+37:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.9e+33)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 8.5e+37)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.9e+33)
		tmp = a * (c * j);
	elseif (j <= 8.5e+37)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.9e+33], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+37], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.90000000000000025e33

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in c around inf 37.2%

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

   if -2.90000000000000025e33 < j < 8.4999999999999999e37

   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 t around inf 55.5%

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

      1. distribute-lft-out-- 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in a around 0 31.0%

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

   if 8.4999999999999999e37 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in a around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in c around inf 40.9%

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

      1. pow1 40.9%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 42.2%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 42.2%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 42.2%

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

      2. *-commutative 42.2%

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

   10. Simplified 42.2%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -800000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -800000000000.0)
   (* x (* y z))
   (if (<= y 4.5e+49) (* j (* a c)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -800000000000.0) {
		tmp = x * (y * z);
	} else if (y <= 4.5e+49) {
		tmp = j * (a * c);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-800000000000.0d0)) then
        tmp = x * (y * z)
    else if (y <= 4.5d+49) then
        tmp = j * (a * c)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -800000000000.0) {
		tmp = x * (y * z);
	} else if (y <= 4.5e+49) {
		tmp = j * (a * c);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -800000000000.0:
		tmp = x * (y * z)
	elif y <= 4.5e+49:
		tmp = j * (a * c)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -800000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 4.5e+49)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -800000000000.0)
		tmp = x * (y * z);
	elseif (y <= 4.5e+49)
		tmp = j * (a * c);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -800000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+49], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e11

   1. Initial program 68.0%

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

   3. Taylor expanded in x around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in z around inf 37.5%

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

      1. *-commutative 37.5%

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

   8. Simplified 37.5%

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

   if -8e11 < y < 4.49999999999999982e49

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in c around inf 30.4%

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

      1. pow1 30.4%

         \[\leadsto \color{blue}{{\left(a \cdot \left(c \cdot j\right)\right)}^{1}} \]

      2. associate-*r* 32.2%

         \[\leadsto {\color{blue}{\left(\left(a \cdot c\right) \cdot j\right)}}^{1} \]

   8. Applied egg-rr 32.2%

      \[\leadsto \color{blue}{{\left(\left(a \cdot c\right) \cdot j\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 32.2%

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

      2. *-commutative 32.2%

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

   10. Simplified 32.2%

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

   if 4.49999999999999982e49 < y

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. *-commutative 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in y around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

      4. *-commutative 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in z around inf 44.8%

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

       1. *-commutative 44.8%

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

   11. Simplified 44.8%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -800000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.2% 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 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 inf 42.1%

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

   1. +-commutative 42.1%

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

   2. mul-1-neg 42.1%

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

   3. unsub-neg 42.1%

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

5. Simplified 42.1%

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

6. Taylor expanded in c around inf 23.3%

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

7. Final simplification 23.3%

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

Developer target: 60.1% 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 2024115 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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